Question : The difference between compound interest and simple interest on Rs. X at 7.5% per annum for 2 years is Rs. 22.50. Find the value of X.
Option 1: Rs. 4000
Option 2: Rs. 5000
Option 3: Rs. 2000
Option 4: Rs. 1900
Correct Answer: Rs. 4000
Solution :
Given: Principal = Rs. X
Rate = 7.5%
Time = 2 years
The difference between compound interest and simple interest, D = Rs.22.50
We know that,
$D=P(\frac{r}{100})^2$
⇒ $22.50=X(\frac{7.5}{100})^2$
⇒ $22.50=X(\frac{3}{40})^2$
⇒ $22.50=X\times\frac{3}{40}\times\frac{3}{40}$
⇒ $X=1600\times2.5$
⇒ $X=4000$
Hence, the correct answer is Rs. 4000.
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