How ARM Payments Are Calculated: Formulas, Index, Margin, Caps
An ARM looks complicated because lenders describe it in legal language. Underneath, it is two formulas and three limits. Once you see the formulas, you can predict every ARM payment for the life of the loan.
The two formulas
Formula 1: The fully-indexed rate
Fully Indexed Rate = Index Value + MarginThe index value changes with the market (typically daily, for SOFR). The margin is fixed for the life of the loan. Your ARM's rate at any adjustment equals the current index value plus the margin, capped by your periodic and lifetime caps.
Formula 2: The amortization payment
M = P · r(1+r)^n / ((1+r)^n − 1)This is the standard mortgage payment formula. M is monthly payment, P is the remaining loan balance, r is the monthly interest rate (annual rate ÷ 12), and n is the number of remaining months. After each ARM adjustment, the payment recalculates using this formula with the new rate and the remaining term.
Index reference table
Every ARM references exactly one index. Knowing the index tells you what your rate will track over the life of the loan.
| Index | Publisher | Current value (illustrative) | Typical lag | Common usage |
|---|---|---|---|---|
| 30-day SOFR | Federal Reserve Bank of New York | ~4.30% | 45 days | Most post-2024 conforming ARMs |
| 90-day SOFR | Federal Reserve Bank of New York | ~4.25% | 45 days | Some jumbo ARMs |
| 1-year Treasury | US Treasury | ~4.20% | 45 days | Legacy ARMs, some portfolio lenders |
| 11th District COFI | FHLB San Francisco | ~3.40% | ~2 months | Legacy western-state ARMs; rare in new originations |
| MTA (12-month moving avg) | Fannie Mae / Freddie Mac | ~4.10% | Smoothed over 12 months | Some low-volatility ARM products |
Caps table: how the limits interact
Your caps determine the worst-case payment path. The naming convention is initial / periodic / lifetime (e.g. "5/2/5").
| Cap type | What it limits | Most common value |
|---|---|---|
| Initial cap | First adjustment from the start rate | 2% or 5% |
| Periodic cap | Each adjustment after the first | 2% per year |
| Lifetime cap | Total rate movement above the start rate, ever | 5% |
| Floor | How low the rate can go | Equal to the margin |
Worked example: 7-year payment path for a 5/1 ARM with caps 5/2/5
Loan: $400,000. Initial rate: 5.25%. Margin: 2.75%. Index: 30-day SOFR (assumed flat at 4.30% for this example). Cap structure: 5/2/5.
| Year | Index value (assumed) | Fully indexed rate | Capped rate (vs prior year) | Payment (P+I) | Notes |
|---|---|---|---|---|---|
| 1 | — | — | 5.25% (start) | $2,210 | Fixed period |
| 2 | 4.30% | 7.05% | 5.25% (start) | $2,210 | Fixed period |
| 3 | 4.30% | 7.05% | 5.25% | $2,210 | Fixed period |
| 4 | 4.30% | 7.05% | 5.25% | $2,210 | Fixed period |
| 5 | 4.30% | 7.05% | 5.25% | $2,210 | Last fixed year |
| 6 (1st adj) | 4.30% | 7.05% | 7.25% (initial cap +2%) | $2,758 | Index wants 7.05%; cap binds at +2% from start |
| 7 | 4.30% | 7.05% | 7.25% (periodic cap binds; same as prior) | $2,758 | Already at lifetime cap; no further increases |
What this example shows. Even if the index fully reverts to a high level (here assumed to be 7.05% fully indexed), the 5/2/5 cap structure on this loan prevents the rate from rising above 7.25% (start rate + 5%). The payment peaks at $2,758/month — a $548/month increase over the start rate. Without caps, the same scenario would have pushed the payment past $3,200.
The rate floor (often missed by borrowers)
Most ARMs have a floor equal to the margin. With a 2.75% margin, your rate cannot drop below 2.75% even if SOFR goes to zero. This is a feature for the lender and a quiet constraint for the borrower. In a deflationary scenario where the index actually went negative (unlikely but possible in some market structures), the floor protects the lender's economics but limits your rate-decline benefit.
How to model your own ARM scenario
The ARM Calculator uses the formulas above to project payments year by year. Enter your loan amount, initial rate, margin, index value, and cap structure, and it shows your monthly P+I for each year of the loan. Compare that path against a fixed-rate alternative using the Fixed vs ARM Calculator to see which structure wins for your assumed hold period.