Question : A sum of Rs. 8,000 will amount to Rs. 8,820 in 2 years if the interest is calculated every year. The rate of compound interest is:
Option 1: 6%
Option 2: 7%
Option 3: 3%
Option 4: 5%
Correct Answer: 5%
Solution :
Sum = Rs. 8,000
Total amount = Rs. 8,820
Time = 2 years
Let $R$ be the rate.
We know, $\text{Total amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒ 8820 = 8000(1+\frac{R}{100})^{2}$
$⇒ \frac{441}{400} = (1+\frac{R}{100})^{2}$
Taking square root on both sides,
$⇒ \frac{21}{20}=1+\frac{R}{100}$
$\therefore R = 5\%$
Hence, the correct answer is 5%.
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