A borrower received a 30-year ARM mortgage loan for $120,000. Rate caps are 3/2/6 (first adjustment/subsequent adjustments/total over the life of the loan). The start rate was 3.50% and the loan adjusts every 12 months for the life of the mortgage. The index used for this mortgage is the LIBOR, which, for this exercise, let’s say was 3.00% at the start of the loan, 5.00% 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’s the initial rate (start rate) and what is the interest rate after the first year?
What is the fully indexed rate after the second year?
What is the borrower’s interest rate after the second adjustment?
What is the maximum interest rate this loan could have?
What would the LIBOR have to be to obtain that interest rate?
To determine the answers to the questions, we need to understand how adjustable-rate mortgages (ARMs) work and how they are calculated.
1. Initial Rate (Start Rate):
The initial rate, also known as the start rate, is the interest rate at the beginning of the loan term. In this case, the start rate is given as 3.50%.
Interest Rate after the First Year:
To calculate the interest rate after the first year, we need to consider the rate caps and the index and margin values.
- Rate Caps: The 30-year ARM has rate caps of 3/2/6. This means that after the first adjustment, the interest rate cannot increase or decrease by more than 3 percentage points.
- Index and Margin: The index used for this loan is the LIBOR, and the margin is 3.00%.
Given that the LIBOR was 3.00% at the start of the loan and 5.00% at the end of the first year, we can calculate the interest rate after the first year as follows:
Start Rate + Index + Margin = Interest Rate
3.50% + 5.00% + 3.00% = 11.50%
However, since the rate caps limit the adjustment to 3 percentage points, the interest rate after the first year will be capped at 6.50%.
Fully Indexed Rate after the Second Year:
The fully indexed rate after the second year considers the index and margin values at the end of the second year. Given that the LIBOR was 4.50% at the end of the second year, we can calculate the fully indexed rate as follows:
Start Rate + Index + Margin = Fully Indexed Rate
3.50% + 4.50% + 3.00% = 11.00%
Again, considering the rate caps, the fully indexed rate after the second year will be capped at 6.50%.
Borrower's Interest Rate after the Second Adjustment:
The borrower's interest rate after the second adjustment is determined by the fully indexed rate after the second year, subject to the rate caps. In this case, the rate would still be capped at 6.50%.
Maximum Interest Rate for this Loan:
The maximum interest rate that this loan could have is determined by the total rate cap over the life of the loan, which is 6%. This means that the interest rate cannot increase or decrease by more than 6 percentage points over the entire term of the loan.
LIBOR Rate Required to Obtain the Maximum Interest Rate:
To determine the LIBOR rate necessary to obtain the maximum interest rate, we subtract the margin and start rate from the maximum interest rate. In this case:
Maximum Interest Rate - Margin - Start Rate = Required LIBOR Rate
6.00% - 3.00% - 3.50% = -0.50%
This calculation shows that the LIBOR rate would need to be at -0.50% in order to achieve the maximum interest rate of 6.00%. However, it's important to note that negative LIBOR rates are highly uncommon in practice.
It's important to keep in mind that the calculations provided are based on the given information and assumptions about the rate caps, index values, margin, and loan terms. In practice, ARM mortgage loan terms may vary, and it's essential to consult with a lender or financial professional for accurate and specific information regarding an individual mortgage loan.