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A certain sum amounts to Rs.5,292 in two years and Rs. 5,556.60 in three years, interest being compounded annually. Find:

(i) The rate of interest

(ii) The original sum.

Answer:

(i)Amount in two years= Rs5,292

Amount in three years= Rs5,556.60

Difference between the amounts of two successive years

= Rs5,556.60 - Rs5,292= Rs264.60

Rs264.60 is the interest of one year on Rs5,292

Rate of interest= Rs \frac{100 \times I}{P \times T} \%=\frac{100 \times 264.60}{5,292 \times 1} \%=5 \%

(ii) Let the sum of money= Rs100

Interest on it for 1st year= 5% of Rs100= Rs5

Amount in one year= Rs100+ Rs5= Rs105

Similarly, amount in two years= Rs105+ 5% of Rs105

= Rs105+ Rs5.25

= Rs110.25

When amount in two years is Rs110.25, sum = Rs100

When amount in two years is Rs5,292, sum = Rs \frac{100 \times 5,292}{110.25}

= Rs4,800

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