Posted by **Anonymous** on Monday, May 2, 2011 at 1:03pm.

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 25-year 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

- math plz help me -
**MathMate**, Monday, May 2, 2011 at 4:45pm
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)^n-1)/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)^300-1)/(0.00575*(1.00575^300))

=$242714.03

Add the down-payment of $15000 to get

$257,714.03 for the total purchase price.

I'll leave (b) for your exercise.

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