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.

Answer 1

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 = ₹ 11,000
Interest rate per annum (r) = 20%
Interest rate quartely = 20%/4 = 5%
Since the interest is compounded quarterly, so there will be 8 conversion periods in two years.
So, n = 8
By using formula for compound interest, we can write
$\text{Amount = P}\left[{(1+\frac{r}{100})}^n\right]$
$\text{Amount}=11,000\left[{(1+\frac{5}{100})}^8\right]$
$\text{Amount}=₹16,247$