Mr Johnson has a thirty year mortgage with end-of-month payments. It has a nominal quarterly interest rate of 4.4% for the first three years and nominal monthly interest rate of 5.7% for the remaining twenty-seven years. The repayment schedule shows level payments except for the final slightly reduced payment. The amount financed is $180,000. Find the amount of each of the first 359 payments. If Mr. Johnson sold the house just after his 36th payment for $200,000, how large a check did he receive?
The accurate way of doing it is to calculate the monthly payment amortized over 30 years @ 4.4% comp. quarterly and find the balance of the morrtgage after 36 months. If we did that, then the monthly payment will be:
=$899.67 and the balance will be=$170,704.35. The difference between this and $200,000=$29,295.65, is what Mr. Johnson would get.
However, I realize that you expect ONE even payment for the 30-year amortization of the mortgage, combining the two interest rates of 4.4% and 5.7%, which can be done. If we did that, the combined interest rate would be about 5.45%. If we use this rate, then the monthly payment will be
=$1,016.53 and the last payment will be =$1,018.40. Using this monthly payment, the balance of the $180,000 mortgage after 36 payments will be =$172,242.71. As a consequence Mr. Johnson will receive =$200,000 - $172,242.71=$27,757.29.
P.S. Under this last scheme, the last payment is $1.87 LARGER, and NOT smaller, than the other 359 payments, primarily due to rounding off of the monthly payment.
