Directions: Answer the questions independently of each other. Mr. Dutt has lent Rs.5000 at a rate of 8% p.a. under Simple Interest and Rs.4000 at a rate of 15% p.a. under Compound Interest (interest compunded annually). For how many years, will the amount accrued under S.I. be more than the amount accrued under C.I.?

The amount under simple interest is given by 5000 + (5000 * 8 * T) / 100 = 5000 + 400T, while the amount under compound interest is 4000 * (1.15)^T. We need to find when 5000 + 400T is greater than 4000 * (1.15)^T. Testing integer values, for T=3 the simple interest amount is 6200 and the compound interest amount is 4000 * 1.520875 = 6083.5, whereas for T=4 the simple interest amount is 6600 and the compound interest amount is 6996.01, so the simple interest amount is only greater for 3 years.

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