The doctrine of interest, both simple & compound explained in a more exact and satisfactory method then [sic] has hitherto been published : discovering the errors of the ordinary tables of rebate for annuities at simple interest, and containing tables for the interest and rebate of money for days, months, and years, both at simple and compound interest, also tables for the forbearance, discomps, and purchase of annulites : as likewise, equation of payments made practicable and useful for all merchants and others : together with divers other useful reflections / ... Sir S. Morland.

THE DOCTRINE OF SIMPLE INTEREST EXPLAINED By a New and Exact Method, And the Errors of the Ordinary Rules and Tables of Rebate discovered and rectified. (Book 1)

CHAP. I.

INterest is either Simple, or Com∣pound.

1. Simple Interest, is the Increase which arises from the Principal only, at 4, 5, 6, 7, &c. per Cent.

2. Compound Interest, is the Increase which arises from the Principal, and also from the Interest thereof.

Thus, if 100 l. be lent at Simple Interest for Two Years, at 6 per Cent. the In∣crease thereof is 12 l. But if at Compound Interest, it gives 6 l. for the first Year, and 6 l. for the second Year, toge∣ther with the Interest of the first 6 l. for the second Year. That is to say: 〈 math 〉〈 math 〉 To which adding the Principal (viz. 100 l.) the Amount of both Principal and Compound Interest, for Two years, is 112.36 l. which by the Table of Reduction in the following Page is 112 l. 7 s. 2 d. 1 q. more by .000626 parts of a Pound.

The Doctrine of Simple Interest is plainly and clearly set forth in the fol∣lowing Propositions.

But that the Practitioner may meet with no difficulty in the respective Ope∣rations, he will here find made ready to his hand Seven short (but very significant) Tables.

TABLE I. Reduction of Shillings, Pence, and Farthings, into Decimal Fractions.

Shil∣lings.	Deci∣mals.		Pence.	Decimals.
			11	.0458333
19	.95		10	.0416666
18	.9		9	.0375
17	.85		8	.03••3333
16	.8		7	.0291666
15	.75		6	.025
14	.7		5	.0208333
13	.65		4	.0166666
12	.6		3	.0125
11	.55		2	.0083333
10	.5		1	.0041666
9	.45
8	.4		Farth.	Decimals.
7	.35
6	.3		3	.003125
5	.25		2	.0020833
4	.2		1	.0010416
3	.15		½	.0005208
2	.1		¼	.0002604
1	.05		1/8	.0001302

TABLE II. The INTEREST of One Pound for One Year. From 1 to 12 per Cent.

Rates per Cent.	Interest.
1	.01
2	.02
3	.03
4	.04
5	.05
6	.06
7	.07
8	.08
9	.09
10	.10
11	.11
12	.12

TABLE III. The INTEREST of One Pound for One Half-Year. From 1 to 12 per Cent.

Rates per Cent.	Interest.
1	.005
2	.01
3	.015
4	.02
5	.025
6	.03
7	.035
8	.04
9	.045
10	.05
11	.055
12	.06

TABLE IV. The INTEREST of One Pound for One Quarter. From 1 to 12 per Cent.

Rates per Cent.	Interest.
1	.0025
2	.005
3	.0075
4	.01
5	.0125
6	.015
7	.0175
8	.02
9	.0225
10	.025
11	.0275
12	.03

TABLE V. The INTEREST of One Pound for One Month. From 1 to 12 per Cent.

Rates per Cent.	Interest.
1	.0008333
2	.0016666
3	.0025
4	.00333
5	.00416
6	.005
7	.00583
8	.00666
9	.0075
10	.08333
11	.09166
12	.1

TABLE VI. The INTEREST of One Pound for One Day. From 1 to 12 per Cent.

Rates per Cent.	Interest.
1	.00002739726
2	.00005479452
3	.00008219178
4	.00010958904
5	.00013698630
6	.00016438356
7	.00019178082
8	.00021917808
9	.00024657534
10	.00027397260
11	.00030136986
12	.00032876712

TABLE VII. THE GOLDEN TABLE OF Trigonal Progression. Of excellent use, in all Calcula∣tions of the Amount or present Worth of Annuities, &c.

Arith. Prog.	Trigonal Prog.
1	1
2	3
3	6
4	10
5	15
6	21
7	28
8	36
9	45
10	55
11	66
12	78
13	91
14	105
15	120
16	136
17	153
18	171

Arith. Prog.	Trigonal Prog.
19	190
20	210
21	231
22	253
23	276
24	300
25	325
26	351
27	378
28	406
29	435
30	465
31	496
32	528
33	561
34	595
35	630
36	666
37	703
38	741
39	780
40	820
41	861
42	903
43	946
44	990
45	1035
46	1081
47	1128
48	1176
49	1225
50	1275
51	1326
52	1378
53	1431
54	1485
55	1540
56	1596
57	1653
58	1711
59	1770
60	1830

Arith. Prog.	Trigonal Prog.
61	1891
62	1953
63	2016
64	2080
65	2145
66	2211
67	2278
68	2346
69	2415
70	2485
71	2556
72	2628
73	2701
74	2775
75	2850
76	2926
77	3003
78	3081
79	3160
80	3240
81	3321
82	3403
83	3486
84	3570
85	3655
86	3741
87	3828
88	3916
89	4005
90	4095
91	4186
92	4278
93	4371
94	4465
95	4560
96	4656
97	4753
98	4851
99	4950
100	5050
101	5151
102	5253

Arith. Prog.	Trigonal Prog.
103	5356
104	5460
105	5565
106	5671
107	5778
108	5886
109	5995
110	6105
111	6216
112	6328
113	6441
114	6555
115	6670
116	6786
117	6903
118	7021
119	7140
120	7260
121	7381
122	7503
123	7626
124	7750

TABLE VIII. A TABLE SHEWING The Number of Days from the Begin∣ning of any Month to the End of any other.

• JAnuary, 31. February, 59. March, 90. April, 120. May, 151. June, 181. July, 212. August, 243. September, 273. October, 304. November, 334. Decem∣ber, 365.
• February, 28. March, 59. April, 89. May, 120. June, 150. July, 181. August, 212. September, 242. October, 273. Novemb. 303. Decemb. 334. Jan. 365.
• March, 31. April, 61. May, 92. June, 122. July, 153. August, 184. Sep∣tember, 214. Octob. 245. Novemb. 275. Decemb. 306. Jan. 337. Febr. 365.
• ...

• April, 30. May, 61. June, 91. July, 122. August, 153. September, 183. Octo∣ber, 214. November, 244. December, 275. January, 306. February 334. March, 365.
• May, 31. June, 61. July, 92. August, 123. September, 153. October, 184. No∣vember, 214. December, 245. Jan. 276. February, 304. March, 335. April, 365.
• June, 30. July, 61. August, 92. Sep∣tember, 122. October, 153. Novemb. 183. December, 214. January, 245. Febr. 273. March, 304. April, 334. May, 365.
• July, 31. August, 62. September, 92. October, 123. Novemb. 153. Decemb. 184. January, 215. February, 243. March, 274. April, 304. May, 335. June, 365.
• August, 31. September, 61. Octob. 92. November, 122. December, 153. Janua∣ry, 184. February, 212. March, 243. April, 273. May, 304. June, 334. July, 365.
• ...

• September, 30. October, 61. No∣vember, 91. December, 122. January, 153. February, 181. March, 212. April, 242. May, 273. June, 303. July, 334. Aug. 365.
• October, 31. November, 61. Decemb. 92. January, 123. February, 151. March, 182. April, 212. May, 243. June, 273. July, 304. August, 335. September, 365.
• November, 30. December, 61. Janu∣ary, 92. February, 120. March, 151. April, 181. May, 212. June, 242. July, 273. Aug. 304. Sept. 334. Octob. 365.
• December, 31. January, 62. Februa∣ry, 90. March, 121. April, 151. May, 182. June, 212. July, 243. August, 274. Sep∣tember, 304. October, 335. Novemb. 365.

Note, That in every Leap-year, Fe∣bruary has 29 Days, and then you must allow a Day more than is here compu∣ted for that Month.

TABLE IX. The Amount of One Pound, put out to Interest, and forborn any Number of Years under 32. At the Rate of 6 per Cent. Simple Interest; And that Interest payable Yearly.

Years.	Amount.
1	1.06
2	1.12
3	1.18
4	1.24
5	1.30
6	1.36
7	1.42
8	1.48
9	1.54
10	1.60
11	1.66
12	1.72
13	1.78
14	1.84
15	1.90
16	1.96
17	2.02
18	2.08
19	2.14
20	2.20
21	2.26
22	2.32
23	2.38
24	2.44
25	2.50
26	2.56
27	2.62
28	2.68
29	2.74
30	2.80
31	2.86

TABLE X. The AMOUNT of One Pound, for any Number of equal Months under 25. At the Rate of 6 per Cent. Simple Interest.

Months.	Amount.
1	1.005
2	1.010
3	1.015
4	1.020
5	1.025
6	1.030
7	1.035
8	1.040
9	1.045
10	1.050
11	1.055
12	1.060
13	1.065
14	1 070
15	1.075
16	1.080
17	1.085
18	1.090
19	1.095
20	1.100
21	1.105
22	1.110
23	1.115
24	1.120

TABLE XI. The AMOUNT of One Pound, for any Number of Days under 366. At the Rate of 6 per Cent. Simple Interest.

Days.	Amount.
1	1.000164383
2	1.000328767
3	1.000493150
4	1.000657534
5	1.000821917
6	1.000986301
7	1.001150684
8	1.001315068
9	1.001479452
10	1.001643835
11	1.001808219
12	1.001972602
13	1.002136986
14	1.002301369
15	1.002465753
16	1.002630136
17	1.002794520
18	1.002958904
19	1.003123287
20	1.003287671
21	1.003452054
22	1.003616438
23	1.003780821
24	1.003945205
25	1.004109589
26	1.004273972
27	1.004438356
28	1.004602739
29	1.004767123
30	1.004931506
31	1.005095890
32	1.005260273

Days.	Amount.
33	1.005424657
34	1.005589041
35	1.005753424
36	1.005917808
37	1.006082191
38	1.006246575
39	1.006410958
40	1.006575342
41	1.006739725
42	1.006904109
43	1.007068493
44	1.007232876
45	1.007397260
46	1.007561643
47	1.007726027
48	1.007890410
49	1.008054794
50	1.008219178
51	1.008383561
52	1.008547945
53	1.008712328
54	1.008876712
55	1.009041095
56	1.009205479
57	1.009369862
58	1.009534246
59	1.009698630
60	1.009863013
61	1.010027397
62	1.010191780
63	1.010356164
64	1.010520547
65	1.010684931
66	1.010849314
67	1.011013698
68	1.011178082
69	1.011342465
70	1.011506849
71	1.011671232
72	1.011835616
73	1.011999999
74	1.012164383
75	1.012328767
76	1.012493150

Days.	Amount.
77	1.012657534
78	1.012821917
79	1.012986301
80	1.013150684
81	1.013315068
82	1.013479451
83	1.013643835
84	1.013808219
85	1.013972602
86	1.014136986
87	1.014301369
88	1.014465753
89	1.014630136
90	1.014794520
91	1.014958903
92	1.015123287
93	1.015287671
94	1.015452054
95	1.015616438
96	1.015780821
97	1.015945205
98	1.016109588
99	1.016273972
100	1.016438356
101	1.016602739
102	1.016767123
103	1.016931506
104	1.017095890
105	1.017260273
106	1.017424657
107	1.017589040
108	1.017753424
109	1.017917808
110	1.018082191
111	1.018246575
112	1.018410958
113	1.018575342
114	1.018739725
115	1.018904109
116	1.019068492
117	1.019232876
118	1.019397260
119	1.019561643
120	1.019726027

Day.	Amount.
121	1.019890410
122	1.020054794
123	1.020219177
124	1.020383561
125	1.020547945
126	1.020712328
127	1.020876712
128	1.021041095
129	1.021205479
130	1.021369862
131	1.021534246
132	1.021698629
133	1.021863013
134	1.022027397
135	1.022191780
136	1.022356164
137	1.022520547
138	1.022684931
139	1.022849314
140	1.023013698
141	1.023178081
142	1.023342465
143	1.023506849
144	1.023671232
145	1.023835616
146	1.023999999
147	1.024164383
148	1.024328766
149	1.024493150
150	1.024657534
151	1.024821917
152	1.024986301
153	1.025150684
154	1.025315068
155	1.025479451
156	1.025643835
157	1.025808218
158	1.025972602
159	1.026136986
160	1.026301369
161	1.026465753
162	1.026630136
163	1.026794520
164	1.026958903

Day.	Amount.
165	1.027123287
166	1.027287670
167	1.027452054
168	1.027616438
169	1.027780821
170	1.027945205
171	1.028109588
172	1.028273972
173	1.028438355
174	1.028602739
175	1.028767123
176	1.028931506
177	1.029095890
178	1.029260273
179	1.029424657
180	1.029589040
181	1.029753424
182	1.029917807
183	1.030082191
184	1.030246575
185	1.030410958
186	1.030575342
187	1.030739725
188	1.030904109
189	1.031068492
190	1.031232876
191	1.031397259
192	1.031561643
193	1.031726027
194	1.031890410
195	1.032054794
196	1.032219177
197	1.032383561
198	1.032547944
199	1.032712328
200	1.032876712
201	1.033041095
202	1.033205479
203	1.033369862
204	1.033534246
205	1.033698629
206	1.033863013
207	1.034027396
208	1.034191780

Day.	Amount.
209	1.034356164
210	1.034520547
211	1.034684931
212	1.034849314
213	1.035013698
214	1.035178081
215	1.035342465
216	1.035506848
217	1.035671232
218	1.035835616
219	1.036000000
220	1.036164383
221	1.036328766
222	1.036493150
223	1.036657533
224	1.036821917
225	1.036986301
226	1.037150684
227	1.037315068
228	1.037479451
229	1.037643835
230	1.037808218
231	1.037972602
232	1.038136985
233	1.038301369
234	1.038465753
235	1.038630136
236	1.038794520
237	1.038958903
238	1.039123287
239	1.039287670
240	1.039452054
241	1.039616437
242	1.039780821
243	1.039945205
244	1.040109588
245	1.040273972
246	1.040438355
247	1.040602739
248	1.040767122
249	1.040931506
250	1.041095890
251	1.041260273
252	1.041424657

Day.	Amount.
253	1.041589040
254	1.041753424
255	1.041917807
256	1.042082191
257	1.042246574
258	1.042410958
259	1.042575342
260	1.042739725
261	1.042904109
262	1.043068492
263	1.043232876
264	1.043397259
265	1.043561643
266	1.043726026
267	1.043890410
268	1.044054794
269	1.044219177
270	1.044383561
271	1.044547944
272	1.044712328
273	1.044876711
274	1.045041095
275	1.045205479
276	1.045369862
277	1.045534246
278	1.045698629
279	1.045863013
280	1.046027396
281	1.046191780
282	1.046356163
283	1.046520547
284	1.046684931
285	1.046849314
286	1.047013698
287	1.047178081
288	1.047342465
289	1.047506848
290	1.047671232
291	1.047835615
292	1.048000000
293	1.048164383
294	1.048328766
295	1.048493150
296	1.048657533

Day.	Amount.
297	1.048821917
298	1.048986300
299	1.049150684
300	1.049315068
301	1.049479451
302	1.049643835
303	1.049808218
304	1.049972602
305	1.050136985
306	1.050301369
307	1.050465752
308	1.050630136
309	1.050794520
310	1.050958903
311	1.051123287
312	1.051287670
313	1.051452054
314	1.051616437
315	1.051780821
316	1.051945204
317	1.052109588
318	1.052273972
319	1.052438355
320	1.052602739
321	1.052767122
322	1.052931506
323	1.053095889
324	1.053260273
325	1.053424657
326	1.053589040
327	1.053753424
328	1.053917807
329	1.054082191
330	1.054246574
331	1.054410958
332	1.054575341
333	1.054739725
334	1.054904109
335	1.055068492
336	1.055232876
337	1.055397259
338	1.055561643
339	1.055726026
340	1.0558••••41••

Day.	Amount.
341	1.056054793
342	1.056219177
343	1.056383561
344	1.056547944
345	1.056712328
346	1.056876711
347	1.057041095
348	1.057205478
349	1.057369862
350	1.057534246
351	1.057698629
352	1.057863013
353	1.058027396
354	1.058191780
355	1.058356163
356	1.058520547
357	1.058684930
358	1.058849314
359	1.059013698
360	1.059178081
361	1.059342465
362	1.059506848
363	1.059671232
364	1.059835615
365	1.060000000

TABLE XII. The PRESENT WORTH of One Pound, due after any Number of Years to come, under 32. At the Rate of 6 per Cent. Simple Interest.

Years to come.	Present Worth.
1	.94339622
2	.89285714
3	.84745762
4	.80645161
5	.76923076
6	.73529411
7	.70422535
8	.67567567
9	.64935064
10	.62500000
11	.60240963
12	.58139534

Years to come.	Present Worth.
13	.56179775
14	.54347826
15	.52631578
16	.51020408
17	.49504950
18	.48076923
19	.46728971
20	.45454545
21	.44247787
22	.43103448
23	.42016806
24	.40983606
25	.40000000
26	.39062500
27	.38167939
28	.37313432
29	.36496350
30	.35714285
31	.34965034

TABLE XIII. The PRESENT WORTH of Due Pound, due after the expira∣tion of any Number of Months under 25. At the Rate of 6 per Cent. Simple Interest.

Months to come.	Present Worth.
1	.99502487
2	.99009900
3	.98522167
4	.98039215
5	.97560975
6	.97087378
7	.96618357
8	.96153846
9	.95693779
10	.95238095
11	.94786729
12	.94339622

Months to come.	Present Worth.
13	.93896713
14	.93457943
15	.93023255
16	.92594444
17	.92165898
18	.91743119
19	.91324200
20	.90909090
21	.90497737
22	.90090090
23	.89686098
24	.89285714

TABLE XIV. The PRESENT WORTH of One Pound, due after the expira∣tion of any Number of Days under 366. At the Rate of 6 per Cent. Simple Interest.

Days to come.	Present Worth.
1	.99983564
2	.99967134
3	.99950709
4	.99934290
5	.99917876
6	.99901467
7	.99885064
8	.99868666
9	.99852273
10	.99835886
11	.99819504
12	.99803128
13	.99786757
14	.99770391
15	.99754031
16	.99737676
17	.99721326
18	.99704982
19	.99688643
20	.99672310

Days to come.	Present Worth.
21	.99655982
22	.99639659
23	.99623341
24	.99607029
25	.99590723
26	.99574421
27	.99558125
28	.99541835
29	.99525549
30	.99509269
31	.99492994
32	.99476725
33	.99460460
34	.99444201
35	.99427948
36	.99411700
37	.993954••7
38	.99379220
39	.99362987
40	.99346761
41	.99330539
42	.99314323
43	.99298112
44	.99281906
45	.99265706
46	.99249511
47	.99233321
48	.99217136
49	.99200957
50	.99184782
51	.99168614
52	.99152450
53	.99136292
54	.99120139
55	.99103991
56	.99087848
57	.99071711
58	.99055579

Days to come.	Present Worth.
59	.99039453
60	.99023331
61	.99007215
62	.98991104
63	.98975000
64	.98958899
65	.98942804
66	.98926714
67	.98910629
68	.98894549
69	.98878475
70	.98862406
71	.98846341
72	.98830283
73	.98814230
74	.98798181
75	.98782138
76	.98766100
77	.98750067
78	.98734040
79	.98718018
80	.98702001
81	.98685989
82	.98669983
83	.98653980
84	.98637984
85	.98621993
86	.98606008
87	.98590027
88	.98574052
89	.98558081
90	.98542116
91	.98526156
92	.98510202
93	.98494253
94	.98478309
95	.98462369
96	.98446435

Days to come.	Present Worth.
97	.98430506
98	.98414582
99	.98398663
100	.98382749
101	.98366841
102	.98350937
103	.98335039
104	.98319146
105	.98303258
106	.98287376
107	.98271498
108	.98255626
109	.98239758
110	.98223896
111	.98208039
112	.98192188
113	.98176340
114	.98160498
115	.98144662
116	.98128830
117	.98113004
118	.98097183
119	.98081367
120	.98065556
121	.98049750
122	.98033949
123	.98018152
124	.98002361
125	.97986576
126	.97970795
127	.97955020
128	.97939250
129	.97923485
130	.97907725
131	.97891970
132	.97876221
133	.97860473
134	.97844734

Days to come.	Present Worth.
135	.97828999
136	.97813269
137	.97797545
138	.97781825
139	.97766111
140	.97750401
141	.97734697
142	.97718997
143	.97703304
144	.97687614
145	.97671930
146	.97656250
147	.97640576
148	.97624906
149	.97609242
150	.97593583
151	.97577928
152	.97562279
153	.97546635
154	.97530996
155	.97515362
156	.97499732
157	.97484108
158	.97468489
159	.97452875
160	.97437266
161	.97421662
162	.97406063
163	.97390470
164	.97374880
165	.97359296
166	.97343717
167	.97328143
168	.97312574
169	.97297009
170	.97281450
171	.97265896
172	.97250346

Days to come.	Present Worth.
173	.97234803
174	.97219263
175	.97203729
176	.97188199
177	.97172675
178	.97157155
179	.97141640
180	.97126131
181	.97110626
182	.97095127
183	.97079631
184	.97064141
185	.97048656
186	.97033177
187	.97017702
188	.97002232
189	.96986767
190	.96971307
191	.96955852
192	.96940401
193	.96924959
194	.96909518
195	.96894083
196	.96878652
197	.96863227
198	.96847806
199	.96832387
200	.96816976
201	.96801570
202	.96786169
203	.96770773
204	.96755382
205	.96739995
206	.96724614
207	.96709237
208	.96693865
209	.96678498
210	.96663136

Days to come.	Present Worth.
211	.96647778
212	.96632426
213	.96617079
214	.96601737
215	.96586399
216	.96571066
217	.96555738
218	.96540415
219	.96525096
220	.96509783
221	.96494475
222	.96479171
223	.96463871
224	.96448578
225	.96433289
226	.96418004
227	.96402725
228	.96387451
229	.96372181
230	.96356916
231	.96341656
232	.96326401
233	.96311151
234	.96295906
235	.96280665
236	.96265429
237	.96250198
238	.96234972
239	.96219750
240	.96204533
241	.96189322
242	.96174114
243	.96158912
244	.96143715
245	.96128522
246	.96113334
247	.96098151
248	.96082973

Days to come.	Present Worth.
249	.96067800
250	.96052631
251	.96037467
252	.96022309
253	.96007154
254	.95992004
255	.95976860
256	.95961720
257	.95946585
258	.95931454
259	.95916329
260	.95901208
261	.95886092
262	.95870981
263	.95855875
264	.95840773
265	.95825676
266	.95810584
267	.95795497
268	.95780414
269	.95765335
270	.95750262
271	.95735194
272	.95720130
273	.95705071
274	.95690016
275	.95674967
276	.95659922
277	.95644882
278	.95629847
279	.95614816
280	.95599790
281	.95584769
282	.95569753
283	.95554742
284	.95539735
285	.95524732
286	.95509735

Days to come.	Present Worth.
287	.95494742
288	.95479753
289	.95464770
290	.95449791
291	.95434817
292	.95419847
293	.95404882
294	.95389923
295	.95374967
296	.95360016
297	.95345070
298	.95330129
299	.95315192
300	.95300261
301	.95285334
302	.95270411
303	.95255493
304	.95240580
305	.95225672
306	.95210768
307	.95195869
308	.95180974
309	.95166084
310	.95151199
311	.95136318
312	.95121442
313	.95106573
314	.95091706
315	.95076844
316	.95061986
317	.95047134
318	.95032285
319	.95017442
320	.95002603
321	.94987769
322	.94972939
323	.94958114
324	.94943204

Days to come.	Present Worth.
325	.94928478
326	.94913667
327	.94898861
328	.94884059
329	.94869262
330	.94854470
331	.94839682
332	.94824898
333	.9481••120
334	.94795346
335	.94780576
336	.94765811
337	.94751051
338	.94736295
339	.94721544
340	.94706798
341	.94692056
342	.94677319
343	.94662587
344	.94647858
345	.94633135
346	.94618416
347	.94603701
348	.94588991
349	.94574286
350	.94559585
351	.94544889
352	.94530198
353	.94515512
354	.94500829
355	.94486151
356	.94471478
357	.94456809
358	.94442145
359	.94427485
360	.94412830
361	.94398179
362	.94383533
363	.94368897
364	.94354254
365	.94339622

TABLE XV. A most useful TABLE for Reduction of Pence and Far∣things into DECIMAL FRACTIONS, to the Hun∣dredth part of a Farthing.

Far∣things.	Dectmal Fractions.
1	.0010416
2	.0020833
3	.0031250

Pence & Far∣things.	Decimal Fractions.
(1)	.0041666
1	.0052083
2	.0062500
3	.0072916
(2)	.0083333
1	.0093750
2	.0104166
3	.0114583
(3)	.0125000
1	.0135416
2	.0145833
3	.0156250

Pence & Far∣things.	Decimal Fractions.
(4)	.0166666
1	.0177708
2	.0187500
3	.0197916
(5)	.0208333
1	.0218750
2	.0229166
3	.0239583
(6)	.0250000
1	.0260416
2	.0270833
3	.0281250
(7)	.0291666
1	.0302083
2	.0312500
3	.0322916
(8)	.0333333
1	.0343750
2	.0354166
3	.0364583
(9)	.0375000
1	.0385416
2	.0395833
3	.0406250
(10)	.0416666
1	.0427082
2	.0437500
3	.0447916
(11)	.0458333
1	.0468750
2	.0479166
3	.0489583

DECIMAL FRACTIONS for every Hundredth part of a Farthing.

Hun∣dred Parts.	Decimal Fractions.
1	.000010416
2	.000020833
3	.000031249
4	.000041666
5	.000052083
6	.000062499
7	.000072916
8	.000083333
9	.000093749
10	.000104166
11	.000114583
12	.000124999
13	.000135416
14	.000145833
15	.000156249
16	.000166666
17	.000177083
18	.000187499
19	.000197916
20	.000208333
21	.000218749
22	.000229166
23	.000239583
24	.000249999
25	.000260416
26	.000270833
27	.000281249
28	.000291666
29	.000302083
30	.000312499

Hun∣dred Parts.	Decimal Fractions.
31	.000322916
32	.000333333
33	.000343749
34	.000354166
35	.000364583
36	.000374999
37	.000385416
38	.000395833
39	.000406249
40	.000416666
41	.000427083
42	.000437499
43	.000447916
44	.000458333
45	.000468749
46	.000479166
47	.000489583
48	.000499999
49	.000510416
50	.000520833
51	.000531249
52	.000541666
53	.000552083
54	.000562499
55	.000572916
56	.000583333
57	.000593749
58	.000604166
59	.000614583
60	.000624999
61	.000635416
62	.000645833
63	.000656249
64	.000666666
65	.000677083
66	.000687499
67	.000697916
68	.000708333

Hun∣dred Parts.	Decimal Fractions.
69	.000718749
70	.000729166
71	.000739583
72	.000749999
73	.000760416
74	.000770833
75	.000781249
76	.000791666
77	.000802083
78	.000812499
79	.000822916
80	.000833333
81	.000843749
82	.000854166
83	.000864583
84	.000874999
85	.000885416
86	.000895833
87	.000906249
88	.000916666
89	.000927083
90	.000937499
91	.000947916
92	.000958333
93	.000968749
94	.000979166
95	.000989583
96	.000999999
97	.001010416
98	.001020833
99	.001031249

The Use of the foregoing TABLES.

BEcause the usual Rate of Interest is 6 per Cent. there are Tables calcu∣lated for the more ready dispatch of Questions relating either to the Amount, or Present Worth of any Sum; but for any other Rate from (1) to (12) the method will be very plain and practica∣ble. I shall begin with some Examples at 6 per Cent.

Example 1. What is the Amount of 540 l. in seven Years, at 6 per Cent. Simple Interest?

Rule.

See for 7 years in the Margin of Table IX. and against it you find 1.42, the Amount of 1 l. in 7 years; multiply

540 by 1.42, and the Product is the Answer.

〈 math 〉〈 math 〉

Example 2. What is the Amount of 540 l. in fifteen Months, at 6 per Cent. Simple Interest?

Rule.

Find 15 Months in the Margin of Table X. and against it is 1.075; by that multiply 540, and the Product is the Answer.

〈 math 〉〈 math 〉

Example 3. What is the Amount of 540 l. in 279 Days, at 6 per Cent. Simple Interest?

Rule.

Find 279 Days in the Margin of Table XI. and against it is 1.0458, (you may take more or less of the Fraction, according as you desire to be more or less exact;) then multiply 1.0458 by 540, and the Product is the Answer.

〈 math 〉〈 math 〉

Example 4. What is the Present Worth of 766.8 l. at the end of 7 Years, at 6 për Cent. Simple Interest?

Rule.

Find 7 Years in Table XII. and against it is .704225; then multiply that by the given Number 766.8, and the Product is the Answer.

〈 math 〉〈 math 〉

Which is within 26 Hundred Parts of a Farthing of the truth, and is a suffi∣cient Proof of the first Example.

Example 5. What is the present Worth of 580.5 l. due after 15 Months, at 6 per Cent. Simple Interest?

Rule.

Find 15 Months in Table XIII. and against it is .93023, &c. this being multiplied by 580.5, is an Answer.

〈 math 〉〈 math 〉

Which is within one Farthing of the truth, and may be made within one Hundredth part of a Farthing of the truth, and is a clear Proof of the second Example.

And after this manner may any Question of this kind be easily and ex∣actly resolved, and where the Sums are very great, the Operation will not be so tedious as that of working by Mr. Cla∣vel's Tables. For a Proof of which, I shall here insert two Examples, one of the Amount, and the other of the pre∣sent Worth of a considerable Sum.

Example 6. Suppose the King borrows of some Bankers 259879 l. 17s. 9d. 3q. for a year and 349 Days; what will be the Amount of Principal and Interest at the expiration of a Year and 349 Days, allowing them 6 per Cent?

The Operation by Mr. Clavel's Tables.

In Mr. Clavel's Tables I can find no more of this Sum at one time than 10000 l. therefore I seek the Interest of that, and find the Interest of 10000 l.

〈 math 〉〈 math 〉

The odd Money I reduce into Deci∣mal Parts of a Pound, by the Decimal Table in Mr. Russel's Appendix to Mr.Cla∣vel, thus, 〈 math 〉〈 math 〉

Then because 200000 is twenty times 10000, I must multiply this Fraction and whole Number by 20, to find the Interest of 200000 l. for a Year, and 349 Days: and also multiply the said whole Number and Fraction by 5, for the In∣terest of 50000, (there being five times 10000 contained in it) for the like time.

Example.

〈 math 〉〈 math 〉

The Interest of the remaining part of the aforesaid Sum, viz. 9879 l. 17 s. (omitting the 9 d. 3 q.) is to be found in this manner: 〈 math 〉〈 math 〉

〈 math 〉〈 math 〉

Reduce the Decimal Fractions of the Interest of 200000, and 50000, into Shillings and Pence, and then is the

〈 math 〉〈 math 〉

The Answer (without considering the Interest of 9 d. 3 q. which is not to be found by Mr. Clavel's Tables) is 290381 l. 19 s. 2 d. 3 q. very near.

The Operation according to the Rules of this little Book is performed by Sim∣ple Addition, thus;

The given Sum redu∣ced by Table I. is 259879.890625

The Amount of 1. l. for 365 and 349 Days, viz. 714 Days, is 1.1173698

Tariffa for the Multiplicand.

1	259879890625
2	519759781250
3	779639671875
4	1039519562500
5	1299399453125
6	1559279343750
7	1819159234375
8	2079039125000
9	2338919015625

The Multiplication contracted, as is directed in the Introduction to this little Book.

〈 math 〉〈 math 〉

This Product, viz. 290381 l. 18 s. 9 d. 3 q. more by 86/100 of a Farthing, is the Answer.

Example 7.

Suppose there will be due after 349 Days, upon the several Branches of the King's Revenue, the Sum of 290381.94139 l. (or 18 s. 9 d. 3 q. more by 36/100 of a Farthing;) and His Majesty have occasion to convert this into ready Money, allow∣ing the Advancers 6 per Cent. what is the present Worth of that Sum? or what must those persons advance in ready Money for the Premises?

Though it be the truest, and most exact way of all other, to Calculate either the Amount or present Worth of Money by Days, yet there is no help at all by Mr. Clavel's Tables to answer this Question.

But by this little Book, The Rule is,

l.

Multiply the given sum 290381.94139 by the Present Worth of 1 l. due at the end of 349 Days (which you will find in Table XIV.) .94574, and the Product is an Answer to the Question.

Tariffa for the Multiplicand.

1	29038194139
2	58076388278
3	87114582417
4	116152776556
5	145190970695
6	174229164834
7	203267358973
8	232305553112
9	261343747251

The Multiplication contracted, as in the Introduction is directed.

〈 math 〉〈 math 〉

After the same manner are resolved any Questions, concerning either the Amount, or present Worth of any Sum, either for Years, Months, or Days. The next thing I shall Treat of is Annuities at Simple Interest, which shall be the Sub∣ject of the following Chapter.

CHAP. II.

Of Annuities at Simple Interest.

THe increase of Annuities is by Mul∣tiplication of the respective Rates of Interest, according to a Trigonal Progression, which may be better seen by comparing the Golden Table of Trigonal Progression in Chap. 1. with the following Table of Trigonal Increase, or Addition of (6) the Rate of Interest per Cent. and after it short Rules, which will hold for finding the Amount, or Present Worth of any Annuity, for any number of years, at any Rate of Simple Interest whatsoever.

TABLE. The Multiplication of any Rates of Interest whatsoever belong∣ing to each Year, for a For∣born Annuity to 100 Years. This Table is Composed from the Golden Trigonal Table.

Years.	A Trigonal Increase, or Addition of Rates of Interest.
1	0
2	1
3	3
4	6
5	10
6	15
7	21
8	28
9	36
10	45
11	55
12	66
13	78
14	91
15	105
16	120

Years.	A Trigonal Increase, or Addition of Rates of Interest.
17	136
18	153
19	171
20	190
21	210
22	231
23	253
24	276
25	300
26	325
27	351
28	378
29	406
30	435
31	465
32	496
33	528
34	561
35	595
36	630
37	666
38	703
39	741
40	780
41	820
42	861
43	903
44	946
45	990
46	1035
47	1081
48	1128
49	1176
50	1225

Years.	A Trigonal Increase, or Addition of Rates of Interest.
51	1275
52	1326
53	1378
54	1431
55	1485
56	1540
57	1596
58	1653
59	1711
60	1770
61	1830
62	1891
63	1953
64	2016
65	2080
66	2145
67	2211
68	2278
69	2346
70	2415
71	2485
72	2556
73	2628
74	2701
75	2775
76	2850
77	2926
78	3003
79	3081
80	3160
81	3240
82	3321
83	3403
84	3486

Years.	A Trigonal Increase, or Addition of Rates of Interest.
85	3570
86	3655
87	3741
88	3828
89	3916
90	4005
91	4095
92	4186
93	4278
94	4371
95	4465
96	4560
97	4656
98	4753
99	4851
100	4950

PROP. I.

To find the Amount of any Annuity, for any given time, and at any Rate of Simple Interest.

General Rule.

TO the Sum of the Annual, half-yearly, Quarterly, or Monthly Payments, add the Product of the Annual, Half-Yearly, Quarterly, of Monthly Rate, multiplied by the Num∣ber in the foregoing Table, answering to the Number of Years, Half-Years, Quarters, or Months, in the Margin, that the Annuity is to continue; and the Total Sum is the true Amount of that Annuity.

Example 1.

What is the true Amount of an Annuity of 100 l. in five Years?

The Number in the foregoing Table answering to 5 in the Margin, is— 10

〈 math 〉〈 math 〉 That multiplied by 6 (the Annual Interest of 100 l.) makes— 60

To which add the five Annual Pay∣ments, viz.— 500

The whole Amount is— 560

Example 2.

What is the Amount of an Annuity of 62 l. in four Years?

The Number in the foregoing Table answering to 4 in the Margin, is— 6

That multiplied by 3.72 (the Annual Interest of 62l. makes 22.32

To which adding the 4 Annual Payments, viz. 4 times 62 l.— 248.00

The whole Amount is— 270.32

PROP. II.

To know the Present Worth of any Annuity for any given Time, at any Rate, accompting Simple Interest.

FOr as much as the Present Worth of an Annuity is in effect, and must be imagined, a Principal, and the whole Amount of the Annuity as the Amount of the said Principal or Present Worth, in so long a time as the Annuity is continued,

The Proportion is, As the Amount of 1 l. for any time, Is to 1 l. So is the Amount of an Annuity, To the Present Worth.

Therefore the Rule is, Divide the Amount of the Annuity by the Amount of 1 l. in the given Time, and the Quotient is an Answer.

Example 1.

What is the Present Worth of an Annuity of 62 l. for four Years?

The Amount of 62 l. per Annum for four years by the foregoing Rules is found to be 270.32, and the Amount of 1 l. forborn four years, by Table IX. is found to be 1.24; wherefore I divide 270.32 by 1.24, thus: 〈 math 〉〈 math 〉

The Quotient 218 l. is the Answer.

Example 2.

What is the Present Worth of an Annuity of 100 l. to continue 100 Years?

The Amount of 100 l. Annuity for 100 years is 39700 l. the Amount of 1 l. put out to Interest for 100 years is 7 l. wherefore divide 39700 by 7, and the Quotient is the Answer.

〈 math 〉〈 math 〉

For Proof of this, let 5671.4 be put out to Interest for 100 years, at 6 per Cent.

〈 math 〉〈 math 〉

Wherefore the Operation is exact and just, though at the same time it is a cer∣tain Argument, that the said Annuity to continue 100 years at Simple Interest, would be valued at above 56 years Pur∣chase; for dividing 5671 by 100 (that is to say, cutting off the two last Figures) the remaining Figures shew it to be 56 years Purchase, over and above the Fraction of .71.

After the same Method,

The Amount of 100l. Annuity in 50 years is 12350l. the Amount of 1 l. put out to Interest at 6 per Cent. for 50 years is 4 l. wherefore dividing the said Amount by (4),

4) 12350 (3087.5

The Quotient, or Present Worth is 3087.5, which is above 30 years Pur∣chase. From whence it is clear and manifest, that all Calculations of Annui∣ties at Simple Interest are absolutely useless and ridiculous: For the truth is, all Pre∣sent Worths or Purchases, either of Annui∣ties, or Principal Sums, due at any time hereafter, ought to be considered in a Geometrical Proportion, from a Purchase for ever, (or to the end of the World) ac∣cording to the several and respective Rates of Compound Interest. And if this be a truth as to Present Worths, it will be also a truth as to the Amounts, (as has been sufficiently explained in the Introduction to this Book.) And consequently, all Calculations, accor∣ding to Simple Interest, ought wholly to be laid aside as erroneous and use∣less.

CHAP. III.

The ERRORS of the ordinary Rules and Tables of Rebate, relating to Annuities, according to the Rate of Simple Interest, discovered and rectified.

ALthough all Tables of Rebate for Annuities at Simple Interest, ought to be wholly rejected as most ridiculous and useless, for the Reasons laid down in the foregoing Chapter, yet I do think it here seasonable, and indeed necessary▪ to animadvert upon the ordinary Rules relating to the present worth of such Annuities, which have been Composed by the respective Authors upon great mistakes, and for want of due reflection upon Arithmetical and Geometrical Pro∣gressions.

I shall mention only two Examples.

The first is a Rule laid down by Mr. John Kersey, in his Appendix, bound

up with Mr. Wingate's Arithmetick, Chap. 5. Pag. 378. Printed 1678. which is the very same with that made use of by Dr. Newton, in his Scale of Interest, pag. 20.

When it is required to find the present worth of an Annuity, by Rebating or Discompting at a given Rate of Simple Interest, the Operation will be as in the following Example, viz.

How much present Money is equivalent to an Annuity of 100 l. per Annum, to continue 5 Years, Rebate being made at the rate of 6 per Cent?

Answer 425 l. 18s. 9d. 2q. very near: Thus,

〈 math 〉〈 math 〉

For, saith he, it is manifest that there must be computed the present worth of 100 l. due at the first Years end. Also the present worth of 100 l. due at the second Years end, and in like manner for the third, fourth, and fifth Years. All which present Worths being added together, the Aggregate or Sum will be the total present worth of the Annuity, that is, 425 l. 18s. 9d. 2q. very near.

I must confess I cannot but wonder how such gross mistakes should pass through the hands of so many Learned and Ingenious Artists. For this very Example I find Published by the same Mr. Kersey, in the year 1650. and since that time, owned and made use of by several others.

But for the right understanding of the truth of this, and all other Questions of this kind. It is necessary to request the Reader to contemplate with me a few things.

1. What is due of an Annuity that is not paid, at the end of the first, second, third, fourth, and fifth years, at Sim∣ple Interest.

1. At the first years end.

	l.
At the first years end there is due the just sum of	100

II. At the second years end. At the second years end, there is due,

	l.
1. For the first year	100
2. For the second year	100
Sum	200

And besides this, For the Interest of the 100 l. due at the first years end, and detained during the whole second year— 6 l.

III. At the third years end. At the third years end, there is due,

	l.
1. For the first year	100
2. For the second year	100
3. For the third year	100
Sum	300

Besides this, there is due,

	l.
1. For the Interest of the first 100 l. for the second year	6
2. For the Interest of the first 100 l. for the third year	6
3. For the Interest of the second 100 l. for the third year	6
Sum	18

IV. At the fourth years end.

	l.
1. For the first year	100
2. For the second year	100
3. For the third year	100
4. For the fourth year	100
Sum	400

Besides this,

	l.
1. For the Interest of the first 100l. for the second year	6
2. The Interest of the first 100l. for the third year	6
3. The Interest of the first 100l. for the fourth year	6
4. The Interest of the second 100l. for the third year	6
5. The Interest of the second 100l. for the fourth year	6
6. The Interest of the third 100l. for the fourth year	6
Sum	36

V. At the fifth years end.

	l.
1. For the first year	100
2. For the second year	100
3. For the third year	100
4. For the fourth year	100
5. For the fifth year	100
Sum	500

Besides this,

	l.
1. For the Interest of the first 100l. for the second year	6
2. For the Interest of the first 100l. for the third year	6
3. For the Interest of the first 100l. for the fourth year	6
4. For the Interest of the first 100l. for the fifth year	6
	24

5. For the Interest of the second 100l. for the third year	6
6. For the Interest of the second 100l. for the fourth year	6
7. For the Interest of the second 100l. for the fifth year	6
8. For the Interest of the third 100l. for the fourth year	6
9. For the Interest of the third 100l. for the fifth year	6
10. For the Interest of the fourth 100l. for the fifth year	6
	36
	24
Sum Total of the Interest for the five years	60
To which adding the five Annual payments, viz.	500
The whole Amount of the Annuity of 100l. forborn five years, is	560

In the next place, I desire the Ingeni∣ous Reader to consider well the third Prop. of Diophantus Alexandrinus, con∣cerning Peligonal Numbers.

ΔΙΟΦΑΝΤΟΥ ΑΛΕΞΑΝΔΡΕΩΣ ΠΕΡΙ ΠΟΛΙΤΟΝΩΝ ΑΡΙΘΜΩΝ.

PROP. III.

〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 &c. It Numbers (how many soever they be) exceed one another by an equal Internal, then the Internal between the greatest and the least, is Multipler of that equal Internal, according to the multitude of Numbers propounded, less by one.

For Example.

Let there be five given Terms, A, B, C, D, E, and let G be the common Interval or Difference.

To apply which, let

• A=100
• G=6

Number of Terms.	Then is,
1	A=A	1	A=100
2	B=A+G	2	B=100+6
3	C=A+G+G	3	100+6+6
4	D=A+G+G+G	4	D=100+6+6+6
5	E=A+G+G+G+G	5	E=100+6+6+6+6

That is to say, the greatest Term is equal to the least, and as many Differences as there are more Terms besides the least. So here E is equal to 100, and 4 Differences, or 4 times 6. And the Sums of those Numbers are the true Amount of an Annuity at Simple Interest; thus,

The Annual Rents, toge∣ther with the Annual Inte∣rests	The Sums of Annual Rents, & Annual Inte∣rests, for there∣spective Years.	The Number of An∣nual Interests, or Differences, that are contained in every re∣spective Sum, besides the Annual Rents.
1	100	1	100
2	100+6	2	206=	1
3	100+6+6	3	318=	3
4	100+6+6+6	4	436=	6
5	100+6+6+6+6	5	560=	10

Therefore the true Amount of an Annuity of 100l. is as follows.

Year.		Amounts
1	100	100
2	100+100+6	206
3	100+100+100+6+6+6	318
4	100+100+100+100+6+6+6+6+6+6	436
5	100+100+100+100+100+6+6+6+6+6+6+6+6+6+6	560

Consequently the Proportion is not as Mr. Kersey makes it, save only for the first year.

But the true proportion holds thus, viz.

			Amounts.	Present worths.
At the	1	years end	As 106 to 100∷ So 100 to	94.33962
2	As 112 to 100∷ So 206 to	183.92856
3	As 118 to 100∷ So 318 to	269.49152
4	As 124 to 100∷ So 436 to	351.61290
5	As 130 to 100∷ So 560 to	430.76923

Now therefore to perfect the Demonstration,

1. The present worth of the first year is	94.33962

2. Because 183.92856 is the present worth of the two first years, therefore if the present worth of the first year (Viz. 94.33962) be deducted out of it, it must needs leave the present worth of the second year, viz.	89.58894
3. Because 269.49152 is the present worth of the three first years, therefore deducting out of it 183.92856, (viz. the present worth of the two first years) it leaves the present worth of the third year, viz.	85.56296
4. So deducting 269.49152 out of 351.61290, there remains the present worth of the fourth year	82.12138
5. And 430.76923 less by 351.61290, is the present worth of the last year, viz.	79.15633
Total Sum of all the present worths	430.76923

To conclude, it is evident from the two last Calculations, and that by clear Demonstration, That,

	l.
1. The Amount of the first year is	100
2. The Amount of the two first years is	206
3. The Amount of the three first years is	318
4. The Amount of the four first years is	436
5. The Amount of all five years is	560

As likewise, That the present Worth,

1. Of the first year is	94.33962
2. Of the two first years is	183.92856
3. Of the three first years is	269.49152
4. Of the four first years is	351.61290
5. Of all five years is	430.76923

And lastly, it is evident and plain, That the present Worth,

1. Of the first year is	94.33962
2. Of the second year is	89.58894
3. Of the third year is	85.56296
4. Of the fourth year is	82.12138
5. Of the fifth year is	79.15633
Total Sum of the present worths	430.76923

Whereas Mr. Kersey makes the Total of the present worths but 425.93933, which is a very great mistake; as are all his particular present worths, (the first only excepted) which he could not well Calculate amiss.

Besides, if 425.93933 be put out for five years, it will amount to no more than 553.714109. Whereas 430.76923 in five years, at 6 per Cent. amounts to 560 l. which is the true Amount of 100 l. per Annum for five years, as has been sufficiently Demonstrated, and agrees

exactly with the foregoing Rule: So that Mr. Kersey in this Example falls short of the truth, as to the present worth, no less than 4.8353, that is, 4l. 16 s. 8 d. 1 q. more by 96/100 of a Farthing. Which Error, if it be so considerable in an An∣nuity of 100 l. per Annum, what would it be in an Annuity of 100000 paid per Annum? No less than 4835 l. 6 s.

2 Example.

A second Example I have borrowed from Mr. Dary, who has truly detected the Error of it, although he has not sufficiently explained the Reason of the Error; and therefore the Reader will find it here more strictly examined and refuted by a plain Demonstration obvi∣ous to the meanest capacity.

The Example is this: What is the present worth of an Annual Rent of 62 l. to be enjoyed four Years to come, allowing the Purchaser 6 per Cent. Simple Interest?

The usual Method, says Mr. Dary, is thus: 〈 math 〉〈 math 〉

Now let the Error of this Operation be traced from the beginning.

1. The Annual Interest of 62 l. per Annum, is 3.72; where∣fore by the foregoing Prop. of Diophantus Alexandrinus, pag. 73.

The Amount of 〈 math 〉〈 math 〉

Therefore the true Amount of an Annuity of 62 l. at each years end, is as follows.

At the end of the 〈 math 〉〈 math 〉

Wherefore the true Calculation of the present Worths is as follows, viz.

At the end of the 〈 math 〉〈 math 〉

Now therefore,

1. The present worth of the first year is—	58.490
2. The present worth of the two first years less by the present worth of the first, that is, from 114.035 deducting 58.490, the present worth of the second year is—	55.545
3. The present worth of the three first years (the present worth of the two first being deducted) that is, from 167.084 deducting 114.035, the remainder of the present worth of the third year is—	53.049
4. Deducting from 218 the present worth of all four years, 167.084 the present worth of the first three years, the remainder (viz. 50.916) is the present worth of the fourth year—	50.916

So then, The present worth, 〈 math 〉〈 math 〉

Whereas the usual way of Rebate makes it not above 216.390, which is less than the truth by 1.610, which is •• l. 12 s. 2 d. 2 q. ferè.

And if 216.390 be put out at Interest at 6 per Cent. for four years, it will amount to no more than 268.3236, which is less than the true Amount of 218 l. viz. 270.32 by 1.9964, which being reduced, is 1 l. 19 s. 11 d. more by 11/100 parts of a Farthing.

All which may serve as a sufficient caution against such erroneous Tables and Calculations.

A second Reflection upon that Example of Mr. John Kersey.

I Must confess that the present Worth of 100 l. payable a year hence is 94.33962; and that the present worth of a single 100 l. payable two years hence, is as he has put it 89.28571; and the present worth of another bare 100 l. payable three years hence is 84.74576; and so to the end. And the Total of those present worths is as he has put it, viz.

〈 math 〉〈 math 〉

And this is part of that very Table which I have calculated (being the twelfth Table of the first Chapter of this first Book) for The present worth of One Pound after any Number of Years under 32.

But reason tells me, that in this Cal∣culation there is no consideration had of the Forbearance of Interest; for certain it is, if the first 100 l. had been paid at the first years end, it might have been put out to Interest, and at the five years end would have given an increase of four times 6 l. or 24 l. at Simple Interest; and so the second 100 l. would have in∣creased in the three last years three times 6 l. or 18l.

That is to say,

	l.
The first 100 l. would increase in the four last years	24
The second 100 l. would increase in the three last years	18
The third 100 l. would increase in the two last years	12
The fourth 100 l. would increase in the last year	6
The whole increase	60

Therefore there would be due, if all were forborn,

	l.
1. At the first years end	100
2. At the second years end	100+06
3. At the third years end	100+12
4. At the fourth years end	100+18
5. At the fifth years end	100+24
	500+60

Now to Calculate the present worth of any, or all of these Sums, let it be considered by what proportion the Cal∣culation ought to be made.

For Example.

Suppose the Annuity to be forborn only two years, and it be required to give the present worth of the two first years.

Whatsoever the Answer is, all will agree, that the Sum which is given in to be the present worth of those two years, being put out to interest, must amount to •••••• at the end of two years.

Therefore I say, As 112 to 100∷ So 206 to 183.92856.

If this be a true Answer, then that Sum, viz. 183.92856, being put out to Interest at 6 per Cent. for two years, must amount to 206.

By the former Rules.

〈 math 〉〈 math 〉

Now this Total Sum wants but ••/100000 of 206.

For, 〈 math 〉〈 math 〉

But now take the Sum of Mr. Kersey's two years present Worths, viz.

〈 math 〉〈 math 〉

Let therefore this Sum be put out to Interest for two years.

Wherefore as before, 〈 math 〉〈 math 〉

〈 math 〉〈 math 〉

Which is less than 206 (the true Amount of an Annuity of 100 l. for two years) by .3396304; which though it be but 6 s. 8 d. and somewhat more in two years time, yet were the Sum greater, or the time longer, it would prove a very considerable Error.

Wherefore I conclude, that Mr. Kersey's Calculations are erroneous as to Annui∣ties, and mine exact: And there needs no further Illustrations or Demonstrati∣ons about it.

The next thing to be Treated of in course, is touching the Equation of several Payments, and reducing them into one entire Payment at a certain time, so as there may be no loss either to Creditor or Debtor.

CHAP. IV.

Equation of Payments Rectified, and made Practicable for all Merchants, and others.

EQuation of Payments is by all agreed to be the reducing of seve∣ral Payments into one entire Payment, at such a time, as neither Creditor or Debtor may be a loser by it, they being both agreed, the one to pay, and the other to receive, the said entire Payment at the appointed time.

Now of the Books that I have met with, and the Men I have discoursed with, about Equation of Payments at Simple Interest, some have adventured to give Rules for it, others have endeavoured to shew that such Rules are erroneous, and some of the most Learned of them have concluded the thing to be absolutely impracticable and impossible; and so

left the poor Merchants to agree as they please about it.

The truth is, they have been, and are all of them, mistaken about the pre∣sent Worths of Annuities at Simple Inte∣rest, and that mistake has begot many others.

The method that I shall therefore take, shall be, First, to expose to the Readers view both the true Amount and present Worth of an Annuity of 100 l. for five years, at several Rates of Interest. And from thence frame, and give a gene∣ral Rule for the reducing of several equal Payments due at equi-distant times, to one entire Payment. And after that, another Rule for reducing of unequal Payments at several times not equi∣distant, to one entire Payment at a cer∣tain time, so as neither he who pays, nor he who receives it, shall be any loser by it.

The Tables of the Amounts and pre∣sent Worths of an Annuity of 100 l. for five years (at different Rates of Interest) do here follow in their order.

TABLE I. At (1) per Cent. Simple Interest.

Years.	The Amount of 100 l. 〈◊〉〈◊〉 1, 2, 3, 4, or 5 Years.	Amount of Annual Payments at the end of 1, 2, 3, 4 or 5 Years.	The present Worth of the first year, the first two years, the first three years, the first four years, or all the five years.	The particular pre∣sent Worths of the first, second, third, fourth, or fifth year	The Amount of the Total present Worth of all the five Pay∣ments, at the end of the first, second, third, fourth, or fifth year.
1	101	100	99.00990	99.00990	490.57142
2	102	201	197.05882	98.04892	495.42856
3	103	303	294.17475	97.11593	500.28570
4	104	406	390.38461	96.20986	505.14285
5	105	510	485.71428	95.32967	509.99999
				485.71428

TABLE II. At (2) per Cent. Simple Interest.

Years.	The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.	Amount of Annual Payments, at the end of 1, 2, 3, 4 or 5 Years.	The present Works of the first two years, the first three years, the first four years, or all the five years.	The particular pre∣sent Works of the first, second, third fourth, or fifth year	The Amount of the Total present Worth of all the five Pay∣ments, at the end of the first, second, third, fourth, or fifth year.
1	102	100	98.03921	98.03921	482.18181
2	104	202	194.23076	96.19155	491.63635
3	106	306	288.67924	94.44848	501.09089
4	108	412	381.48148	92.80224	510.54543
5	110	520	472.72727	91.24579	519.99999
				472.72727

TABLE III. At (3) per Cent. Simple Interest.

Years.	The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.	Amount of Annual Payments, at the end of 1, 2, 3, 4 or 5 Years.	The present Worth of the first year, the first two years, the first three years, the first four years, or all the five years.	The particular pre∣sent Worths of the first, second, third, fourth, or fifth year.	The Amount of the Total present Worth of all the five Pay∣ments, at the end of the first, second, third, fourth, or fifth Year.
1	103	100	. 97.08737	97.08737	474.69564
2	106	203	191.50943	94.42206	488.52173
3	109	309	283.48623	91.97680	502.34782
4	112	418	373.21428	89.72805	516.17390
5	115	530	460.86956	87.65528	529.99999
				460.86956

TABLE IV. At (4) per Cent. Simple Interest.

Years.	The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.	Amount of Annual Payments, at the end of 1, 2, 3, 4 or 5 Years.	The present Worth of the first year, the first two years, the first three years, the first four years, or all the five years.	The particular pre∣sent Worths of the first, second, third, fourth, or fifth year.	The Amount of the Total present Worth of all the five Pay∣ments, at the end of the first, second, third, fourth, or fifth year.
1	104	100	96.15384	96.15384	468.00000
2	108	204	188.88888	92.73504	486.00000
3	112	312	278.57142	89.68254	504.00000
4	116	424	365.51724	86.94582	522.00000
5	120	540	450.00000	84.48276	540.00000
				450.00000

TABLE V. At (5) per Cent. Simple Interest.

Years.	The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.	Amount of Annual Payments, at the end of 1, 2, 3, 4 or 5 Years.	The present Worth of the first year, the first two years, the first three years, the first four years, or all the five years.	The particular pre∣sent Worths of the first, second, third, fourth, or fifth year.	The Amount of the Total present Worth of all the five Pay∣ments, at the end of the first, second, third, fourth, or fifth year.
1	105	100	95.23809	95.23809	461.99999
2	110	205	186.36363	91.12554	483.99999
3	115	315	273.91304	87.54941	505.99999
4	120	430	358.33333	84.42029	527.99999
5	125	550	439.99999	81.66666	549.99999
				439.99999

TABLE VI. At (6) per Cent. Simple Interest.

Years.	The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.	Amount of Annual Payments, at the end of 1, 2, 3, 4, or 5 Years.	The present worth of the first year, the first two years, the first three years, the first four years, or all the five years.	The particular pre∣sent Worths of the first, second, third, fourth, or fifth year.	The Amount of the Total present Worth of all the five Pay∣ments, at the end of the first, second, third, fourth, or fifth year.
1	106	100	94.33962	94.33962	456.61538
2	112	206	183.92856	89.58894	482.46153
3	118	318	269.49152	85.56296	508.30769
4	124	436	351.61290	82.12138	534.15384
5	130	560	430.76923	79.15633	559.99999
				430.76923

TABLE VII. At (10) per Cent. Simple Interest.

Years.	The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.	Amount of Annual Payments, at the end of 1, 2, 3, 4, or 5 Years.	The present worth of the first year, the first two years, the first three years, the first four years, or all the five years.	The particular pre∣sent Worths of the first, second, third, fourth, or fifth year.	The Amount of the Total present Worth of all the five Pay∣ments, at the end of the first, second, third, fourth, or fifth year.
1	110	100	90.90909	90.90909	440.00000
2	120	210	175.00000	84.09090	480.00000
3	130	330	253.84615	78.84615	520.00000
4	140	460	328.57142	74.72527	560.00000
5	150	600	400.00000	71.42858	600.00000
				399.99999

Observations upon the foregoing Tables.

1. IT is observable, That as the Rate of Interest increases, the present Worth decreases; that is to say,

For the present Worth of an Annuity of 100 l. for five years,

At	1	per Cent. is	485.71428
2	472.72727
3	460.86956
4	450.00000
5	439.99999 &c.
6	430.76923
10	399.99999 &c.

2. It is no less observable, That an Annuity of 100l. increases by a Trigo∣nal Progression of the respective Rates. But the Present Worth increases by an Unitarian Addition of the Rate to the Principal for each year respectively. And these two ways are very different the one

from the other, as may be seen by com∣paring them together, as follows in the Example of an Annunity of 100l. at 6 perCent. Simple Interest.

			Amount of the Annui∣ty for each of the five years.	Amount of the present Worth of the Amuity for each of the five years.
At the	1	years end	100	456.61538
2	206	482.46153
3	318	508.30769
4	436	534.15384
5	560	559.99999 &c.

And yet how different soever they are at their first setting out, and by the way, yet the further they go, the nearer they come together, and at last agree to an insensible difference, and such as may be diminished in insinitum, either to the Hundredth, or Theirsandth, or any less part of a Farthing whatsoever can be desired.

3. As a consequence of the foregoing Observation:

If A. be to pay B. 100l. per Annum for five years, and they agree that the 500l. shall be paid at one entire Pay∣ment, they must be sure to pitch upon such a time, as that the said 500l. being put out to Interest from that time to the end of five years, may be equal to the whole Amount of those five Annual Payments.

For Example.

Let the Rate of Interest be 6 per Cent. per Annum, and the Time of paying the said 500l. be at the end of three years, and so there are two years to come.

If the said 500l. for two years, at 6 per Cent. will amount to 560l. (which is the whole Amount of the Annuity at the five years end) the Time is right, if not, it is a false Time.

But the Annual Interest of 500l. is 30l. therefore in two years it is 60l. and that added to 500, makes 560l. And therefore it was a just time to pay the said 500l. at one entire Payment. For so B. has at the five years end, the whole

effect of his Annuity improved to the utmost, at 6 per Cent. Simple Interest.

And B. having paid nothing before of the Annuity, and being obliged to pay nothing of it afterwards; but having enjoyed it for three years (which is the best part of it) already, and being to enjoy it two years more; the 500l. he now pays, is only as a Purchase of the Amount of the whole Annuity, which will be due at the five years end, viz. 560 l. and so gives the Present Worth of 560 l. from the three years end to the 5 years end; and so he pays not a Farthing more than the true worth of it. And for that true worth of it, to the end of the 5 years he has enjoyed, and must enjoy the said Annuity it self to the end of the said five years. And so neither A. nor B. have the least wrong or loss, neither the one by paying, nor the other by recei∣ving, this one entire Payment of 500 l. at the three years end; and if either or both should sell their concerns, it would be the same thing.

4. It is observable that the present Worth of the said Annuity, at any Rate of Interest, does at the three years end ex∣ceed the Aggregate of the said five Sums, (or 500 l.)

For Example.

The present Worth of an Annuity of 100 l. per Annum to continue five years, does at the end of three years, Amount,

At	1	per Cent. to	500.28570
2	501.09089
3	502.34782
4	504.00000
5	505.99999
6	508.30769
10	520.00000

5. It being as evident from this last Observation, That the present Worth of the whole Annuity being put out to Inte∣rest for three years, will at any Rate of Interest, exceed the Aggregate of all

the five Payments, and the greater the Rate of Interest is, the greater is that Excess.

For Example.

At (1) per Cent. the Excess is but . 28570; at (2) per Cent. the Excess is somewhat more, viz. 1.09089; at (3) per Cent. it is 2.34782; at (10) per Cent. it is 20l. and at (15) per Cent. it would be much more.

And it being likewise evident by all the foregoing Tables, whatever the Rate of Interest be, That 500l. more by the Interest of 500l. for two years, is equal to the whole Amount of the Annuity of 500l. for five years. That is to say,

The Interest of 500 l. for two years,

At (1) per Cent. is 10 l. which added to 500 l. makes the Amount	510 l.
At (2) per Cent. is 20 l. which added to 500 l. makes the Amount	520 l.

At (3) per Cent. is 30 l. which added to 500 l. makes the Amount	530 l.
At (4) per Cent. is 40 l. which added to 500 l. makes the Amount	540 l.
At (5) per Cent. is 50 l. which added to 500 l. makes the Amount	550 l.
At (6) per Cent. is 60 l. which added to 500 l. makes the Amount	560 l.

And lastly, it being sufficiently evi∣dent by the third Observation, That if the 500 l. be paid at one entire Payment, at the end of three years, or, which is all one, two years before the Annuity be at an end; neither Creditor nor Debtor can have the least wrong, or suffer the least loss.

It may therefore be safely concluded, That it is practicable and possible to give a good and true Rule for Equation of seve∣ral Payments; and likewise, that it is no way necessary (as some very Learned

Artists would needs have perswaded me) to try that Rule by this Mark, viz. That the present Worth of the said 500 l. at the three Years end, must be the present Worth of the whole Amount of the said An∣nuity. For by what has been already proved, the present Worth of the whole Annuity at any Rate of Interest, will at the three years end exceed the said 500 l.

Now therefore I shall proceed to give two General Rules.

The first, for Equation of several equal Payments at equi-distant times.

The second, for Equation of several unequal Payments at several times not equi-distant.

1. General Rule.

For Equation of any given Number of equal Payments due at equi-distant Times.

Rule.

Out of the whole Amount of the An∣nuity, of Monthly Payment, deduct

the Aggregate of the several Pay∣ments, and the Remainder, if Annual, multiply by 365; if Monthly, by 30.416; then divide the Product by the Annual, or Monthly Interest of the said Aggre∣gate, and the Quotient is the number of Days, before the end or Term of the Annuity, or Monthly Payment, when the said Aggregate may be paid with∣out loss to either Creditor or Debtor.

1. Example.

Let the Annuity be 100 l.

The time it is to continue five years.

The whole Amount of the An∣nuity	560
The Aggregate of the several Payments	500
The Annual Interest of the Ag∣gregate (viz. 500)	30

Now suppose A. be obliged to pay to B. 100 l. per Annum for five years, but they both agree that A. shall pay to B. the Aggregate 500 l. at one entire Pay∣ment.

And then the Question is, at what time the said 500 l. is to be paid?

Therefore as the Rule directs, 〈 math 〉〈 math 〉 That divided by 30, gives a Quotient, which is the true number of Days before the end of the said Annuity, when the said 500 l. is to be paid, viz. 730

Those 730 Days divided by 365, gives a Quotient of two years.

So then the true time of paying the said Aggregate of several payments, (viz. 500 l.) is two years before the end of five years; that is at the end of the third year.

2. Example.

A. is to pay B. 62 l. per Annum for four years; but they agree that A. shall pay the Aggregate of the several Sums, (viz. 248) at one entire Payment.

If the Annual Payment be	62.00
The Amount of that in four years, at 6 per Cent. will be	270.32
The Aggregate of the several Payments, or four times 62, is	248.00
The Annual Interest of the said Aggregate	14.88

Wherefore, 〈 math 〉〈 math 〉

This 22.32 is first to be multiplied by 365, which is 8146.80.

That Product 8146.80 being divided by the Annual Interest of the Aggregate 248, viz. 14.88, gives a Quotient of 547.5 Days.

This Quotient 547 Days and ••/10, or a half, is a true Answer to the Question; that is to say, 547 Days and a half, or one Year, and 172 Days and a half, be∣fore the end of four years, is the just time to pay the said Aggregate, or 248, at one entire Payment; so as neither he who pays it, nor he who receives it, may be a loser.

But that all things may be exposed clearly to the Readers view, I shall here repeat the thing, and set down the whole Operation.

1. The Annual Payment for four years is	62.00 l.
2. The whole Amount of this in four years is	270.32 l.
3. The Aggregate, or four years Payments, that is, four times 62l. is	248.00 l.
4. The Annual Interest of the said Aggregate is	14.88 l.

Now the Question is, what is the true time for paying the said Aggregate, or 248, at one entire Payment?

To Answer this, I proceed according to the aforesaid Rule. 〈 math 〉〈 math 〉

2. I multiply this Remainder by 365, thus, 〈 math 〉〈 math 〉

3. This Product I divide by the Annual Interest of the Aggregate, viz. 14.88.

Tariffa for the Divisor.
1	1488
2	2976
3	4464
4	5952
5	7440
6	8928
7	10416
8	11904
9	13392
10	14880

〈 math 〉〈 math 〉

And the Quotient 547.5, is an An∣swer to the Question.

That is to say, (as before) one year, and 172 days, and a half, before the end of four years.

Or, which is the same thing, two years, and 192 days and a half, after the Agreement, must the 248 l. be paid at one entire Payment; and for the Reasons aforesaid, there is no loss to either A. or B.

For Proof of this,

Let 248 l. be put out to Interest at 6 per Cent. for one year, and 172 days and a half, that is, 547.5 days (which is the Quotient, or the time given from the Payment thereof to the end of the Annuity) and if it make up the whole Amount of the Annuity, viz. 270.32, the Operation is right.

Tariffa for the Mul∣tiplicand.
1	00016438356
2	00032876712
3	00049315068
4	00065753424
5	00082191780
6	00098630136
7	00115068492
8	00131506848
9	00147945204
10	00164383560

For Example.

〈 math 〉〈 math 〉

Then I make the following Tariffa, and proceed to multiply the foregoing Pro∣duct by 248.

Tariffa for the Multiplicand.
1	089999999100
2	179999998200
3	269999997300
4	359999996400
5	449999995500
6	539999994600
7	629999993700
8	719999992800
9	809999991900

〈 math 〉〈 math 〉

Wanting but 1/10000 (which is not the Hundredth part of a Farthing) of the true Amount of the whole Annuity, viz. 270.32, and therefore the Opera∣tion is just.

And thus may any Question of this nature be resolved, to a Day, and parts of a Day; for if both these last Questions had been made for Months, the same Rule must have been observed.

For Example.

If A. is to pay to B. 100 l. per Month for five Months, when may he pay the 500 l. at one entire Payment, at the Rate of 6 per Cent?

The Payments being Monthly, 〈 math 〉〈 math 〉

Therefore, 〈 math 〉〈 math 〉

In pursuance of the aforesaid General Rule. 〈 math 〉〈 math 〉

Let therefore 5 be multiplied by 30.416, or the true number of Days that are in one equal Month. 〈 math 〉〈 math 〉

And let that (152.080) be divided by 2.500, or the Monthly Interest of 500 l. at 6 per Cent.

Tariffa for the Divisor.
1	25
2	50
3	75
4	100
5	125
6	150
7	175
8	200
9	225

〈 math 〉〈 math 〉

The Quotient (60.832) is a true Answer in Days.

That is to say, 60 Days and 832/1000 of a Day, (which makes two equal Months) before the end of five Months; or (which is all one) three Months after the agreement, or after the first day, when the said Debt was growing due, is the just time of paying the 500 l. at one entire Payment.

For Proof of this.

If 500 l. be put out to Interest at 6 per Cent. for two equal Months, or 60.832 Days, and does give 5 l. it makes the 500 l. become 505 l. which is the full Amount of those five Months Pay∣ments, and is a just Answer to the Que∣stion.

But, 〈 math 〉〈 math 〉

And the Operation is exact.

And this I take to be sufficient for the Resolution of any Question of this nature.

I shall proceed in the next place to Discourse about unequal Payments, at times not equi-distant.

A brief Discourse concerning the Equation of unequal Payments at Times not equi-distant.

For Example.

A Merchant owes 500 l. to be paid at three several unequal Payments, viz. at the end of four Months 300 l. at the end of six Months 100 l. and at the end of twelve Months 100 l. but the Debtor agrees with the Creditor to dis∣charge the Debt (viz. 500 l.) at one entire Payment.

The Question is, at what time this 500 l. may be paid, without damage or prejudice to either Creditor or Debtor?

The General Rule is this.

First find the true Amount of each of the Sums, from the first day of the A∣greement, to the last day of Payment, as supposing them to be forborn to the last. Then out of that deduct the Aggregate

of the respective Payments, and multi∣ply the Remainder, if Annual, by 365; if Monthly, by 30.4166; and the Pro∣duct divide by the Annual or Monthly Interest of the said Aggregate, and the Quotient is the Number of Days from the last Day of Payment, ac∣compting backwards.

The Operation is as follows.

First, the length of Time from the day of the Agreement, to the last day of Payment, is just twelve Months.

So then,

1. In the first place, 300 l. pay∣able after 4 Months, and be∣ing forborn to the end of 12 Months, has 8 Months Inte∣rest to accompt for, viz.	12.000
2. In the second place, 100 l. payable after 6 Months, and being forborn to the end of 12 Months, has 6 Months Interest to accompt for, viz.	3.000
3. To these Sums adding the	500.000
The whole Amount is	515.000

Then, 〈 math 〉〈 math 〉

And the Proportion is this.

If 2.5 be the Interest of 500 l. for one Month, how many Months Interest will 15 make?

Wherefore divide 15 by 2.5, and the Quotient is the Answer to the Question.

Tariffa for the Divisor.
1	25
2	50
3	75
4	100
5	125
6	150
7	175
8	200
9	225

The Operation is this. 〈 math 〉〈 math 〉

That is to say, if the said 500 l. be paid six Months before the end of twelve Months or (which is all one) at the end of

six Months, there will be no loss or damage either to Creditor or Debtor.

For Proof of this,

1. In the first place, 300l. was due at 4 Months end, and being con∣tinued 2 Months longer, the In∣terest thereof for 2 Months is 3 l. the whole Amount is	303 l.
2. In the next place, 100 l. paid at 6 Months end, is the time it was due	100 l.
3. In the last place, the other 100 l. paid 6 Months before the time, there must be an abatement made of 3 l.	97 l.
Total Sum	500 l.

So that in the first Sum there is an increase of 3 l. and in the last there is a decrease of 3 l. which are to be set one against the other; and the whole Amount is the Aggregate of the respe∣ctive Sums, and being paid at the end of 6 Months makes the Equation just 500 l.

After this manner may any Number of unequal Sums payable at any Number of Times not equi-distant, be Equated, and a time set for the Payment of the Aggregate; and not only so, but if the Debtor A. owe to B. 100l. per Annum, or per Month, for any Number of Years or Months, and A. and B. agreeing toge∣ther that it shall be in the power of A. to pay to B. the true value of his Preten∣sions at the end of any of the Years or Months, it is very Practicable, for the present Worth of the whole Amount at the end of any of the Years or Months resolves the doubt, and is an Answer the Question.

For Example.

A. owes to B. 100 l. per Annum for five years, and they agree that A. shall buy it off at the end of any of the four years, for at the end of 5 years nothing less than the whole 560 l. will pay the Dein.

1. The present worth of 560 l. (or the whole Amount) at the first years end, is

451.6129

2. The present worth of 560 l. at the second years end, is	474.5762
3. The present worth of 560 l. at the third years end, is	500, 0000
4. The present worth of 560 l. at the fourth years end, is	528.3018
5. The present worth of 560 l. at the fifth years end, is	560, 0000

Thus I have as briefly as the nature of the thing would permit, explained the Doctrine of Simple Interest, as likewise that of Annuities, and Equation of several Pay∣ments at Simple Interest, which is of ex∣cellent use for 6 12, or 18 Months, because the difference between Simple and Com∣pound Interest is not material in so short a time.

But for as much as the business of An∣••uities, or Purchases, for any considerable Number of years, does most properly and truly belong to the Doctrine of Com∣pound Interest, I shall make that the Sub∣ject of the following Book.