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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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