Question

Directions: Consider the following case and share your response to the following five questions with your instructor

Case: A borrower received a 30-year ARM mortgage loan for $200,000. Rate caps are 3/2/6. The start rate is 3.50% and the loan adjusts every 12 months for the life of the mortgage. The index used for this mortgage is LIBOR (for this exercise, 3.00% at the start of the loan, 4.45% at the end of the first year, and 4.50% at the end of the second year). The margin on the loan is 3.00%, which remains the same for the duration of the loan.

1. What is the initial rate (start rate) the borrower will pay during the first year?

2. What is the interest rate the borrower will pay after the first rate adjustment? (Hint: Remember to use the “stair step method” for determining the new interest rate.)

3. What is the fully indexed rate after the second year?

4. What is the maximum interest rate the borrower will pay during the 30-year term for this loan?

5. If the interest rate is at its maximum, what would the LIBOR index have to be to reach the maximum interest rate?

Answer 1

Initial start rate for the first year=3.50% (as given in the problem)

Interest rate the borrower will pay after the first rate adjustment= 6.5%

Being lower of the following two:

(a ): 3.50% (start rate) + 3% (Cap for the first year) = 6.5%

(b ): 4.45% (Index-LIBOR) + 3% (Margin) = 7.75%

Fully indexed rate after the second year = Index (LIBOR at the end of first year) + Margin

=4.50% + 3% = 7.50%

Maximum interest rate the borrower will pay during the 30-year term for this loan

= Start rate + Life time loan cap = 3.50% + 6% = 9.50%

Index (LIBOR) in the event of the loan reaching the maximum interest rate=

Maximum rate as above – Margin= 9.50%-3% = 6.50%