Suppose you have taken out a $325,000 fully-amortizing fixed rate mortgage loan that has a term of 30 years and an interest rate of 5.5%. In month 10 of the mortgage, how much of the monthly mortgage payment does the interest portion consist of?
A) $370.68
B) $1,474.64
C) $1,489.58
D) $1,845.31

Question

Quizplus · Accepted Answer

To calculate the interest portion of the 10th month's payment, you first need to know the monthly mortgage payment amount. Using the formula for a fixed-rate mortgage payment, which is P = [rPv / (1 - (1 + r)^-n)], where P is the monthly payment, Pv is the present value of the loan (or loan amount), r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (loan term in years multiplied by 12). For this loan, r = 5.5%/12 = 0.0045833, n = 30*12 = 360, and Pv = $325,000. Plugging these values into the formula gives the monthly payment. Once the monthly payment is known, the interest for the 10th month is calculated by multiplying the remaining balance after 9 payments by the monthly interest rate. The initial calculation shows that the monthly payment (not directly calculated here but can be derived using the formula) remains constant, and the interest portion decreases over time as the principal is paid down. The correct interest portion for the 10th month closely aligns with choice B, considering the declining balance method used in amortizing loans, where earlier payments consist more of interest and less of principal.

Suppose You Have Taken Out a $325,000 Fully-Amortizing Fixed Rate