Question

Quincy Durant, who had his 75th birthday last month, has been offered a reverse mortgage by the Selleck National Bank. The terms of the reverse mortgage call for Mr. Durant to receive a fixed monthly income payment over his remaining 10-year life expectancy, with the monthly income payment being determined by setting the future value of the monthly payments to be received by Mr. Durant equal to 90 percent of the current $400,000 value of his home. At the end of 10 years Mr. Durant expects to sell his home and repay these monthly payments along with the accrued interest on his monthly borrowings over the previous 10 years. Assuming that that the interest rate on the reverse mortgage is 4.20 percent, compare the monthly amount that Mr. Durant will receive from the reverse mortgage with the monthly payment for a conventional 10-year mortgage loan in the amount of $360,000 with a monthly compounded interest rate of 4.20 percent.?

Answer 1

Compute the monthly rate of interest, using the equation as shown below:

Monthly rate = Annual rate of interest/ Number of period in a year

                      = 4.2%/ 12 months

                      = 0.35%

Hence, the monthly rate is 0.35%.

Compute the amount received under a reverse mortgage, using the equation as shown below:

Monthly receipts = Future value*PVIF_{0.35%, 120}/ PVIFA_{0.35%, 120}

                            = $400,000*90%*0.6575/ 97.8489

                            = $2,419.04

Hence, the monthly receipts under the reverse mortgage are $2,419.04.   

Compute the monthly payment of loan under the conventional loan, using the equation as shown below:

Monthly payment = Present value/ PVIFA_{0.35%, 120}

                             = $360,000/ 97.8489

                             = $3,679.14

Hence, the monthly payment of the loan is $3,679.14.

The monthly receipts of the loan under a reverse mortgage are $2,419.04 and the monthly loan payment under the conventional loan is $3,679.14.

Notes:

1.

The PVIF factor is calculated by using the below-mentioned formula:

PVIF factor = 1/ (1 + Rate of interest)^{Time period}

2.

The PVIFA factor is calculated by using the below-mentioned formula:

PVIFA factor = {1 - (1 + Interest rate)^{-Time period}}/ Rate of interest