The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne.

CHAP. IX. The use of the Line in Questions of Interest and Annuities.

PROB. 1. A sum of money put out to Use, and the Interest forborn for a certain time, to know what it comes to at the end of that times, counting Interest upon In∣terest at any rate propounded.

Take the distance with your Com∣passes between 100, and the Increase of 100 l. for one Year, (which you

must do very exactly) and repeat it so many times from the principal as it is forborn years, and the point of the Compasses will stay on the Prin∣cipal with the Interest, and increase according to the rate propounded.

Example.

I desire to know how much 125 l. being forborn 6 year will be increa∣sed, according to the rate of 6 l. per cent. reckoning Interest upon Interest or Compound-Interest.

Extend the Compasses from 100 to 106; that extent being 6 times re∣peated from 125, shall reach to 177 l. the principal increased with the inte∣rest at the term of 6 years, at the rate propounded.

But if it were required for any number of Months, then first find what 100 is at one Month, then say thus, If 100 give 10 s. at one month, what shall 125 be at 6 months end? facit 75 s. And the work is thus:

First say, If 100 give 10 s. at one months end, What shall 125? and

it makes 12 s. 6 d. then say, If one month require 12 s. 6 d. What shall six months require? facit 75 s. that is three pound fifteen shillings, the thing required to be found.

PROB. 2. A sum of money being due at any time to come, to find what it is worth in ready money.

This question is only the inverse of the other; for if you take the space between 106 and 100, and turn it back from the sum proposed, as many times as there are years in the questi∣on, it shall fall on the sum required.

Example.

Take the distance between 106 and 100, and repeat it 6 times from 177, and it will at last fall on 125, the sum sought.

PROB. 3. A yearly Rent, Pension, or Annuity being forborn for a certain term of years, to find what the Arrears come to at any rate propounded.

First you must find the principal that shall answer to that Annuity, then

find to what sum the Principal would be augmented at the rate and term of years propounded; then if you sub∣stract the principal out of that sum the remainder is the Arrears required.

Example.

A Rent, or Annuity, or Pension of 10 pound the year, forborn for 15 years, What will the arrears thereof come to at the rate of 6 per cent. com∣pound interest?

The way first to find the principal that doth answer to 10 l. is thus: If 6 pound hath a 100 for his principal, What shall 10 have? facit 166 l. 16 s. or 166 l. 8 s. for the extent from 6 to 10 will reach from 100 to 166-8. which is 166 l. 16 s. Then by the first Problem of this Chapter, 166 l. 16 s. forborn 15 year, will come to 398 l. then substract 166 l. 16 s. out of 398 pound, and the remainder, viz. 231 pound 4 shillings is the sum of the arrears required. But note, in working this question, your often turning, un∣less your first extent be most precisely

exact, you may commit a gross error, to avoid which, divide your number of turns into 2, 3, or 4 parts, and when you have turned over one part, as here 5, for three times 5 is 15, open the Compasses from thence to the principal, and then turn the other two turns, viz. 10-15. and this may avoid much errour, or at the least much mitigate it; for in these que∣stions the larger the Line is, the bet∣ter.

PROB. 4. A yearly Rent or Annuity being pro∣pounded, to find the worth in ready money.

First, find by the last what the ar∣rears come to at the term propoun∣ded, and then what those arrears are worth in ready money, and that shall be the value of it in ready money.

Example.

What may a Lease of 10 l. per ann. having 15 year to come be worth in ready money? I find by the last Pro∣blem that the arrears of 10 l. per ann.

forborn 15 years, is worth 23 l. 14 s. And likewise I find by the second Problem that 231 l. 4 s. is worth in ready money 96 l. 16 s. and so much may a man give for a Lease of 10 l. per ann. for fifteen years to come, at the rate of 6 l. per cent.

But if it were not to begin present∣ly, but to stay a certain term longer, then you must adde that time to the time of forbearance; as suppose that after 5 years it were to begin, then you must say, 231 l. 4 s. forborn 20 years is worth in ready money, and it is 72 pound 8 shillings; and that shall be the value of the Lease required.

PROB. 5. A sum of money being propounded, to find what Annuity to continue any number of years, at any rate pro∣pounded, that sum of money will pur∣chase.

Take any known annuity, and find the value of it in ready money; this being done, the proportion will be thus: As the value found out is to the

annuity taken, so is the summe pro∣pounded to the annuity required.

Example.

What annuity to continue fifteen years will 800 l. purchase, after the rate of 6 l. per cent. Here first I take 10 l. per ann. for fifteen year, and find it to be worth in ready money 96 l. 16 s. by the last Problem; then I say, as 96 l. 8 s. is to 10, so is 800 to 82-7, which is 82 l. 14 s. and so much neer do I conclude will an annuity of 82 l. 14 s. per ann. be worth for fifteen years, after the rate of 6 l. per cent. viz. 800 l.