Discussion
A man gets a simple interest of ₹ 2,000 on a certain principal at the rate of 5% per annum in 4 years. What compound interest will he get on twice the principal in 2 years at the same rate ?
Answer: C
The compound interest is ₹ 2,050.
From the simple interest, \(2000 = P \times 0.05 \times 4\), so \(P = 10000\). Twice the principal is 20000, and compound interest for 2 years at 5% is:
\[ \begin{aligned} CI &= 20000\left[(1.05)^{2} - 1\right] \\ &= 20000 \times 0.1025 = 2050 \end{aligned} \]
Simple interest on 20000 for 2 years would be 2000; the extra 50 is the interest earned in the second year on the first year's interest of 1000. 2,250 would need a rate of about 5.5%.
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