Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 9% interest compounded monthly.What is the size of the mortgage with these terms?

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Quizplus · Accepted Answer

To find the size of the mortgage, we use the formula for the monthly payment (PMT) for a fixed-rate mortgage, which is derived from the formula for the present value of an annuity: PMT = [P * r(1 + r)^n] / [(1 + r)^n - 1], where P is the principal amount (size of the mortgage), r is the monthly interest rate (annual rate / 12), and n is the total number of payments (years * 12). Rearranging the formula to solve for P gives us P = PMT * [(1 + r)^n - 1] / [r(1 + r)^n]. Plugging in the given values (PMT = $1,200, r = 9% / 12 = 0.0075, n = 30 * 12 = 360), we find the size of the mortgage. Calculating with these values gives us a principal amount close to $149,138.24.

Your Real Estate Agent Mentions That Homes in Your Price