Last updated: 2026-05-25

Definition and structure

An adjustable-rate mortgage (ARM) is a home loan where the interest rate stays fixed for an initial period — typically 3, 5, 7, or 10 years — and then resets annually based on a market index. The loan name encodes this structure: a 5/1 ARM is fixed for 5 years, then adjusts every 1 year thereafter. The appeal is a lower intro rate than the prevailing 30-year fixed; the risk is that the post-adjustment rate is unknown at origination.

How the math works

Initial monthly payment

During the fixed period, the ARM behaves identically to a fixed-rate loan. The monthly principal-and-interest payment uses the standard PMT formula:

\text{P\&I}_0 = L \cdot \frac{(r_0/12)(1 + r_0/12)^n}{(1 + r_0/12)^n - 1}

where L is the loan amount, r₀ the initial annual rate (e.g. 0.055 for 5.5%), and n the total months (term × 12). On a $400,000 loan at 5.5% for 30 years, this is approximately $2,271/month.

Balance at adjustment

At the end of the fixed period (month _t_f × 12), the remaining principal is:

B_{\text{adj}} = L \cdot (1 + r_0/12)^{t_f \cdot 12} - \text{P\&I}_0 \cdot \frac{(1 + r_0/12)^{t_f \cdot 12} - 1}{r_0/12}

Mortgage amortization is front-loaded with interest: after 5 years of payments on a $400,000 5.5% loan, roughly 92% of the original principal ($369,800) is still outstanding.

Post-adjustment payment

When the rate resets to r₁, the lender re-amortizes the remaining balance over the remaining term:

\text{P\&I}_1 = B_{\text{adj}} \cdot \frac{(r_1/12)(1 + r_1/12)^{n_{\text{rem}}}}{(1 + r_1/12)^{n_{\text{rem}}} - 1}

where n_rem = (total term − fixed years) × 12. At a post-adjustment rate of 7.5%, the payment on the remaining $369,800 over 25 years becomes approximately $2,733/month — a $462 increase from the intro period.

Lifetime comparison

Total lifetime interest under each product:

I_{\text{ARM}} = \text{P\&I}_0 \cdot t_f \cdot 12 + \text{P\&I}_1 \cdot (n - t_f \cdot 12) - L

I_{\text{fixed}} = \text{P\&I}_{\text{fix}} \cdot n - L

The ARM advantage (positive = ARM wins) is simply the difference:

\text{Savings} = I_{\text{fixed}} - I_{\text{ARM}}

Worked example

Scenario: $400,000 loan, 30-year term, 5/1 ARM at 5.5% intro vs. 30-year fixed at 7%.

Metric	ARM (5.5% → 7.5%)	Fixed (7.0%)
Monthly P&I (intro)	$2,271	—
Monthly P&I (after adj.)	$2,733	—
Monthly P&I (fixed)	—	$2,661
Balance at month 60	$369,800	—
Lifetime interest	~$556,200	~$558,000
Net ARM advantage	~$1,800	—

With the post-rate at 7.5%, the ARM saves only about $1,800 over its life — essentially a wash. The five years of intro savings (about $390/month below the fixed payment) are nearly cancelled out by paying half a point above the fixed rate for the remaining 25 years. Break-even sits right around 7.5%: nudge the post-rate higher and the ARM quickly costs more than the fixed, while pulling it down toward 7% or 6% widens the ARM's advantage to roughly $38,000 or $107,000. The rate at which savings cross zero is the break-even rate.

Rate caps

Real ARM contracts include two types of rate caps that bound the worst case:

Periodic cap: maximum increase per adjustment (typically 1% or 2%).
Lifetime cap: maximum total increase above the initial rate (typically 5%). A 5/1 ARM at 5.5% intro with a 5% lifetime cap cannot exceed 10.5%.

This calculator models a single assumed post-rate rather than a capped path. Treat the post-adjustment input as a stress-test value — enter the initial rate plus the lifetime cap to see the true worst-case payment and total cost.

When an ARM makes sense

An ARM tends to work best in three situations:

A planned sale or refinance before the fixed period ends. A borrower who exits at year 4 on a 5/1 ARM never experiences the adjustment, so the intro-rate savings are pure upside.
An expectation that rates will fall. If the post-rate ends up below the current 30-year fixed, the ARM wins on both the intro discount and the post-rate.
Income flexibility. A borrower who can absorb a $400–$600 payment jump without financial stress carries the rate risk comfortably.

An ARM is a poor fit when the borrower plans to stay in the home for the full term and needs payment certainty, when the post-rate at the lifetime cap would strain the budget, or when intro savings are narrow (under $100/month) relative to a fixed — too narrow to compensate for the rate risk.

What this calculator does not model

Annual adjustments after year one of the variable period. Real ARMs adjust every year; this calc simplifies to one post-rate for the entire remaining term.
Margin and index. The actual post-rate equals an index (SOFR or CMT) plus the lender's margin. This calc treats the post-rate as a direct input.
Closing costs, points, and origination fees. These affect the true break-even when comparing an ARM against a fixed loan.
Tax effects. The mortgage interest deduction (subject to the $750k cap and the standard-vs-itemize choice) varies by borrower and is not modeled.

For monthly payment with property tax, insurance, and PMI, see the Mortgage Payment Calculator. To compute how large a loan your income supports, see the Mortgage Affordability Calculator.

Disclaimer

This calculator provides estimates for educational purposes and general planning only. It does not constitute financial advice. Mortgage rates, terms, and eligibility depend on lender underwriting, credit profile, and market conditions. Consult a licensed mortgage professional before making borrowing decisions.

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