Question

A sum of Rs.$16000$ earns a compound interest of Rs.$2522$ in $18$months, when the interest of compounded half-yearly.Find the rate of interest.

Answer 1

Amount at the end of 18 months $16000+2522=18522$

Now, we know that for CI

$A=P(1+\frac{r}{n}{)}^{nt}$

where $P=16000t=18months=\frac{3}{2}years$

$n=2$ (as it is compounded half-yearly)

$r=$ rate of interest

$A=$ Amount

So,

$18522=16000(1+\frac{r}{2}{)}^{\frac{3}{2}\ast 2}$

$\Rightarrow \frac{18522}{16000}=(1+\frac{r}{2}{)}^3$

$\Rightarrow \sqrt[3]{3\frac{18522}{16000}}=(1+\frac{r}{2})$

$\Rightarrow 10.5=1+\frac{r}{2}$

$\Rightarrow r=19$

So, Rate of interest is $19\%$