math

A couple can afford to make a monthly mortgage payment of $850. If the mortgage rate is 2% and the couple intends to secure a 30-year mortgage, how much can they borrow? (Round your answer to the nearest cent.)

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  1. Use the mortgage payment formula:
    and assume 2% is per annum and compounded monthly,

    A=PR^n(R-1)/(R^n-1)
    where
    A=monthly payment ($850)
    n=number of months (=30)
    P=principal (amount borrowed)
    R=monthly interest rate + 1
    =(0.02/12+1)

    Solve for P
    P=A(R^n-1)/(R^n(R-1))
    It should be close to $230,000

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