# math plz help me

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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 -

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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