Posted by **MathHelp** on Tuesday, October 4, 2011 at 10:57pm.

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

- math -
**Steve**, Wednesday, October 5, 2011 at 5:06am
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.

## Answer this Question

## Related Questions

- SOMEBODY HELP ME WITH MATH!!!!!! - A person wishes to borrow $20,000 and has the...
- math - Cassandra is repaying an installment loan of $3,500 with 20 equal monthly...
- Business Math - Cassandra is repaying an installment loan of $3,500 with 20 ...
- Business Finance - Cassandra is repaying an installment loan of $3500 with 20 ...
- eco - Suppose a person pays $80 of annual interest on a loan that has a 5 ...
- math - Cassandra is repaying an installment loan of 3,500 with 20 equal payments...
- Maths - In order to make some home improvements, a home owner spent $40,000. He ...
- Math and Society - You can afford monthly payments of $1200. If current mortgage...
- math - I need help calculating (a) the total installment price. (b) the carrying...
- Finance - You have decided to buy a car that costs $34,100. The dealer offers ...