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)

Answer:


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

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