A sum of money, deposited at some rate p.c.p.a. of compound interest, doubles itself in 4 years. In

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6.Interest

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A sum of money, deposited at some rate $p.c.p.a.$ of compound interest, doubles itself in $4$ years. In how many years will it become $16$ times of itself at the same rate?

A

$16$

B

$12$

C

$10$

D

$8$

Solution

(a) Let the amount be $A,$ rate of interest be rand the required time be $t$ years. Now, according to the question,

$2 A=A\left(1+\frac{r}{100}\right)^{4}$

$\Rightarrow 2=\left(1+\frac{r}{100}\right)^{4}$

Again, $16 A=A\left(1+\frac{r}{100}\right)^{t}$

$\Rightarrow 16=\left(1+\frac{r}{100}\right)^{t}$

$\Rightarrow(2)^{4}=\left(1+\frac{r}{100}\right)^{t}$

Now, putting the value of 2 from Eqn. (1) in Eqn. (2), we get

$\left(1+\frac{r}{100}\right)^{4 \times 4}=\left(1+\frac{r}{100}\right)^{t}$

$\Rightarrow \quad t =(4 \times 4)=16$ years

Standard 13

Quantitative Aptitude

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