A sum of Rs. 24,000 is lent out for 2 years at compound interest, the rate of interest being 10% per year. The borrower returns some paying at the end of the first year and on paying Rs. 12,540 at the end of the second year the total debt is cleared. Calculate the amount of money returned at the end of the first year.

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Solution

Amount at the end of 1 year=Principal+Interest
Interest= $\frac{P R T}{100} = \frac{24000 \times 1 \times 10}{100} = R s .2400$
$∴$ Amount at the end of 1 year $= 24000 + 2400 = R s .26400$

Interest for the 2 year $= \frac{26400 \times 10 \times 1}{100} = R s .2640$
Amount at the end of 2 year $= 26400 + 2640 = R s .29040$

Let he return Rs.x at the end of first year
$∴ 29040 - x = 12540$
$\Rightarrow x = 29040 - 12540$
$\Rightarrow x = R s .15000$

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