Question

A partially amortizing FRM loan with the following terms is being made: Fixed rate with 3 discount point charges, constant payments, 12% interest rate for 20 years, $100,000 mortgage amount with a balloon payment of $50,000 scheduled at the end of year 20. The borrower will prepay at the end of year 5 with one percent of prepayment penalty. What is the effective rate of interest. Show calculations using a financial calculator (i.e. I=, N=, PMT=, etc.) Hint: Answer should be 12.97%

Answer 1

Pmt with balloon payment = [ loan amount × ( 1 + rate ) ^ no of payment - balloon payment ] / [ { ( 1 + rate ) ^ no of payment - 1} / rate]

= [ $100,000 × ( 1 + 0.01) ^ 240 - $ 50,000] / [{(1 + 0.01) ^ 240 - 1} / 0.01]

= [ $ 100,000 × 10.89 - $ 50,000] / [ ( 10.89 - 1) 0.01]

= $ 1,039,000 / 989

= $ 1,050. 56

total amount paid in 5 years = 60 × $ 1,050.56 = $63,003.60

outstanding amount after 60 payments as per amortization schedule = $ 95,790

Prepayment Penalty paid = $95,790 × 0.01 = $ 957.90

Total amount paid other than principal = $ 63,003.60 + $95,790 + $ 957.90 - $ 100,000

= $ 59,751.50

as per above formula effective rate of interest would be = 11.97 %