Question

A $20,000 mortgage is being repaid with 20 annual installments at the end of each year. The borrower makes five payments and then temporarily unable to make payments for the next two years. Find the expression of the revised payment to start at the end of the 8th year If the loan is still to be repaid at the end of the original 20 years.

Answer 1

To calculate the revised annual installment payment of a $20,000 mortgage after five payments with a two-year pause, one needs to calculate the remaining balance after 5 years, adjust it for two years of interest, and then find the present value of this adjusted balance over the remaining 12 years to pay off the original term.

Step-by-step explanation:

To determine the revised payment schedule for a mortgage, we need to use the concept of the present value of an annuity. The loan in question is a $20,000 mortgage with 20 annual installments. Five payments have been made, and we need to find the new annual payment starting at the end of the 8th year to pay off the remaining balance by the end of the original 20 years.

We first need to calculate the balance after the 5th payment using the present value of the remaining 15 payments at the given interest rate. Then, considering the two-year payment pause, we adjust this balance forward by two years to account for the interest accrued during this period.

Lastly, to find the revised payment, we calculate the present value of the adjusted balance over the remaining years (12 years starting from year 8 to year 20), again using the formula for the present value of an ordinary annuity. The new revised payment will be equal to this amount divided by 12.