Question

A few years ago, you got married and bought a house with an adjustable rate mortgage with the following terms: Loan: $240,000 Term: 20 years Initial Rate: 4% Margin: 2% over the Index Rate Lifetime Max: 4.5% The index rate was 2% in year 1, 1.5% in year 2, 4% in year 3, 1% in year 4, and 1% in year 5. a) What is your loan balance at year 5? (5pts) b) What is the effective interest rate is paid off after year 5 (10 pts)?

Answer 1

Given,

Initial rate= 4%

Margin =2%. Reset frequency= yearly

Interest cap : Life time 4.5%

Index for Year 2= 1.5%. Therefore,

Interest rate for year 2= Minimum of (1.5%+2% = 3.5%, Initial rate of 4%+ Lifetime cap of 4.5%= 8.5%)= 3.5%

Index for Year 3= 4%. Therefore,

Interest rate for year 3= Minimum of (4%+2% = 6%, Initial rate of 4%+ Lifetime cap of 4.5%= 8.5%)= 6%

Index for Year 4= 1%. Therefore,

Interest rate for year 4= Minimum of (1%+2% = 3%, Initial rare of 4%+ Lifetime cap of 4.5%= 8.5%)= 3%

Index for Year 5= 1%. Therefore,

Interest rate for year 5= Minimum of (1%+2% = 3%, Initial rate of 4%+ Lifetime cap of 4.5%= 8.5%)= 3%

Answers:

Loan balance at year 5= $196,043.15

Amount to pay off in 5 years= Loan balance + last month payment

= $196,043.15 + $1,353.84 = $197,396.99

Effective cost of borrowing if paid off after 5 years= 3.938%

Calculations as below: