Question : The compound interest received on INR 18,000 for 2 years is INR 7,920 when the interest is compounded annually. What is the rate of interest per annum?
Option 1: 15%
Option 2: 12.5%
Option 3: 20%
Option 4: 25%
Correct Answer: 20%
Solution :
Given: Compound interest = INR 7920
Principal = INR 18,000
Time = 2 years
Compound interest $= \text{Principal}×((1+\frac{\text{Rate}}{100})^{\text{Time}}-1)$
⇒ $7920=18000×((1+\frac{\text{Rate}}{100})^{2}-1)$
⇒ $\frac{7920}{18000}=((1+\frac{\text{Rate}}{100})^{2}-1)$
⇒ $\frac{11}{25}+1=(1+\frac{\text{Rate}}{100})^{2}$
⇒ $\frac{36}{25}=(1+\frac{\text{Rate}}{100})^{2}$
⇒ $\frac{6}{5}=1+\frac{\text{Rate}}{100}$
⇒ $\frac{6}{5}-1=\frac{\text{Rate}}{100}$
⇒ $\frac{1}{5}=\frac{\text{Rate}}{100}$
$\therefore$ Rate $= 20$%
Hence, the correct answer is 20%.
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