from which fubtract unity, and the remainder will be the

ratio.

Or, Having found the amount of 11. for the time, as above directed, look for it in Table 1ft, even with the given time, and directly over the amount you will find the ratio.

EXAMPLES.

At what rate per cent. per annum wil 600l. amount to 7571. 9s. 8d. in 4 years ?

600)757,48614(1,2624769.-Now the time being 4 years the 4th root of this quotient minus I will be the ratio.

1,26247690)1,123599+ and 1,123599(1,05999+ and 1,05999-1,06 Anf.

DISCOUNT BY COMPOUND INTEREST.

CASE I.

The fum or debt to be discounted, the time and rate given to find the prefent worth.

RULE. Divide the debt by that power of the amount of 1 for 1 year, denoted by the time, and the quotient will be the prefent worth, which, fubtracted from the debt will leave the difcount.

EXAMPLES.

1. What is the prefent worth, and discount, of 600l. due 3 years hence, at 61. per cent. per annum compound intereft ?

3

Divide by 1,063 1,19101)600,00000(503,7741=== £503 1552 prefent worth; and £600-£503 15 54= £96 4s. 6d. Discount.

By

By TABLE 2d. In this table, corresponding to the time and rate, we

have,839619-prefent worth of it for the time and rate. Mult. by 600 debt, or principal.

503,771400

prefent worth of the debt.

2. What is the prefent worth of 312l. 10s. due 2 years hence, at 4 per cent. per annum, compound intereft? Anf. 2861 3s 3d 2,97qrs. 3. What ready money will difcharge a debt of 10col. due 4 years hence, at 51. per cent. per annum, compound intereft ? · Anf. 8221. 14s. od. 2,304 qrs.

ANNUITIES OR PENSIONS IN ARREARS, AT COMPOUND INTEREST.

CASE I.

When the annuity, or penfion, the time it continues and the rate per cent are given, to find the amount.

. I

RULE I. Make the 1ft term of a Geometrical Progreffion, and the amount of 11. for 1 year at the given rate per cent. the ratio.

of

2. Carry the feries to fo many terms as the number years, and find its fum.

3. Multiply the fum, thus found, by the given annuity, and the product will be the amount fought. Or, Multiply the amount of 11. for 1 year into itself fo many times as there are years, lefs by 1; then multiply this product by the annuity; and fubtract the annuity therefrom; laftly, divide the remainder by the ratio less 1, and the quotient will be the amount.

EXAMPLES.

EXAMPLES.

1. What will an annuity of 6ol. per annum, payable yearly, amount to in 4 years, at 61. per cent. ?`

First Method.

+1,06+1,062 +1,06|3X60=£2621. 9s. 64d.

Second Method.

1,06X1, 06X1,06X 1,06X60-60

1,06—1.

=262,49

Or, BY TABLE III.

Multiply the tabular number under the rate, and oppofite the time, by the annuity, and the product will be the amount.

2. What will an annuity, of 60l. per annum, amount to in 20 years, allowing 61. per cent. compound intereft?

Under 6 per cent and oppofite 20 in table 3d, you E will find tabular number 36,78559.

Multiply by 60 Annuity.

2207,1354022071 25. Bd. (the Anf

CASE II.

When the amount, rate per cent and time are given, to find the annuity, penfion, Sc...

RULE. Multiply the whole amount by the amount of 1 for 1 year, from which fubtract the whole amount ; divide the remainder by that pow wer of the amount of 11. for 1 year, figned by the number of years, made les by unity, and the quotient will be the answer.

EXAMPLES.

EXAMPLES.

1. What annuity, being forborne 4 years, will amount to 262,47696, at 61 per cent. compound intereft? 262,47696X1,06-262,47696

1,06X1,06X1,06X1,06-1

== 60*

Or, By TABLE III.

Divide the amount by the tabular number under the rate. and oppofite to the time, and the quotient will be the annuity.

2. What annuity being forborne 20 years, will amount to £2207,354, at 61 per cent compound interest? Tabular amount 36,78559)2207,13540(60 :: Anfang 2207,13540

When the annuity, amount and Fatio are given, to find the

RULE

time.

ASI, ASHW+ Multiply the amount by the ratio, to this product add the annuity, and from the fum fubtract the amount; this remainder being divided by the annuity, the quotient will be that power of the ratio fignified by the time, which being divided by the amount of L for year and this quotient by the fame. till, nothing re main, the number of thefe divifions, will be equal to the time Or, look for this number under the given rate in Table I. and in a line with it you will fee the time."

1

In what time will 60l. per annum, payable yearly, amount to 262, 47696 allowing 61. per cent. compound intereft for the forbearance of payment

In Table I. under the given rate, you will find 1,262476, and in a line under years, you will find 4.

PRESENT WORTH OF ANNUITIES, &c. AT COMPOUND INTEREST.

When the annuity, &c. rate and time are given, to find the prefent worth.

RULE* 1. Divide the annuity by the ratio, or the amount of il. for 1 year, and the quotient will be the prefent worth of 1 year's annuity.

2 Divide the annuity by the fquare of the ratio, and the quotient will be the prefent worth for two years.

3 in like manner, find the prefent worth of each year by itself, and the fum of all these will be the prefent value of the annuity fought.

Or, Divide the annuity &c. by that power of the ratio fignified by the number of years, and fubtract the quotient from the annuity: This remainder being divided by the ratio lefs I, the quotient will be the prefent worth. EXAMPLES.

1. †What ready money will purchase an annuity

of

The amount of an annuity may also be found for years and parts of a year, thus:

I. Find the amount for the whole years, as before. 2. Find the intereft of that amount for the given parts of a year

3Add this intereft to the former account, and it will give the whole amount required.

The prefent worth of an annuity for years and parts of a year, may be found thus:

1. Find the prefent worth for the whole years as before.

2. Find the present worth of this prefent worth, discounting for the given parts of a year, and it will be the whole prefent worth required

4 Questions in this cafe may also be answered by first finding the amount of the given annuity by Cafe of annuities in arrears, page 308, and then the prefent worth or principal, by Cafe 2, of Compound Interest, 305.