Socius mercatoris: or The merchant's companion: in three parts. The first, being a plain and easie introduction to arithmetick, vulgur and decimal, the extraction of the square and cube roots, with a table of 200 square roots, and their use in the resolution of square equations. The second, a treatise of simple and compound interest and rebate, with two tables for the calculation of the value of leases or annuities, payable quarterly, the one for simple, the other compound interest, at 6 per cent. per annum, with rules for making the like for any other rate. The third, a new and exact way of measuring solids in the form of a prismoid and cylindroid, with the frustums of pyramids and of a cone: whereunto is added, some practical rules and examples for cask-gauging. By John Mayne, philo-accomptant.

The VSE of the TABLE.

This Table sheweth the Discompt of 1 l. per Quarter at 6 per Cent. per Annum, Com∣pound Interest, and if the Tabular Number for so many Quarters as the Lease is to continue be multiplied by the Quarterly Payment, that Product is the present Value of that Lease in ready money.

Example.

A Lease of 40 l. per Annum (viz. 10 l. per quarter) for 21 years, being to be sold, what is it worth in ready money?

84 quarters per Table = 48.102221

The quarterly Rent = 10 〈 math 〉〈 math 〉

The Answer is 481 l. 0 s. 5 d. ••/4; ferè.

But if the question be, What quarterly Rent for 21 years will a given Sum purchase? Then divide the given Sum by the Tabular Number for so many quarters.

Example.

〈 math 〉〈 math 〉

A Gentleman having a Lease of certain Church Lands, worth 200 l. per Annum more than the reserved Rent, for 14 years to come, surrenders the same, upon condition the Chapter shall make him a new Lease for 31 years without a present Fine, but advan∣cing the old Rent 10 l. per quarter during the whole term of 31 years; what doth he gain by the bargain, accompting Compound Interest on both sides?

56 quarters per Table = 38.006

The quarterly Rent = 50 〈 math 〉〈 math 〉

124 quarters per Table = 56.955 〈 math 〉〈 math 〉

The Answer is 377 l. 18 s. the new Lease being so much more worth than the old one.

240 l. is demanded for the Lease of a House for 7 years, the Tenant offers 100 l. and an advance of Rent equivalent to the rest of the Fine required, what ought this Rent to be?

〈 math 〉〈 math 〉

The Advance of Rent ought to be 6 l. 2 s. 8 d. per quarter.

There is a Lease of 200 l. per Annum, viz. 50 l. per quarter, for 13 ¼ years, to be sold, what is it worth at 6 per Cent. Simple, and what at 6 per Cent. Compound Interest?

Simple.

53 quarters per Table = 38.779748 〈 math 〉〈 math 〉

Compound.

53 quarters per Table = 36.659861 〈 math 〉〈 math 〉 Which subtracted from 1938.987440 Leaves 105.99439

Whereby it appears, that it is cheaper to the Purchaser at Compound Interest than at Simple Interest by 106 l.

Six Questions performed by the aid of the Canon of Logarithms.

Quest. 1. A Gentleman pays 350 l. for a Lease in Reversion, to commence at the end of 13 years and a quarter, and to continue for 21 years and 3 quarters, what quarterly Rent may he lett the Premises for, after he comes to be in possession thereof, so as to gain 8 per Cent. Compound Interest for his money?

The Logarithm of 350l. = 2,544008

Worth of 1l. forborn 53 quarters = 0,442865

Log. of the Increase of 350l. = 2,986873

Worth of 1l. for 87 quarters = 1,621420

Log. of 23.198 = 1,365453

The Answer = 23 l. 3 s. 11 d. ½ ferè.

Quest. 2. A Citizen having taken a Lease of a House and Shop for 21 years, at 370 l. Fine, and 100 l. per Annum, viz. 25 l. per quarter, Rent, at the end of two years is willing to leave it for 300 l. and the old Rent, or to have such an increase of Rent, during the whole term yet to come, as may reim∣burse him his Fine paid, with Compound Interest at 6 per Cent. per Annum: What

ought he to receive in advance of Rent, and what doth he offer to lose of his Fine paid in taking 300 l.

2,568202 = 370l.

1,682165 = The worth of 1l. per quarter for 84 quarters.〈 math 〉〈 math 〉

0,886037 The Advance of Rent ought to be 7l. 13s. 10d. ¼ ferè.

1,652198 The worth of 1l. per quarter for 76 quarters.〈 math 〉〈 math 〉

2,545235 The present Fine ought to be 350l. 18s. 10d.

Whereby it appears, there is 50 l. 18 s. 10 d. offered to be lost in putting off the House and Shop aforementioned.

Quest. 3. A sells a House to B for 800 l. to be paid with Interest upon Interest by 100 l. per Annum, viz. 25 l. per quarter, how many quarters Rent ought B to pay before A is satisfied for his 800 l. with Compound Interest at 6 per Cent. per Annum, and what ought the last Payment be?

〈 math 〉〈 math 〉

The last Payment 13 l. 3 s. 4 d. ferè.

Quest. 4. A lends unto B a certain Sum of ready money, and accepts a Rent Charge of 40 l. quarterly for 7 years in satisfaction, finding it paid him his Principal with Interest upon Interest at 8 per Cent. within 13 l. 4 s. 6 d. what was the Money lent?

1,602060 The Logarithm of 40l.

1,565196 The Logarithm of the worth of 1l. quarterly for 48 quarters.〈 math 〉〈 math 〉

3,167256 The Logarithm of the worth of 40l. per quarter for 48 quarters.〈 math 〉〈 math 〉

0,177140 The Logarithm of the increase of 1l. forborn 28 quarters.

2,986188 The Logarithm of 968.7.

The Money lent was 968 l. 14 s.

Quest. 5. A Testator leaving one Son and two Daughters, bequeaths out of his Estate (be∣ing 600 l. per Annum for 11 years) to his eldest Daughter 500 l. per Annum for 4 years next coming, at the end whereof, to his younger Daughter 300 l. per Annum for 7 years, and to his Son the Remainder of the

Estate for the whole time: Q. Which had the greatest Portion, and by how much, calculating their several Annuities at 6 per Cent. Compound Interest?

0,539716 Logarithm of the worth of 1l. per annum for 4 years.

2,698970 The Logarithm of 500l.〈 math 〉〈 math 〉

3,238686 = 1732.55.〈 math 〉〈 math 〉

0,746820 The Logarithm of the worth of 1l. per annum for 7 years.

2,477121 The Logarithm of 300l. 〈 math 〉〈 math 〉

0,101232 The Logarithm of the worth of 1l. forborn 4 years.〈 math 〉〈 math 〉

3,122709 = 1326.47.〈 math 〉〈 math 〉

0,896905 The Log. of the present worth of 1l. per annum for11 years. 〈 math 〉〈 math 〉

2,896905 = 788.68

0,746820 The Log. of the present worth of 1l. per annum for 7 years.

2,301029 The Logarithm of 200l.〈 math 〉〈 math 〉

0,101232 The Logarithm of the worth of 1l. forborn 4 years. 〈 math 〉〈 math 〉

The Sons Portion —1673:00:05

The eldest Daughters Portion 1732:11:00

The youngest Daughters — 1326:09:04¾

〈 math 〉〈 math 〉

Proof.

0,896905 The Logarithm of the worth of 1l. per annum for 11 years.

2,778151 The Logarithm of 600l.〈 math 〉〈 math 〉

3,675056 The Logarithm of 4732l.

Quest. 6. A Merchant sold 16 Kintals of Cy∣prus Cottons for 320 l. to be paid at two six-months; the Buyer having Money by him, offers to pay the Money presently,

provided the Merchant allow him Discompt at 6 per cent. Compound Interest. Q. What ought the Merchant to receive?

2,505149 The Logarithm of 320l.

0,018979 The Logarithm of 1l. forborn 9 months, the equated time, acor∣ding to the Table of Mean Time, Pag. 110.〈 math 〉〈 math 〉

2,486170 The Logarithm of 306.316.

The Answer 306 l. 6 s. 4 d. ferè.