Question

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

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

Answer 1

The correct option is C

$₹961$

Given Principal, $P$ $=₹4000$

Rate of Interest, $r$$=10\%$

Time $=2$years and $3$ months

First we take $n=2$years.

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

$$\begin{gathered} =4000{\left(1+\frac{10}{100}\right)}^2 \\ =4000\times {\left(1+0.1\right)}^2 \\ =4000\times {\left(1.1\right)}^2 \\ =4840 \end{gathered}$$

Now principal $=4840$

Simple interest for $3$ months, $I=Pnr$

$$\begin{gathered} =4840\times \left(\frac{3}{12}\right)\times \left(\frac{10}{100}\right) \\ =121 \end{gathered}$$

Amount after $2$ years $3$ months $=4840+121$

$=4961$

Compound interest $=4961-4000$

$=961$

Therefore, the compound interest$=961$