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 calculate the interest rate at each adjustment period, we need to follow these steps:
1. Determine the initial adjusted rate:
- Start rate: 3.50%
- Initial adjustment cap: 3/100 (3%)
- Index rate: 3.00%
- Margin: 3.00%
The initial adjusted rate is calculated by summing the start rate, the index rate, and the margin:
Initial adjusted rate = Start rate + Index rate + Margin
= 3.50% + 3.00% + 3.00%
= 9.50%
However, the initial adjustment cap is 3%, so the rate can only increase by a maximum of 3% in the first adjustment period. Since the calculated initial adjusted rate is higher than this cap, we need to cap the rate at 6.50% (Initial adjusted rate + Initial adjustment cap).
Therefore, the initial adjusted rate is capped at 6.50%.
2. Determine the periodic interest rate cap:
- Periodic interest rate cap: 2/100 (2%)
The periodic interest rate cap defines the maximum increase or decrease in the interest rate at each adjustment period. In this case, the cap is 2%, which means the interest rate can only increase or decrease by a maximum of 2% relative to the previous adjusted rate.
3. Determine the lifetime interest rate cap:
- Lifetime interest rate cap: 6/100 (6%)
The lifetime interest rate cap defines the maximum increase or decrease in the interest rate over the life of the loan. In this case, the cap is 6%, which means the interest rate can only increase or decrease by a maximum of 6% relative to the initial adjusted rate.
Now that we have determined the caps, let's calculate the interest rate at each adjustment period using the given information:
Year 1:
- Index rate: 4.45%
- Periodic interest rate cap: 2%
Since the initial adjusted rate was capped at 6.50% and the index rate increased to 4.45%, the new adjusted rate for the next adjustment period will be calculated as follows:
New adjusted rate = Previous adjusted rate + (Index rate - Previous adjusted rate) * Periodic interest rate cap
New adjusted rate = 6.50% + (4.45% - 6.50%) * 2%
= 6.50% - 2.10%
= 4.40%
The new adjusted rate for year 1 is 4.40%.
Year 2:
- Index rate: 4.50%
- Periodic interest rate cap: 2%
Using the same formula as before, we calculate the new adjusted rate for the second adjustment period:
New adjusted rate = Previous adjusted rate + (Index rate - Previous adjusted rate) * Periodic interest rate cap
New adjusted rate = 4.40% + (4.50% - 4.40%) * 2%
= 4.40% + 0.10% * 2%
= 4.40% + 0.20%
= 4.60%
The new adjusted rate for year 2 is 4.60%.
So, the interest rate for the 30-year ARM mortgage loan in year 1 is 4.40%, and in year 2 it is 4.60%.