Question

Your grandfather takes a reverse mortgage on his house for $100,000 at 8 percent for five years, annual annuity payments. What payment will he receive? How much interest does he pay on the loan? What is the balance owed if he decides to repay the loan at the end of year 2?

Answer 1

a). Annual Payment = [Mortgage Amount * r] / [1 - (1 + r)^-n]

= [$100,000 * 0.08] / [1 - (1 + 0.08)^-5]

= $8,000 / 0.3194 = $25,045.65

b). Total Amount Paid = Annual Payment * Total no. of Payments

= $25,045.65 * 5 = $125,228.23

Total Interest Paid = Total Amount Paid - Loan Amount = $125,228.23 - $100,000 = $25,228.23

c). Interest paid in 1st payment = Unpaid loan Balance * Interest Rate

= $100,000 * 0.08 = $8,000

Principal Repayment in 1st payment = Annual Payment - Interest paid in 1st payment

= $25,045.65 - $8,000 = $17,045.65

Loan Balance after 1st payment = Unpaid loan Balance - Principal Repayment in 1st payment

= $100,000 - $17,045.65 = $82,954.35

Interest paid in 2nd payment = Unpaid loan Balance * Interest Rate

= $82,954.35 * 0.08 = $6,636.35

Principal Repayment in 2nd payment = Annual Payment - Interest paid in 1st payment

= $25,045.65 - $6,636.35 = $18,409.30

Loan Balance after 2nd payment = Unpaid loan Balance - Principal Repayment in 1st payment

= $82,954.35 - $18,409.30 = $64,545.05