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 which for this exercise is 3% 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% which remains the same for the duration of the loan.
question; What is the initial rate the borrower will pay during the first year? \
question; What is the interest rate the borrower will pay after the first rate adjustment?
question; What is the fully indexed rate after the second year?
question: What is the maximum interest the borrower will pay during the 30 year term of the loan?
question; If the interest rate is at its maximum what would the LIBOR index to be reach to maximum interest rate?
3.00%
To calculate the answers to these questions, we'll follow the steps below:
1. Determine the initial rate the borrower will pay during the first year:
Start rate: 3.50%
Initial index rate: 3%
Margin: 3%
Initial rate = Start rate + Initial index rate + Margin
= 3.50% + 3% + 3%
= 9.50%
Therefore, the initial rate the borrower will pay during the first year is 9.50%.
2. Calculate the interest rate the borrower will pay after the first rate adjustment:
End of the first year index rate: 4.45%
New rate = Start rate + End of first year index rate + Margin
= 3.50% + 4.45% + 3%
= 11.95%
Therefore, the interest rate the borrower will pay after the first rate adjustment is 11.95%.
3. Determine the fully indexed rate after the second year:
End of the second year index rate: 4.50%
New rate = Previous rate + Index rate change + Margin
= 11.95% + (4.50% - 3%) + 3%
= 14.45%
Therefore, the fully indexed rate after the second year is 14.45%.
4. Calculate the maximum interest the borrower will pay during the 30-year term of the loan.
The loan has rate caps of 3/2/6, which means the interest rate can only increase by a maximum of 3% after the first year, 2% after subsequent adjustments, and 6% over the entire lifetime of the loan.
Starting from the initial rate:
Maximum rate = Initial rate + Rate cap for the first year = 9.50% + 3% = 12.50%
Therefore, the maximum interest the borrower will pay during the 30-year term of the loan is 12.50%.
5. Calculate the LIBOR index needed to reach the maximum interest rate:
Maximum rate = Start rate + LIBOR index + Margin
Rearranging the equation:
LIBOR index = Maximum rate - Start rate - Margin
= 12.50% - 3.50% - 3%
= 6%
Therefore, if the interest rate is at its maximum, the LIBOR index would need to be 6% to reach the maximum interest rate.
Please keep in mind that these calculations are based on the provided information and assumptions.
To answer these questions, let's break down the information provided step by step:
1. What is the initial rate the borrower will pay during the first year?
The initial rate is given as 3.50%. This is the rate the borrower will pay during the first year of the loan.
2. What is the interest rate the borrower will pay after the first rate adjustment?
The loan adjusts every 12 months. To calculate the interest rate after the first adjustment, we need to add the index value (LIBOR) to the margin.
- Start Rate + Index (LIBOR) + Margin = Interest Rate
- 3.50% + 3.00% + 3.00% = 9.50%
Therefore, the borrower will pay an interest rate of 9.50% after the first rate adjustment.
3. What is the fully indexed rate after the second year?
To calculate the fully indexed rate after the second year, we need to add the index value (LIBOR) to the margin.
- Start Rate + Index (LIBOR) + Margin = Interest Rate
- 3.50% + 4.50% + 3.00% = 11.00%
Therefore, the fully indexed rate after the second year is 11.00%.
4. What is the maximum interest the borrower will pay during the 30-year term of the loan?
The loan has rate caps of 3/2/6. This means that the interest rate cannot increase by more than 3% after the first adjustment, 2% after subsequent adjustments, and 6% over the life of the mortgage.
- Start Rate + Maximum Caps = Maximum Interest Rate
- 3.50% + 3% (first adjustment cap) = 6.50% (maximum interest rate after the first adjustment)
- 6.50% + 2% (subsequent adjustment cap) = 8.50% (maximum interest rate after the second adjustment)
- 8.50% + 6% (lifetime cap) = 14.50% (maximum interest rate over the 30-year term)
Therefore, the maximum interest the borrower will pay during the 30-year term of the loan is 14.50%.
5. If the interest rate is at its maximum, what would the LIBOR index need to reach the maximum interest rate?
To calculate the LIBOR index necessary to reach the maximum interest rate, we need to subtract the start rate and margin from the maximum interest rate.
- Maximum Interest Rate - Start Rate - Margin = LIBOR Index
- 14.50% - 3.50% - 3.00% = 8.00%
Therefore, the LIBOR index would need to be 8.00% in order to reach the maximum interest rate.