Question : On a certain sum of money lent out at 16% p.a. the difference between the compound interest between 1 year, payable half-yearly and the simple interest for 1 year is Rs. 56. The sum is:
Option 1: Rs. 1080
Option 2: Rs. 7805
Option 3: Rs. 8750
Option 4: Rs. 5780
Correct Answer: Rs. 8750
Solution :
Let the Principal amount be $P$.
Difference between Compound Interest and Simple Interest for 2 terms = $\frac{PR^{2}}{100^{2}}$ where $R$ is the rate of interest per term and $P$ is principal.
Here $R$ for six months = $\frac{16}{2}$% = 8%
So, 56 = $P[\frac{8^2}{100^2}]$
⇒ $P$ = 8750
Hence, the correct answer is Rs. 8750.
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