# math

posted by MathHelp

A person takes out a monthly installment loan of \$2000 with an annual percentage rate of 13.0% if the person can afford no more than \$70 per month, then which of the following terms are feasible? a) 8 months b ) 12 months c) 18 months d) 24 months e) 36 months

1. Steve

Massaging the formula for the monthly payment

M = Pr/(1-(1+r)^-n) gives

n = log(M/(M-Pr)) / log(1+r)

With r = .13/12 = 0.010833333
M = 70
P = 2000

M/(M-Pr) = 70/(70 - 2000 * 0.01083333) = 1.448

log 1.448/log 1.010803333 = 34.3, so the 36 month term looks good.

You can also ballpark this by estimating:

13%/year is about 1%/month. 1% of 2000 is 20.
So, the payments start out with \$20 interest, leaving \$50 going to principal.

2000/50 = 40, which is bigger than 36, but later payments include less interest, so the term would be less than 40. 36 is the best choice.

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