# THE FARMER INVESTED MONEY WITH COMPOUND INTEREST (CAMBRIDGE PAST PAPER)

Three years ago the farmer invested \$3750 at a rate of 4% per year compound interest.

(i) Calculate the total value of his investment after the 3 years.
(ii) The farmer wants to spend his investment on buying goats.
Goats cost \$126 each.
Work out the maximum number of goats he can buy and how much money is left over.

Mathematics Cambridge IGCSE Test (0580 m16 qp 32)

i)    The formula of Compound Interest is

A=P (1+R/100)^T

This formula is applied when for each year we calculate the interest from previous year, until T years. So we calculate the interest compoundly.

The Amount A is the total of money with its interest, after T years.
In this question:

P = \$3750
After first year = \$3750 + 4% x \$3750 = \$3900
After second year = \$3900 + 4% x \$3900 = \$4056
After third year = \$4056 + 4% x \$4056 = \$4218.24
Or simply use the formula

A=\$3750(1+4/100)^3

A=\$4218.24

(ii)  Number of goats will be calculated as

=\$4218.24/126
=33.49

Exact the maximum number of goats he can buy are 33 goats.

The remaining money after he bought goats is 60.24