Multiple choice

Mr. X wants to take a loan of 10 lakh to buy his dream car. He approaches two financers, F1 and F2, for the loan. Both financers agree to give the loan but at different terms. F1 charges interest at 20% per annum, compounded annually, while F2 charges simple interest at 25% per annum. If Mr. X wants to repay the loan in a single payment at the end of n years, find the maximum value of n for which F1 is a better preference for Mr. X when compared to F2.

  1. 3

  2. 4

  3. 2

  4. 5

  5. d
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

F1 amount: 10(1+0.2)^n = 10(1.2)^n. F2 amount: 10(1+0.25*n). We need 1.2^n < 1+0.25n. For n=1, 1.2 < 1.25 (True). For n=2, 1.44 < 1.5 (True). For n=3, 1.728 < 1.75 (True). For n=4, 2.0736 > 2.0 (False). Thus, max n is 3.

AI explanation

F1 is better when its total repayment is lower, meaning 1000000 * (1.2)^n is less than 1000000 * (1 + 0.25n). Testing the options, for n=3, compound interest gives a factor of 1.728 while simple interest gives 1.75, making F1 better. For n=4, compound interest gives a factor of 2.0736 while simple interest gives 2, meaning F2 becomes better, so the maximum value for n is 3.

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