Question

An ARM is made for $50,000 for 30 years with the following terms:

Initial interest rate = 1 percent                 Index = 1-year Treasuries

Payments reset each year                         Margin = 200 basis points

Interest rate cap = none                            Payment cap = none

Discount points = 1 point

Negative amortization is not allowed

Based on estimated forward rates, the 1-year Treasury yields to which the ARM is tied is forecasted as follows:

Beginning of year (BOY) 2 = one percent (1%); (BOY) 3 = two percent (2%); (BOY) 4 = 3.5%; (BOY) 5 = 5%

Compute the interest rate, monthly payments, and loan balances for each year for this unrestricted ARM, and the yield for the entire five-year period.

Answer 1

Discount Rate is 1%

Loan Amount is 50,000

The Upfront Payment is Discount Rate*Loan Amount = 1%*50,000 = 500

Total Principal is Loan Amount + Upfront Payment = 50,000 + 500 = 50,500

5-year yield for $52000 = ((1+1%)*(1+3%)*(1+4%)*(1+5.5%)*(1+7%))^{1/5} - 1 = 4.08%

Amount = 4.08% times $50500 = $2060.20

5-year yield for $50000 (Loan amount without fees) = 2060.20/50000 = 4.12%