Discussion
The amount of a certain sum invested at simple interest for 3 years and \(6\frac{1}{2}\) years at the same rate of interest p.a. is ₹ 14808 and ₹ 18084, respectively. What is the rate of interest p.a.?
Answer: D
The rate of interest is 7.8 per cent per annum. With simple interest the amount grows by the same sum every year. From 3 years to 6 1/2 years is 3 1/2 years, and the amount rises by 18084 - 14808 = 3276, so the yearly interest is \[\frac{3276}{3.5} = 936\] The principal is the amount at 3 years minus 3 years of interest: 14808 - 2808 = 12000. Rate: \[\frac{936}{12000} \times 100 = 7.8\ \%\] Options such as 8.4 and 8.5 per cent do not give these amounts: 12000 at 8.4 per cent would give 12000 + 3024 = 15024 after 3 years.
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