A borrower received a 30-year ARM mortgage loan for $200,000. Rate caps are 3/2/6 (initial
adjustment cap/periodic interest rate cap/lifetime interest rate cap). 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 3.00% 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.
where do i see the responses?
no
no
Can you show me the math in how this is calculated please?
To calculate the payments on this 30-year ARM mortgage loan, we need to follow these steps:
Step 1: Determine the interest rate for the initial adjustment period.
The initial adjustment cap for this loan is 3, which means the interest rate can increase or decrease by a maximum of 3% from the start rate.
The start rate is 3.50% and the index rate (LIBOR) is 3.00% at the start of the loan.
So, the interest rate for the initial adjustment period would be 3.50% + 3.00% = 6.50%.
Step 2: Calculate the monthly payment for the initial adjustment period.
To calculate the monthly payment, we can use the formula for a fixed interest rate mortgage payment: P = (P0 * r) / (1 - (1 + r)^(-n)).
Where:
P = Monthly Payment
P0 = Loan amount ($200,000 in this case)
r = Monthly interest rate (6.50% divided by 12)
n = Total number of payments (30 years = 30 x 12 = 360 payments)
Using these values, we can calculate the monthly payment.
Step 3: Determine the interest rate for the subsequent adjustment periods.
For the periodic interest rate cap of 2, the interest rate can increase or decrease by a maximum of 2% from the previous rate.
The interest rate at the end of the first year is 4.45%, which is within the 2% cap (6.50% + 2.00% = 8.50%).
So, the interest rate for the second year would be 4.45%.
Step 4: Calculate the monthly payment for the second year.
Using the interest rate of 4.45% and applying it to the remaining loan balance ($200,000), we can calculate the monthly payment using the same formula as in Step 2.
Step 5: Repeat Step 3 and Step 4 for subsequent years until the end of the 30-year term.
The interest rate at the end of the second year is 4.50%, which is also within the 2% cap (4.45% + 2.00% = 6.45%).
So, the interest rate for the third year would be 4.50%.
Repeat Step 4 for each subsequent year until reaching the end of the 30-year term, adjusting the interest rate according to the index rate and the interest rate cap.
By following these steps, you can calculate the monthly payments for each year of the 30-year ARM mortgage loan.