math
posted by MathHelp on .
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

Massaging the formula for the monthly payment
M = Pr/(1(1+r)^n) gives
n = log(M/(MPr)) / log(1+r)
With r = .13/12 = 0.010833333
M = 70
P = 2000
M/(MPr) = 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.