Question

Calculate the compound interest on ₹ 2000 over a period of 1 year at 20% per annum if the interest rate is compounded half yearly.

• A. ₹ 420
• B. ₹ 400
• C. ₹ 100
• D. ₹ 300

Answer 1

The correct option is A ₹ 420

Given
Compound interest = ₹ 2000
Interest rate per annum (r) = 20%
Now, interest rate for half year = $\frac{20}{2}$ = 10 %

Since, the interest is compounded half yearly, so there will be two conversion periods in the year.

So, n = 2

By using formula for compound interest, we can write

$Amount=P\left[{(1+\frac{r}{100})}^n\right]$

$Amount=2000\left[{(1+\frac{10}{100})}^2\right]$

Amount $=₹2420$

Now,
Compound Interest = Amount - Principal
Compound Interest = ₹ 2420 - ₹ 2000
Compound Interest = ₹ 420