Question

# Govind borrows Rs. 18,000 at 10$$\%$$ simple interest. He immediately invests the money borrowed at 10$$\%$$ compound interest, compounded half-yearly. How much money does Govind gain in one year?

Solution

## Given that, Govind borrows $$Rs.\ 18000$$ at $$10\%$$ simple interest to invest at $$10\%$$ compound interest returns.To find out: Amount of money Govind gains in one year.As per simple interest, amount at the end of one year $$(A)= P\left(1 + \dfrac{TR}{100}\right)$$Here, $$P = Rs. 18,000,\ R = 10\%\ and \ T = 1\ year$$$$\therefore \ A= 18000\left(1 + \dfrac{1\times 10}{100}\right)$$$$\Rightarrow 18000\times \dfrac{11}{10}$$$$\therefore \ A= Rs.\ 19800$$Hence, Govind will have to return $$Rs.\ 19800$$ after one year.He invests the money he borrowed at $$10\%$$ compound interest, compounded half-yearly. Hence, the rate will become half and the time period will be double.$$\therefore \ P = Rs. \ 18,000,\ R = 5\%\ and\ n = 2$$As per compound interest, amount at the end of one year $$= P\left(1 + \dfrac{R}{100}\right)^{n}$$$$= 18000\left(1 + \dfrac{5}{100}\right)^{2}$$$$= 18000\left(\dfrac{21}{20}\right)^{2}$$$$=18000\times \dfrac{441}{400}$$$$= Rs.\ 19845$$Hence, the amount Govind will get after one year of investment is $$Rs.\ 19845$$.So, amount gained by him in one year $$Rs.\ 19845 - Rs.\ 19800 = Rs.\ 45$$.Hence, Govind gains $$Rs.\ 45$$ in one year.Mathematics

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