### Question 7

SSC-CGL 2020 Mar 4 Shift 3

A sum of Rs 8000 is invested at the rate of 10% amounts to Rs 9261 if compounded half-yearly. What will be the amount if the rate of interest is doubled?

### Solution in Detail

A = 9261, P = 8000, compounding is half-yearly, so R = 10% ÷ 2 = 5% = 1/20, but t = ?

Observe $\displaystyle \frac{9261}{8000} = \bigg(\frac{21}{20}\bigg)^3$

$\displaystyle \equiv \bigg(1 + \frac{1}{20}\bigg)^3$

$\displaystyle \therefore t = 3$ units

To find A = ? Compounding remains half-yearly, so R is doubled to 2 x (1/20) = 1/10, t also remains = 3, and P is also 8000.

$\displaystyle \therefore A = 8000 \bigg(1 + \frac {1}{10}\bigg)^3$

$\displaystyle = 8000 \times \frac{1331}{1000} $

$\displaystyle = 10648 \text{ Rs. }\underline{Ans}$

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