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
To calculate the ARM (Adjustable Rate Mortgage) payment, we need to consider the rate caps, index rate, margin rate, and loan amount.
1. First, let's determine the maximum interest rate for the loan. The rate caps provided are 3/2/6. The first number represents the initial cap, which means the first rate adjustment after the initial fixed-rate period cannot exceed 3% higher than the start rate. The second number represents the periodic cap, which means each subsequent adjustment cannot exceed 2% higher than the previous rate. The third number represents the lifetime cap, which means the rate cannot exceed 6% higher than the start rate at any point during the life of the mortgage.
For this scenario, the start rate is 3.50%. Therefore, the maximum rate for the first adjustment would be 3.50% + 3% = 6.50%. The subsequent adjustment caps would be calculated based on this maximum rate.
2. Next, we need to determine the index rate. The index used for this mortgage is LIBOR. For the first year, the index rate is given as 3.00%, at the end of the first year it is 4.45%, and at the end of the second year it is 4.50%.
3. Now let's calculate the adjusted interest rate for each year. To calculate the adjusted rate, we add the margin rate to the index rate. The margin rate is 3.00% in this case, which remains constant throughout the loan term.
- At the start of the loan: Adjusted rate = Index rate (3.00%) + Margin rate (3.00%) = 6.00%.
- At the end of the first year: Adjusted rate = Index rate (4.45%) + Margin rate (3.00%) = 7.45%.
- At the end of the second year: Adjusted rate = Index rate (4.50%) + Margin rate (3.00%) = 7.50%.
4. Now let's calculate the monthly payment amount using the adjusted interest rate, loan amount, and loan term. The loan term is 30 years, which means there are 360 monthly payments.
To calculate the monthly payment, we can use the loan amortization formula:
Monthly Payment = (Loan Amount x Adjusted Rate / 12) / (1 - (1 + Adjusted Rate / 12) ^ -n)
Where:
- Loan Amount = $200,000
- Adjusted Rate (Year 1) = 6.00% / 100 = 0.06
- Adjusted Rate (Year 2) = 7.45% / 100 = 0.0745
- Adjusted Rate (Year 3) = 7.50% / 100 = 0.075
- n = 360 months
Using the formula, we can calculate the monthly payments for each year separately.
5. For the first year payment:
Monthly Payment (Year 1) = ($200,000 x 0.06 / 12) / (1 - (1 + 0.06 / 12) ^ -360) = $1,199.10
6. For the second year payment:
Monthly Payment (Year 2) = ($200,000 x 0.0745 / 12) / (1 - (1 + 0.0745 / 12) ^ -360) = $1,330.60
7. For the third year payment:
Monthly Payment (Year 3) = ($200,000 x 0.075 / 12) / (1 - (1 + 0.075 / 12) ^ -360) = $1,334.60
Please note that these calculations assume the loan is fully amortizing over the 30-year term. However, ARMs typically have different amortization schedules and might have additional features like negative amortization or interest-only periods. Always consult the specific terms and conditions of your loan for an accurate payment calculation.