math plz help me
posted by Anonymous on .
A couple purchasing a home budget $1700 per month for their loan payment. If they have $15,000 available for a down payment and are considering a 25year loan, how much can they spend on the home at each of the following rates? (Round your answers to the nearest cent.)
(a) 6.9% compounded monthly
$ 1
(b) 7.1% compounded monthly
$ 2

The $15,000 can be added at the end to the total purchase price, but does not affect the mortgage calculations.
The formula for the mortgage calculations is:
P(1+i)^n = R((1+i)^n1)/i
where
i=interest rate per period (month)
n=number of periods (months)
R=monthly payment
P=amount to borrow
(a) at 6.9% p.a.,
i=0.069/12=0.00575
n=12*25 years = 300 months
R=$1700 = monthly payment
Solve for P
P=R((1.00575)^3001)/(0.00575*(1.00575^300))
=$242714.03
Add the downpayment of $15000 to get
$257,714.03 for the total purchase price.
I'll leave (b) for your exercise.