A sum of money lent at compound interest amounts to ₹ 1460 in 2 years and to ₹ 1606 in 3 years.

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6.Interest

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A sum of money lent at compound interest amounts to ₹ $1460$ in $2$ years and to ₹ $1606$ in $3$ years. The rate of interest (In $\%$) per annum is

A

$12$

B

$11$

C

$10.5$

D

$10$

Solution

(d) Let the amount be $A$ and the rate of interest be $r \%$ Then,

$A\left(1+\frac{r}{100}\right)^{2}=1460$

$A\left(1+\frac{r}{100}\right)^{3}=1606$

On dividing eqn. (1) by eqn. (2), we get

$1+\frac{r}{100}=\frac{1606}{1460}$

$\Rightarrow \frac{r}{100}=\frac{1606}{1460}-1=\frac{146}{1460}=\frac{1}{10}$

$\therefore r=\frac{100}{10} \%=10 \%$

Standard 13

Quantitative Aptitude

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