Question

Utopis Bedding Comforter Vretta Ashton Holmes-Ou Question 3 of 4 A mortgage for a condominium had a principal balance of $47,100 that had to be amortized over the remaining period of 7 years. The interest rate was fixed at 5.32% compounded semi-annually and payments were made monthly a. Calculate the size of the payments. Round up to the next whole number b. If the monthly payments were set at $822, by how much would the time period of the mortgage shorten? o year(s) 0 months c. If the monthly payments were set at $822, calculate the size of the final payment. S0.00 Round to the nearest cent Next Question

Answer 1

Answer a:

$672

Working:

Loan amount = $47,100

Interest rate (compounded semiannually) = 5.32%

Effective annual rate = (1 + 5.32%/ 2)^2 - 1 = 5.390756%

Monthly interest rate = (1 + 5.390756%) ^(1/12) -1 = 0.4384981207987%

Number of monthly payments = 7 * 12 = 84

Monthly payment = PMT(0.4384981207987%, 84, -47100, 0, 0) = $671.52

Answer (b):

[ 1 ]Year 5 months

Working:

If Monthly payment = $822

Number of months required = NPER (0.4384981207987%, 822, -47100, 0, 0) = 66.13309827 months or 67 months

Time period would shorten by = 84 - 67 = 17 months or 1 year and 5 months

Answer (c):

$109.61

Working:

Principal balance at the of 66th payment = PV (0.4384981207987%, (66.13309827 - 66), -822, 0, 0) = $109.1358

Final payment in 67th month = 109.1358 * (1 + 0.4384981207987%) = $109.61