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
To determine the interest rate for an Adjustable Rate Mortgage (ARM) at any given time, you would need to calculate the total interest rate by adding the index rate and the margin rate.
In this case, the index used is LIBOR, and the margin rate is 3.00%. The index rate for the first year is 3.00% and for the second year is 4.50%. Let's calculate the interest rate over the course of the mortgage.
1. Start rate: The start rate is given as 3.50%. This rate will remain fixed for the initial period, which in this case is 1 year.
2. First adjustment: At the end of the first year, the loan will adjust based on the index rate and the margin rate. The index rate is 4.45% and the margin rate is 3.00%. So the interest rate for the second year will be 4.45% + 3.00% = 7.45%.
3. Subsequent adjustments: For the subsequent years, the interest rate will be subject to adjustment every 12 months. At the end of the second year, the index rate is 4.50% and the margin rate remains at 3.00%. Therefore, the interest rate for the third year will be 4.50% + 3.00% = 7.50%.
It's important to note that the rate caps limit how much the interest rate can change at each adjustment and over the life of the loan. The rate caps in this example are 3/2/6. This means:
- Initial Adjustment Cap: The interest rate cannot increase or decrease by more than 3% during the first adjustment at the end of the initial period (1 year).
- Periodic Interest Rate Cap: The interest rate cannot increase or decrease by more than 2% at each subsequent adjustment.
- Lifetime Interest Rate Cap: The interest rate cannot increase or decrease by more than 6% over the life of the loan.
These rate caps ensure that the interest rate adjustments are gradual and within certain limits to protect borrowers from sudden and significant changes in their mortgage payments.
To calculate the initial adjustment, periodic interest rate cap, and lifetime interest rate cap, you'll need to understand how the adjustment works.
Here's a breakdown of the given information:
Loan amount: $200,000
Start rate: 3.50%
Rate caps: 3/2/6 (initial adjustment cap/periodic interest rate cap/lifetime interest rate cap)
Adjustment period: 12 months
Index (LIBOR) rates:
- Start of the loan: 3.00%
- End of the first year: 4.45%
- End of the second year: 4.50%
Margin: 3.00%
Now let's calculate the adjustments step-by-step:
1. Determine the initial adjustment:
To calculate the initial adjustment, subtract the index rate at the start of the loan from the current start rate.
Initial adjustment = Start rate - Start index rate
Initial adjustment = 3.50% - 3.00%
Initial adjustment = 0.50%
2. Calculate the indexed rate at the end of the first year:
Indexed rate = Start index rate + Margin
Indexed rate (end of first year index) = 3.00% + 3.00%
Indexed rate (end of first year index) = 6.00%
3. Apply the initial adjustment cap:
Compare the initial adjustment with the initial adjustment cap (3/100).
If the initial adjustment exceeds the cap, then use the cap value instead.
Initial adjustment cap = Start rate × (initial adjustment cap/100)
Initial adjustment cap = 3.50% × (3/100)
Initial adjustment cap = 0.105 (rounded to 3 decimal places)
Since the initial adjustment (0.50%) is less than the cap (0.105), the initial adjustment remains unchanged.
4. Calculate the adjusted rate at the end of the first year:
Adjusted rate (end of first year) = Start rate + Initial adjustment
Adjusted rate (end of first year) = 3.50% + 0.50%
Adjusted rate (end of first year) = 4.00%
5. Calculate the periodic interest rate cap:
Periodic interest rate cap = Adjusted rate × (periodic interest rate cap/100)
Periodic interest rate cap = 4.00% × (2/100)
Periodic interest rate cap = 0.08 (rounded to 2 decimal places)
6. Apply the periodic interest rate cap to the indexed rate at the end of the first year:
If the adjusted rate (4.00%) plus the periodic interest rate cap (0.08) exceeds the indexed rate (6.00%), then the adjusted rate is limited to the indexed rate.
Adjusted rate (end of first year cap) = min(Indexed rate (end of first year), Adjusted rate (end of first year) + Periodic interest rate cap)
Adjusted rate (end of first year cap) = min(6.00%, 4.00% + 0.08)
Adjusted rate (end of first year cap) = min(6.00%, 4.08%)
Adjusted rate (end of first year cap) = 4.08%
7. Calculate the indexed rate at the end of the second year:
Indexed rate (end of second year) = Indexed rate (end of first year) + Margin
Indexed rate (end of second year) = 6.00% + 3.00%
Indexed rate (end of second year) = 9.00%
8. Apply the lifetime interest rate cap:
Compare the adjusted rate (end of first year cap) with the lifetime interest rate cap (6/100).
If the adjusted rate exceeds the cap, then use the cap value instead.
Adjusted rate (end of first year cap) cap = min(Adjusted rate (end of first year cap), Start rate + (lifetime interest rate cap/100))
Adjusted rate (end of first year cap) cap = min(4.08%, 3.50% + (6/100))
Adjusted rate (end of first year cap) cap = min(4.08%, 3.86%)
Adjusted rate (end of first year cap) cap = 3.86%
So, the final adjusted rate at the end of the first year is 3.86%.
Note: This calculation only covers the initial adjustment and the first two years. Further adjustments will depend on the future LIBOR rates and the specific terms of the ARM mortgage.