Question

Calculate the compound interest on ₹ 500 over 1 year and 6 months at 20% per annum if the interest rate is compounded half-yearly.

• A. ₹ 167.75
• B. ₹ 165.50
• C. ₹ 160
• D. ₹ 665.50

Answer 1

The correct option is B ₹ 165.50

Given
Principal = ₹ 500
Interest rate (r) = 20%

Since, the interest is compounded half yearly, there will be three conversion periods in the one year six months

So, n = 3
and r = $\frac{20}{2}$ or 10% compounded half yearly

By using formula for compound interest, we can write
$\text{Amount = P}\left[{(1+\frac{r}{100})}^n\right]$

$\text{Amount}=500\left[{(1+\frac{10}{100})}^3\right]$

$\text{Amount}=500\left[{\left(\frac{11}{10}\right)}^3\right]$

$\text{Amount}=₹665.50$

Compound interest $=A-P=₹665.50-₹500=₹165.50$