Discussion

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?

Answer: C

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

Find the rate from the simple-interest statement first.

\[ \frac{R \times 6}{100} = 0.60 \quad\Longrightarrow\quad R = 10\% \]

Now compound Rs. 12,000 for three years at that rate:

\[ \text{CI} = 12000\left[(1.1)^{3} - 1\right] = 12000(1.331 - 1) \]

\[ = 12000 \times 0.331 = \text{Rs. } 3972 \]

Simple interest for the same three years would be Rs. 3600; the extra Rs. 372 is the compounding.

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