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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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