Kerry's mortgage loan will require payments of $855 at the end of every month for four years and at that time her loan balance outstanding will be $78,591. The interest rate is 7.7% compounded semi-annually. How much did she borrow?

Question

Quizplus · Accepted Answer

The correct answer is A.The present value of the loan can be calculated using the formula:PV = PMT * [1 - (1 + r/n)^(-nt)] / (r/n)where:PV is the present value of the loanPMT is the monthly paymentr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:PMT = $855r = 7.7% = 0.077n = 2 (since the interest is compounded semi-annually)t = 4Plugging these values into the formula, we get:PV = $855 * [1 - (1 + 0.077/2)^(-2*4)] / (0.077/2)= $855 * [1 - (1.0385)^(-8)] / 0.0385= $855 * [1 - 0.8062] / 0.0385= $855 * 0.1938 / 0.0385= $93,400Therefore, Kerry borrowed $93,400.

Kerry's Mortgage Loan Will Require Payments of $855 at the End