Compound Interest Problem

GRE Quant Problem Solving
1

Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?

A. 333
B. 383
C. 402
D. 433
E. 483

Have you ever had that moment in an exam when you think you’ve solved a question correctly but the answer choices are nowhere close to your answer? I felt exactly like that on this problem.

I calculated the final amount that Louie has to pay as : 1331$ (1100$ in the first year, 1210$ in the second year and finally 1331$ in the 3rd year). Since she has the pay it in 3 equal amounts, 1331/3 = 443.6 $ and no answer choice is quite close to that except for (D) (which is the wrong answer).

2

I think the she pays interest for 2 months , as she is going to repay it in third month.
so 10001.11.1=1210/3======403.3

1 Like
3

Lets take your answer and work it backwards :

Given : Initial amount = $1000 and we had an interest of 10% per month compound monthly in ,3 equal monthly payments.

Month One : 1100 -433 =657
Month Two : 657 x 11/10 =723 -443 = 280 (rounding this :722.7 to 723)
Month Three : 308 -443 = -ve (Error) [280 x 1.1 = 308]

Taking choice C:
Month One : 1100 -402 =698
Month Two : 698 x 11/10 =768 -402 = 366 (rounding this :767.8 to 768)
Month Three : 366 x 11/10 -402 = 402-402 = 0 —> Ans (You may get .someting left if you took estimations)

4

Ohh this makes sense!! Thank you so much :slight_smile:

5

Yeah that is the correct way to do it