Question : A sum of Rs. 3200, invested at 10% p.a. compounded quarterly, amounts to Rs. 3362. Compute the time.
Option 1: $\frac{1}{2}$ year
Option 2: $1$ year
Option 3: $2$ years
Option 4: $\frac{3}{4}$ year
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Correct Answer: $\frac{1}{2}$ year
Solution :
Given:
Principal = Rs. 3200
Amount = Rs. 3362
Rate = 10% per annum = $\frac{10}{4}=\frac{5}{2}$ per quarter
$\text{Compound interest + Principal}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
⇒ $3362 = 3200×(1+\frac{5}{2×100})^n$
⇒ $\frac{3362}{3200}=(\frac{41}{40})^n$
⇒ $\frac{1681}{1600}=(\frac{41}{40})^n$
∴ $(\frac{41}{40})^2=(\frac{41}{40})^n$
Comparing the powers, $n = 2$ quarters or $\frac{1}{2}$ year.
Hence, the correct answer is $\frac{1}{2}$ year.
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