Question

At what rate per cent per annum, will Rs.32000 yield a compound interest of Rs.5044 in 9 months interest being compounded quarterly ?

• A. 25
• B. 23
• C. 20
• D. 18

Answer 1

The correct option is C 20

Principal = Rs.32000

Amount $=Rs.(32000+5044)=Rs.37044$

Rate $=r\%$ p.a. or $\frac{r}{4}\%$ per quarter

Time = 9 months = 3 quarters i.e., $n=3$

$\therefore$ Applying $A=P{(1+\frac{r}{100})}^n$ we have

$37044=32000{(1+\frac{r}{400})}^3\Rightarrow \frac{37044}{32000}={(1+\frac{r}{400})}^3$

$\Rightarrow \frac{9261}{8000}={(1+\frac{r}{400})}^3\Rightarrow {\left(\frac{21}{20}\right)}^3={(1+\frac{r}{400})}^3$

$\Rightarrow 1+\frac{r}{400}=\frac{21}{20}\Rightarrow \frac{r}{400}=\frac{21}{20}-1=\frac{1}{20}\Rightarrow r=\frac{400}{20}=20\%p.a.$