A woman has bought a house and makes mortgage payments of $400 every two-weeks for 25 years.If the mortgage interest rate is j₂ = 7%,what is the size of her original mortgage loan? (Answer to nearest dollar)

Question

Quizplus · Accepted Answer

The correct answer is A because the present value of the mortgage payments is equal to the original mortgage loan. The present value of the mortgage payments can be calculated using the formula:PV = PMT * [1 - (1 + r/n)^(-nt)] / (r/n)where:PV is the present value of the mortgage paymentsPMT is the mortgage payment amountr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, the mortgage payment amount is $400, the annual interest rate is 7%, the number of compounding periods per year is 26 (since there are 26 two-week periods in a year), and the number of years is 25. Plugging these values into the formula, we get:PV = $400 * [1 - (1 + 0.07/26)^(-26*25)] / (0.07/26)PV = $400 * [1 - (1.0026923)^(-650)] / 0.0026923PV = $400 * [1 - 0.284085] / 0.0026923PV = $400 * 0.715915 / 0.0026923PV = $123,927.02Therefore, the size of the original mortgage loan is $123,927.

A Woman Has Bought a House and Makes Mortgage Payments