Question

Assume a 30-year fully amortizing mortgage, monthly pay in arrears of $250,000 at 5%. What is the amount of interest and the amount of principal, respectively, in the 36^th payment?

Answer 1

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

Monthly rate = Annual rate/ 12 months

                      = 5%/ 12 months

                      = 0.41666666666%

Hence, the monthly rate is 0.41666666666%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                   = {1 – (1 + 0.00416666666)-360}/ 0.41666666666%

             = 186.281617216

Hence, the present value annuity factor is 186.281617216.

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

Monthly payment = Loan value/ PVIFA

                            = $250,000/ 186.281617216

                            = $1342.0540563

Hence, the monthly loan payment is $1342.0540563.

Compute the interest and the principal amount in 36th payment, using MS-excel as shown below:

The result of the above excel table is as follows:

Hence, the interest and the principal amount in 36th payment is $994.61013 and $347.44393 respectively.