The compound interest on a sum for two years is ₹1,560 and the corresponding simple interest is ₹1,500. Find the compound interest on the same sum at the same rate of interest for three years.
₹2,434.80
Yearly simple interest \(= \dfrac{1500}{2} = 750\).
Difference between two-year compound and simple interest \(= 1560 - 1500 = 60\). This equals one year's interest on the first-year interest of ₹750, so \(60 = \dfrac{750 \times R}{100}\), giving \(R = 8\%\).
Principal from SI: \(1500 = \dfrac{P \times 8 \times 2}{100}\), so \(P = 9{,}375\).
Three-year compound interest \(= P\left[(1 + R/100)^3 - 1\right] = 9375\left[(1.08)^3 - 1\right]\).
\((1.08)^3 = 1.259712\), so CI \(= 9375 \times 0.259712 = 2434.80\).
Hence, the compound interest for three years is ₹2,434.80.
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Important Questions from Simple and Compound Both
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The compound interest on a certain sum for 3 years at 8% per annum is Rs. 1,94,784. What is the simple interest on the $\frac{9}{10}$ part of the sum for the same time but at a rate of interest per annum which is $1\frac{1}{2}$ time the rate of interest per annum as applicable for compound interest?
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