# 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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