Question

# A sum of Rs. 12,000 deposited at compound interest doubles after 5 years. After 20 years it will becomeA) Rs. 1,20,000B) Rs. 1,92,000C) Rs. 1,24,000D) Rs. 96,000

Hint: In order to find out the value of compound interest after 5 years, we have to use the formula for compound interest mentioned below,
$A = P{\left( {1 + \dfrac{r}{100}} \right)^{nt}}$
Where, $A =$ final amount
$P =$ initial principal balance
$r =$ interest rate
$n =$ number of times interest applied per time period
$t =$ number of times period elapsed

In the first case we have 5 year time and an amount of 24000 and principal amount is 12000. So, by applying the above mentioned formula we will get,
24000 = 12000${\left( {1 + \dfrac{r}{{100}}} \right)^5}$
$\Rightarrow \dfrac{{24000}}{{12000}} = {\left( {1 + \dfrac{r}{{100}}} \right)^5} \\ \Rightarrow 2 = {\left( {1 + \dfrac{r}{{100}}} \right)^5} \\$
We have to find out the value of compound interest after 20 years. For that the value of exponent must be 20.
Multiply the exponent of both sides by 4
${2^4} =$ ${\left( {{{\left( {1 + \dfrac{r}{{100}}} \right)}^5}} \right)^4}$
16$= {\left( {1 + \dfrac{r}{{100}}} \right)^{20}}$
Multiply P that is 12000 on both sides,
$16 \times 12000 = {\left( {1 + \dfrac{r}{{100}}} \right)^{20}} \times 12000$
We can see that here ${\left( {1 + \dfrac{r}{{100}}} \right)^{20}} \times 12000$ is the amount formula for 20 years.
So,
Amount $= {\text{ 12000}}\left( {16} \right) = 192000$
After 20 years it will become Rs. 192000.
$\therefore$ Option B is correct.

Note: In this particular question, to find out the value of compound interest we have to use the general formula for compound interest. We can easily solve this question by deriving the amount formula like we did in the question. Also it is important to note that compound interest is different from simple interest as compound interest is based on the principal amount and the interest accumulates on it every period.