Discussion

What compound interest will Rs. 5000 fetch in 3 years 10 months at 30% per annum?

Answer: D

\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]

For a period of whole years plus a part year, compound over the whole years and then apply simple interest for the remainder.

\[ A = 5000 \times (1.30)^{3} \times \left(1 + 0.30 \times \tfrac{10}{12}\right) \]

\[ (1.30)^{3} = 2.197 \quad\Longrightarrow\quad 5000 \times 2.197 = 10{,}985 \]

\[ 10985 \times 1.25 = 13{,}731.25 \]

\[ \text{CI} = 13731.25 - 5000 = \text{Rs. } 8731.25 \]

The ten months contribute \( 0.30 \times \tfrac{10}{12} = 0.25 \), so the final factor is 1.25 - a quarter, not a full year's 30%.

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