Question

The compound interest on Rs. 100 at the rate of 10% per annum, interest compounded half yearly, after one year is __________.

• A. Rs. 10
• B. Rs. 11
• C. Rs. 10.50
• D. Rs. 10.25

Answer 1

Answer: (D)

Rs. 10.25

Given that,

Principal amount $=100$
Rate $\left(r\right)=10\%$

Time $=1$ year

We know that,

Compound interest $=A-P=P{[1+\frac{R}{100}]}^n-P$

As it is compounded half-yearly, Rate $=\frac{r}{2}$
Time $=2n$

So, C.I $=P{[1+\frac{r}{100\times 2}]}^{2n}-P$
$=100{[1+\frac{10}{100\times 2}]}^{2\left(1\right)}-100$

$=100\left(\frac{21}{20}\right)\left(\frac{21}{20}\right)-100$

$=\frac{441-400}{4}$
$=\frac{41}{4}$
$=10.25$

Therefore, Compound interest $=10.25Rs$