SOLUTION: the following formula gives the monthly cost <i>M</i> of a mortgage if the principle (the amount borrowed) is <i>p</i> dollars, which is to be totally repaid in <i>n</i> months

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: the following formula gives the monthly cost <i>M</i> of a mortgage if the principle (the amount borrowed) is <i>p</i> dollars, which is to be totally repaid in <i>n</i> months      Log On


   

Question 115180: the following formula gives the monthly cost M of a mortgage
if the principle (the amount borrowed) is p dollars,
which is to be totally repaid in n months,
and the monthly interest rate (as a decimal) is r.
M=%28rp%29%2F%281-%281-r%29%5E%28-n%29%29
simplify the formula
and find the monthly cost of a mortgage with a principal of $120,000 and a monthly rate of 0.8%, to be totally repaid in 25 years.
do i just plug in the numbers?
i can do that, but i just dont know how to simplify this equation.. please help
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Yes, you just plug in the numbers, just remember that you need n MONTHS, so you need n=25%2A12=300, and 0.8% expressed as a decimal is .008.

The only thing wrong with what you are trying to do is that you have -n as an exponent and it should be +n.

M=%28rp%29%2F%281-%281-r%29%5E%28n%29%29
M=%28.008%2A120000%29%2F%281-%281-.008%29%5E%28300%29%29
M=960%2F%281-.992%5E300%29
M=960%2F%281-0.0898466%29
M=1054.77

By the way, that is a HORRIBLE interest rate - .008 * 12 = .096 => 9.6% Shop around, you should be able to get something in the neighborhood of 6%, or 0.5% per month. Do the arithmetic and see what the difference in the payment would be in that case.