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.
What is the initial rate (start rate) the borrower will pay during the first year?
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.)
What is the fully indexed rate after the second year?
What is the maximum interest rate the borrower will pay during the 30-year term for this loan?
If the interest rate is at its maximum, what would the LIBOR index have to be to reach the maximum interest rate?
To calculate the rates and the maximum rate for the given ARM mortgage loan, we can follow these steps:
Step 1: Determine the initial rate (start rate) for the first year:
The initial rate is given as 3.50%.
Step 2: Determine the interest rate after the first year:
Since the loan adjusts every 12 months, we need to calculate the interest rate after the first adjustment.
Start Rate + Index = New Interest Rate
3.50% + 4.45% = 7.95%
However, the rate cap limits the increase to a maximum of 3%.
The new interest rate cannot exceed the sum of start rate and the first cap, which is 3.50% + 3% = 6.50%.
Therefore, the interest rate after the first adjustment will be 6.50%.
Step 3: Determine the fully indexed rate after the second year:
After the second year, the index is given as 4.50%.
Start Rate + Index = New Interest Rate
3.50% + 4.50% = 8.00%
However, the rate cap limits the increase to a maximum of 2%.
The new interest rate cannot exceed the sum of start rate and the second cap, which is 3.50% + 2% = 5.50%.
Therefore, the fully indexed rate after the second year will be 5.50%.
Step 4: Determine the maximum interest rate for the 30-year term:
The maximum interest rate is determined by the sum of the start rate and the final cap.
Start Rate + Final Cap = Maximum Interest Rate
3.50% + 6% = 9.50%
Therefore, the maximum interest rate the borrower will pay during the 30-year term is 9.50%.
Step 5: Determine the LIBOR index that would reach the maximum interest rate:
To find the LIBOR index needed to reach the maximum interest rate, subtract the start rate from the maximum interest rate and you get the required increase.
Maximum Interest Rate - Start Rate = Required Increase
9.50% - 3.50% = 6.00%
Then, add the required increase to the start index to find the LIBOR index needed.
Start Index + Required Increase = LIBOR Index
3.00% + 6.00% = 9.00%
Therefore, the LIBOR index would have to be at 9.00% to reach the maximum interest rate.
So, to summarize:
1. The initial rate (start rate) for the first year is 3.50%.
2. The interest rate after the first adjustment is 6.50%.
3. The fully indexed rate after the second year is 5.50%.
4. The maximum interest rate for the 30-year term is 9.50%.
5. If the interest rate is at its maximum, the LIBOR index would have to be 9.00%.
To calculate the answers to these questions, we need to understand ARM (Adjustable Rate Mortgage) and the rate caps. Let's break down the steps to find the answers:
Step 1: Determine the initial rate (start rate):
The start rate is given as 3.50%. This is the rate the borrower will pay during the first year.
Step 2: Determine the interest rate after the first rate adjustment:
To calculate this, we'll use the "stair step method." First, we need to check if the interest rate will hit the first rate cap, which is 3%. Since the LIBOR index at the end of the first year is 4.45% (given), it exceeds the 3% rate cap. Therefore, the interest rate will adjust to the sum of the start rate (3.50%) and the margin (3.00%), which equals 6.50%.
Step 3: Determine the fully indexed rate after the second year:
Again, we'll use the "stair step method." The LIBOR index at the end of the second year is given as 4.50%. Now, we need to check the second rate cap, which is 2%. Since 4.50% does not exceed 2%, the interest rate does not reach the second cap. Therefore, the interest rate will adjust to the sum of the LIBOR index (4.50%) and the margin (3.00%), resulting in a fully indexed rate of 7.50%.
Step 4: Determine the maximum interest rate for the 30-year term:
The rate caps for this mortgage are 3/2/6. The third rate cap is 6%. Since the interest rate does not exceed the third rate cap during the first two adjustments, it remains at 7.50% (the fully indexed rate after the second year) for the remaining term of the loan.
Step 5: Calculate the LIBOR index needed to reach the maximum interest rate:
To calculate this, we'll subtract the margin from the maximum interest rate. The maximum rate is 6% (third rate cap). Hence, the LIBOR index would need to be 3% (6% - 3%) to reach the maximum interest rate.
Therefore, the answers to the questions are as follows:
1. The initial rate (start rate) the borrower will pay during the first year is 3.50%.
2. The interest rate the borrower will pay after the first rate adjustment is 6.50%.
3. The fully indexed rate after the second year is 7.50%.
4. The maximum interest rate the borrower will pay during the 30-year term is 7.50%.
5. If the interest rate is at its maximum, the LIBOR index would have to be 3% to reach the maximum interest rate.