EXAMPLE I.

What will £480 amount to, in 7 years, at 4 per cent com.

pound interest?

Here p = 480, R= 1.04, and t = to 7, to find a.

Amount of £1, in 7 years, at 4 per cent, 1.315932

480

£631.647

EXAMPLE II.

What will £500 amount to, in 55 years, 50 days, at 5 per

cent, compound interest?

Here p = 500, R = 1.05, and t= 55, to find a.

1. What will £1000 amount to, in 10 years, compound interest ?

at 4 per cent,

2. What is the present worth of £500, due 7 years henoe, allowing discount at the rate of 4 per cent, compound interest?

3. At what rate of compound interest will £1250 amount to £1645, in 7 years?

4. In what time will £500 amount to £1000, or any sum double itself, at 5 per cent, compound interest?

5. Required the amount of 1 penny, lent out at 5 per cent, compound interest, for 1000 years.

6. Required the amount of £100, for 100 years, 120 days, at 5 per cent.

ANNUITIES.

An Annuity is a term employed to denote any periodical income, payable annually, or at other intervals of time.

ANNUITIES IN ARREARS.

Let m = the arrear of any annuity (a) unpaid for the time (t) and compound interest reckoned on each payment, from the time it should have been paid; then the most common cases that occur, in transactions of this kind, may be resolved by the following Theorems:

1. max.

Log. a.

mr

Rt-1

or Log. m Log. (Rt-1) - Log. r +

=

=

2. a=R or Log, a Log. m+Log. r-Log. (R-1)

When the annuity is payable at any other interval than a year, and t is equal the number of times that payment is made, R is equal the amount of £1, for 1 of those times, and a equal the sum paid each time.

The sum which would yield a perpetual annuity of £1, at the given rate of interest, is called the Perpetuity.

EXAMPLE.

What will an annuity of £50, payable annually, amount to, in 30 years, at 4 per cent?

This example is resolved by Theorem 1st, where a ≈ 50, r = .045, R=1.045, and t = 30, to find m.

1. Required the amount of an annuity of £100, payable year

ly, in 15 years, 5 per cent, compound interest?

2. What annuity will amount to £1000, in 15 years, at 5 per cent, per annum, compound interest?

3. In what time will an annuity of £20, payable yearly, amount to £890, at 5 per cent?

4. At what rate will an annuity of £50, payable yearly, for 30 years, amount to £3050. 7s.?

What will an annuity of £17. 10s., payable quarterly, amount to, in 5 years, at 5 per cent?

6. What is the present value of 60 years possession of an estate of £100, to commence at the expiration of 40 years, interest at 3 per cent ?

PRESENT WORTH OF ANNUITIES.

The present worth of any given annuity may be found by the following theorems, where P represents its present worth, or purchase money, and the other letters the same things as in the preceding theorems.

1.

Rt-1

p=ax or Log pLog.(R-1) —Log.rRt+a

TRt

or Loga log R+log.p+log.r-log. (Rt--1)

If the annuity be to continue for ever, then Rt and R-1 may be considered as the same, and therefore