Question : A sum becomes Rs. 1,352 in 2 years at 4% per annum compound interest. The sum is:
Option 1: Rs. 1,225
Option 2: Rs. 1,270
Option 3: Rs. 1,245
Option 4: Rs. 1,250
Correct Answer: Rs. 1,250
Solution :
Total amount = Principal + Compound interest = Rs. 1,352
Rate = 4%
Time = 2 years
Let $P$ be the principal.
We know, $\text{Total amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒ 1352 = P(1+\frac{4}{100})^{2}$
$⇒ 1352 = P(\frac{26}{25})^{2}$
$\therefore P = \frac{1352×25×25}{26×26}= 1250$
Hence, the correct answer is Rs. 1,250.
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