Adjustable Rate Mortgage (ARM) Calculator

What is an Adjustable Rate Mortgage (ARM) Calculator?

An Adjustable Rate Mortgage (ARM) Calculator is a financial tool that helps borrowers estimate their monthly payments on a mortgage with an interest rate that changes periodically. Unlike fixed-rate mortgages, ARMs have interest rates that adjust based on market conditions after an initial fixed-rate period.

Formula for ARM Calculation

The formula for calculating the monthly payment on an ARM is similar to that of a fixed-rate mortgage, but it needs to be applied twice: once for the initial rate period and again for the adjusted rate period.

1. For the initial fixed-rate period:

\[P = L \times \frac{r(1+r)^n}{(1+r)^n-1}\]

2. For the adjusted rate period, we first calculate the remaining balance:

\[B = L \times \frac{(1+r)^m - (1+r)^{m-n}}{(1+r)^n-1}\]

Then we use this balance to calculate the new payment:

\[P_{adjusted} = B \times \frac{r_{adjusted}(1+r_{adjusted})^{n_{remaining}}}{(1+r_{adjusted})^{n_{remaining}}-1}\]

Where:

• P = Monthly Payment
• L = Loan Amount
• r = Monthly Interest Rate (Annual Rate / 12)
• n = Total Number of Payments
• B = Remaining Balance
• m = Number of Payments Made
• r_adjusted = Adjusted Monthly Interest Rate
• n_remaining = Remaining Number of Payments

Calculation Steps

1. Calculate the initial monthly payment using the initial interest rate and total loan term.
2. Calculate the remaining balance at the end of the initial fixed-rate period.
3. Calculate the new adjusted interest rate (initial rate + adjustment, not exceeding the rate cap).
4. Calculate the new monthly payment using the remaining balance, adjusted rate, and remaining loan term.

Example

Let's consider a scenario with the following details:

• Loan Amount: $300,000
• Initial Interest Rate: 3.5% per year
• Loan Term: 30 years
• Adjustment Period: 5 years
• Rate Adjustment: 1% per adjustment
• Rate Cap: 8.5%

Calculation:

1. Initial monthly payment: $1,347.13
2. Remaining balance after 5 years: $273,035.84
3. Adjusted interest rate: 4.5% (3.5% + 1%, not exceeding 8.5% cap)
4. Adjusted monthly payment: $1,504.52

In this example, the borrower would pay $1,347.13 per month for the first 5 years, then the payment would adjust to $1,504.52 for the next adjustment period, assuming no further rate changes.

Note: It's important to understand that with an ARM, your payments can increase significantly over time if interest rates rise. Always consider your long-term financial situation and the potential for rate increases when choosing an ARM.