Question

The compound interest on Rs 4000 at 10% per annum for 2 years 3 months, compounded annually is

• A. Rs $961$
• B. Rs$916$
• C. Rs $900$
• D. Rs$896$

Answer 1

Answer: (A)

Principal $\left(P\right)=Rs.4000$

Rate of Interest $\left(r\right)=10\%$

Time $=2$ years and $3$ months

Here first we take $n=2$ years.

$\Rightarrow$ Amount for first $2$ years $\left(A\right)=P{(1+\frac{r}{100})}^n$

$=4000{(1+\frac{10}{100})}^2$

$=4000{\left(\frac{11}{10}\right)}^2$

$=4000\times \frac{121}{100}$

$=Rs.4840$

$\Rightarrow$ The amount after two years $=Rs.4840$

$\Rightarrow$ Now, Principal $=Rs.4840$

Simple interest for last $3$ months i.e. $\frac{1}{4}years$ $=\frac{PRT}{100}$

$=\frac{4840\times 10\times 1}{100\times 4}$

$=Rs.121$

$\Rightarrow$ Amount after $2$ years and $3$ months $=Rs.4840+Rs.121=Rs.4961$

$\Rightarrow$ $C.I.=A-P$

$=Rs.4961-Rs.4000$

$=Rs.961$

$\therefore$ The compound interest is $Rs.961$