Question : What sum will give Rs. 244 as the difference between simple interest and compound interest at 10% in $1\frac{1}{2}$ years compounded half-yearly?
Option 1: Rs. 40,000
Option 2: Rs. 36,000
Option 3: Rs. 32,000
Option 4: Rs. 28,000
Correct Answer: Rs. 32,000
Solution :
As interest is compounded, half-yearly
T = $\frac{3}{2}$×2 = 3 half-yearly
R = $\frac{10}{2}$ = 5% half-yearly
By applying the formula:
Difference = Principal$(\frac{R}{100})^2(3+\frac{R}{100})$, where $R$ is the rate of interest per six months compounded half-yearly.
Putting the value, we get:
244 = Principal$[(\frac{5}{100})^2(3+ \frac{5}{100})]$
⇒ 244 = Principal$(\frac{1}{400})(\frac{61}{20})$
⇒ Principal = $\frac{244×8000}{61}$ = 32000
Hence, the correct answer is Rs. 32,000.
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