Question

The difference between amount accumulated due to simple interest and compound interest on a sum for 2 years at $20\%$ per annum is ₹ 440. Calculate the amount to be paid if the interest rate is compounded quarterly.

• A. ₹ 14741
• B. ₹ 13458
• C. ₹ 12987
• D. ₹ 10872

Answer 1

Answer: (A)

Given
The principal amount is the same for both simple and compound interest at 20% for 2 years.
According to question,
$P+C.I.-(P+S.I).=440$
$\Rightarrow P{(1+\frac{20}{100})}^2-1-\frac{P\times 20\times 2}{100}=440$
$\Rightarrow P[{\left(\frac{6}{5}\right)}^2-1-\frac{2}{5}]=440$
$\Rightarrow P\times 0.04=440$
$\Rightarrow P=11000$
Now
Principal = ₹ 11000
Interest rate per annum (r) = 20%
Interest rate quartely =20%/4 = 5 %
Since the interest is compounded quarterly, so there will be 6 conversion periods in two years.
So, n = 6
By using formula for compound interest, we can write
$\text{Amount = P}\left[{(1+\frac{r}{100})}^n\right]$
$\text{Amount}=11000\left[{(1+\frac{5}{100})}^6\right]$
$\text{Amount}=₹14741$