Question : The compound interest on Rs. 20,000 at 5% per annum, compounded annually, is Rs. 2,050. What is the time period?
Option 1: 2.5 years
Option 2: 2 years
Option 3: 4 years
Option 4: 3 years
Correct Answer: 2 years
Solution :
Let the time be $T$.
Principal = Rs. 20,000
We know, $\text{Compound interest}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}-\text{Principal}$
Given that the compound interest is Rs. 2,050.
⇒ $2050 = 20000 × (1 + 0.05)^T – 20000$
⇒ $20000 × (1.05)^T = 22050$
⇒ $(\frac{21}{20})^T=\frac{22050}{20000}$
⇒ $(\frac{21}{20})^T=\frac{441}{400}$
⇒ $(\frac{21}{20})^T=(\frac{21}{20})^2$
⇒ $T = 2$
Hence, the correct answer is 2 years.
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