Question

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 semiannually. To the nearest $100, how much did she borrow?

Answer 1

To find out how much Kerry borrowed, we can use the formula for the present value of an annuity. The present value of an annuity formula is Payment * [(1 - (1 + r)^(-n))/r], where Payment is the monthly payment, r is the interest rate compounded semiannually, and n is the number of payments. Substituting the given values and solving the equation will give us the amount Kerry borrowed, rounded to the nearest $100.

Step-by-step explanation:

To find out how much Kerry borrowed, we can use the formula for the present value of an annuity:

Present Value = Payment * [(1 - (1 + r)^(-n))/r]

Where:

• Payment = $855 (monthly payment)
• r = 7.7% (interest rate compounded semiannually)
• n = 4 * 12 = 48 (number of payments)

Substituting the values into the formula, we have:

Present Value = 855 * [(1 - (1 + 0.077/2)^(-48))/(0.077/2)]

Solving this equation will give us the amount Kerry borrowed, rounded to the nearest $100.