Question

Nagma invested $Rs.6000$ in a company at compound interest which is compounded semi-annually. She receives $Rs.7986$ after $18$ month from the company, then the rate of interest per annum is:

Answer 1

Given: Principle amount $P=Rs.6000$ and Amount $A=Rs.7986$
Let say the rate of interest $=r\%$
time $t=18$months
Since $1$ month $=\frac{1}{12}$ year
So, $18$ months $=\frac{18}{12}$ year
Thus, time $t=\frac{3}{2}$ year
Interest is compounded semi-annually.
$\Rightarrow n=2\times t$
$\Rightarrow n=2\times \left(\frac{3}{2}\right)$
$\therefore n=3$

Since, we have $A=P(1+\frac{r}{100}{)}^n$
By substituting given values, we get

$7986=6000(1+\frac{r}{100}{)}^3$
$\Rightarrow (1+\frac{r}{100}{)}^3=\frac{7986}{6000}$
$\Rightarrow (1+\frac{r}{100})=(1331{)}^{\frac{1}{3}}$
$\Rightarrow (1+\frac{r}{100})=11$
$\Rightarrow \frac{r}{100}=11-1$
$\Rightarrow \frac{r}{100}=10$

It gives $r\%=10\%$

Hence, the rate of interest $=10\%$ per annum.