Multiple choice

Amit invested a certain amount of money under schemes A and B in the ratio 2 : 1. Scheme A offers simple interest at an annual rate of 10% while scheme B offers compound interest at the rate of 20% per annum, compounded annually. After ๐‘› years, the total amount Amit received from scheme B was higher than the total amount he received from scheme A. Find the minimum value of ๐‘›.

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Amount A = 2x(1 + 0.1n). Amount B = x(1.2)^n. We need 1.2^n > 2 + 0.2n. For n=6: 1.2^6 = 2.98, 2 + 1.2 = 3.2 (False). For n=7: 1.2^7 = 3.58, 2 + 1.4 = 3.4 (True).

AI explanation

Let the investments in schemes A and B be 2x and x respectively. The amount received from scheme A after n years is 2x * (1 + 0.10n), and the amount from scheme B is x * (1 + 0.20)^n. We need x * (1 + 0.20)^n > 2x * (1 + 0.10n), which simplifies to (1.2)^n > 2 + 0.2n. Checking the values, for n = 6 we have 2.986 > 3.2 (false), and for n = 7 we have 3.583 > 3.4 (true). The minimum value of n satisfying this inequality is 7.

Keep practicing โ€” related questions