On a certain sum, the simple interest for 2 years is ₹4,500 and the compound interest for 2 years at the same rate is ₹4,770. What is the rate of interest?

💡 Solution & Explanation

Simple interest for one year = ₹4,500 ÷ 2 = ₹2,250. Compound interest is higher only because, in year 2, interest is also earned on year 1's interest: ₹4,770 − ₹4,500 = ₹270. That extra is the year-2 interest on ₹2,250, so the rate = 270 ÷ 2,250 × 100 = 12%. The principal is then ₹2,250 × 100 ÷ 12 = ₹18,750.