Ben recently paid off his school loans and is looking to buy a home.He has qualified for an APR of 5.2% and plans on making payments for the next 15 years.He anticipates he can afford a monthly payment of $660.00.How much of a mortgage can Ben afford?

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Quizplus · Accepted Answer

To determine how much of a mortgage Ben can afford, we use the formula for calculating the present value of an annuity, which is what a mortgage essentially is. The formula is: $P = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where $P$ is the present value (or the amount of the mortgage), $PMT$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments.Given:- APR (annual percentage rate) = 5.2% or 0.052 as a decimal.- Monthly interest rate $r = \frac{0.052}{12}$.- Monthly payment $PMT = $660$.- Total number of payments over 15 years $n = 15 \times 12$.Plugging these values into the formula:$P = 660 \times \left(\frac{1 - (1 + \frac{0.052}{12})^{-15 \times 12}}{\frac{0.052}{12}}\right)$Calculating this gives a value around $82,371, which means Ben can afford a mortgage close to this amount.

Ben Recently Paid Off His School Loans and Is Looking