Question : At what rate percent per annum will a sum of INR 15, 625 amount to INR 21, 952 in three years, if the interest is compounded annually?
Option 1: 12%
Option 2: 8%
Option 3: 9%
Option 4: 10%
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Correct Answer: 12%
Solution :
Principal (P) = INR 15, 625
Time (T) = 3 years
Amount (A) = INR 21, 952
Amount = $P(1 + \frac{R}{100})^T$
Let the rate of interest per annum be $R$.
21952 = 15625$(1 + \frac{R}{100})^3$
⇒ $\frac{21952}{15625} = (1 + \frac{R}{100})^3$
⇒ $\sqrt[3]{(\frac{21952}{15625})} = 1 + \frac{R}{100}$
⇒ $\frac{28}{25} = 1 + \frac{R}{100}$
⇒ $\frac{28}{25} - 1 = \frac{R}{100}$
⇒ $R = (\frac{3}{25}) \times 100$
⇒ $R = 3 \times 4$
⇒ $R = 12\%$
$\therefore$ The rate percent per annum is 12%.
Hence, the correct answer is 12%.
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