Discussion
Raju invested Rs. 77500 in ICICI bank. In two years how much compound interest will he get, if the first year rate of interest was 10% and second year had 2% more than first year?
Answer: B
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
The rates differ by year, so multiply the two growth factors rather than raising one to a power. The second year's rate is \( 10 + 2 = 12\% \).
\[ A = 77500 \times 1.10 \times 1.12 \]
\[ = 77500 \times 1.232 = 95{,}480 \]
\[ \text{CI} = 95480 - 77500 = \text{Rs. } 17{,}980 \]
Averaging the rates to 11% and squaring would give Rs. 17,975.98 - close, but not the same, because compounding is not linear in the rate.
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