Question : At what rate of compound interest (compounding annually) per annum will a sum of Rs. 1,000 become Rs. 1,060.90 in 2 years?
Option 1: 2% per annum
Option 2: 4% per annum
Option 3: 3% per annum
Option 4: 5% per annum
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Correct Answer: 3% per annum
Solution :
Given: Total amount = Rs. 1,060.90, Principal = Rs. 1,000, Time = 2 years
Let the rate be $r$.
We know, $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒1060.90 = 1000 \left(1 + \frac{r}{100}\right)^2$
$⇒(\frac{100+r}{100})^2=\frac{10609}{10000}$
$⇒(\frac{100+r}{100})^2=(\frac{103}{100})^2$
$⇒\frac{100+r}{100}=\frac{103}{100}$
$⇒100+r=103$
$⇒r = 3\%$
Hence, the correct answer is 3% per annum.
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