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?

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Solution

Given that, Govind borrows $R s . 18000$ 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 $(A) = P (1 + \frac{T R}{100})$
Here, $P = R s . 18, 000, R = 10 % a n d T = 1 y e a r$

$∴ A = 18000 (1 + \frac{1 \times 10}{100})$

$\Rightarrow 18000 \times \frac{11}{10}$

$∴ A = R s . 19800$

Hence, Govind will have to return $R s . 19800$ 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.
$∴ P = R s . 18, 000, R = 5 % a n d n = 2$
As per compound interest, amount at the end of one year $= P {(1 + \frac{R}{100})}^{n}$

$= 18000 {(1 + \frac{5}{100})}^{2}$

$= 18000 {(\frac{21}{20})}^{2}$

$= 18000 \times \frac{441}{400}$

$= R s . 19845$

Hence, the amount Govind will get after one year of investment is $R s . 19845$ .

So, amount gained by him in one year $R s . 19845 - R s . 19800 = R s . 45$ .

Hence, Govind gains $R s . 45$ in one year.

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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?

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?