What this calculator does
See what your adjustable-rate mortgage (ARM) payment could be now, and after each time the rate resets. An ARM starts with a rate that's fixed for a few years. Then the rate resets on a regular schedule. At each reset, the new rate is a market rate (the index) plus a fixed extra amount (the margin). Limits called caps keep it from moving too far. This calculator follows that process month by month. You see the payment at the start, at the first reset and at every reset after. It uses index rates you choose.
Nobody knows where the index will be in five or seven years. So the calculator also works out the worst case. That's the payment if the rate rises by the full cap at every reset, until it hits the lifetime ceiling. That number comes straight from the loan terms. Lenders and careful borrowers use it to judge whether an ARM is affordable.
Where it's used
Why this math matters outside the classroom:
- Budget stress test. A buyer checks that a 5/6 ARM starting at $2,398.20 a month would still be affordable at the $3,630.26 worst case.
- Fixed or adjustable. A family planning to move in six years compares a 7/1 ARM's lower start with a fixed loan's steady payment.
- Reading loan terms. A borrower works out that a 6% start with a 5-point lifetime cap can never go above 11%.
- Piecewise payments. Students model a payment that is recalculated from a geometric-series formula each time the rate changes.
- Lending disclosures. Loan officers show borrowers how a 2/1/5 cap structure limits payment shocks at each reset.
Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter the loan amount, the starting rate, the term and the length of the fixed-rate period.
- Choose how often the rate changes after that. Then enter the margin from the loan terms.
- Enter the index rate you want to assume at each reset, in order. The last value is reused for later ones.
- Enter the first, periodic and lifetime caps, and a floor if your loan has one. Then compare the payment on your index path with the worst case.
What the inputs mean
- Fixed-rate period
- A 5/6 ARM has a 5-year fixed period, and it adjusts every 6 months after that. A 7/1 or 10/1 ARM adjusts every year.
- Margin
- The fixed amount added to the index. It's set in the loan documents, and it doesn't change.
- Assumed index rate at each adjustment (%)
- The market rate your loan follows. Enter values to try out different futures. For example, try today's level, then higher and lower paths. These are guesses you choose, not forecasts.
- Initial adjustment cap
- The most the rate can change at the first reset, in percentage points. Caps are often written as three numbers, such as 2/1/5. They mean first reset, each later reset, and lifetime.
- Periodic adjustment cap
- The most the rate can change at each later reset.
- Lifetime cap
- How far above the starting rate the rate can ever go. With a 6% start and a 5-point cap, the ceiling is 11%.
- Rate floor
- Many loans never go below the margin, and that's what a blank floor assumes. Some loan papers set the floor at the starting rate instead.
- Round the new rate to the nearest 0.125%
- Loan papers commonly round the index plus margin to the nearest one-eighth of a point, before applying the caps.
Formula and method
payment = B × i ÷ (1 − (1 + i)^(−m)), with i = rate ÷ 1200 and m = months left fully indexed rate = index + margin (rounded to the nearest 0.125 if chosen) new rate = fully indexed rate, kept within current rate ± cap then kept between the floor and initial rate + lifetime cap worst case: new rate = min(current rate + cap, initial rate + lifetime cap)
In the formulas, B is the balance you still owe, and i is the monthly interest rate (the yearly percent ÷ 1200). m is the number of months left. The "fully indexed rate" is the index plus the margin. The loan starts as an ordinary fixed-rate mortgage over the full term. At each reset, the balance you still owe is spread again over the months left, at the new rate. That's how most ARMs work out the new payment.
The caps limit how far the rate can move. The first cap applies at the first reset, and the periodic cap at each later one. The lifetime cap applies over the whole life of the loan. Sometimes the fully indexed rate falls outside the allowed range. Then the rate stops at the edge of the range. It may keep moving toward the fully indexed rate at later resets.
Worked example
A $400,000, 30-year 5/6 ARM starts at 6%, with a 2.75 margin and 2/1/5 caps. You assume the index will be 4.25% at the first reset. Then it goes to 4.5%, 4.75% and 5%, and stays at 5% after that.
- Initial payment for the first 60 months: $2,398.20.
- First reset, month 61: 4.25 + 2.75 = 7.00%, within the 2-point cap. Spreading the $372,217.43 balance over 300 months gives $2,630.76.
- The rate then steps to 7.25%, 7.5% and 7.75%, each within the 1-point periodic cap. The payment peaks at $2,806.71 from month 79.
- Worst case: 8%, 9%, 10%, then the 11% ceiling, where the payment reaches $3,630.26.
Result: With these guesses, the payment rises from $2,398.20 to a peak of $2,806.71. You'd pay $583,795.72 of interest over the loan. If the index climbs as far as the caps allow, the payment could reach $3,630.26, and interest $823,825.05.
Understanding the result
The highest payment on your index path is what happens if your guesses are right. The worst-case payment is what the loan terms allow, whatever the index does. So it's the safer number to test your budget against.
If you expect to sell or refinance before the fixed period ends, the starting payment matters most. If you might keep the loan longer, compare the worst case with a fixed-rate loan's payment.
Try several index paths: flat, rising and falling. Because of the floor and caps, falling rates usually help less than rising rates hurt.
Assumptions and limitations
- You pay once a month, at the end of each month. At each reset, the payment is worked out again to repay the balance over the months left.
- Index values are the ones you enter. The calculator uses no live market data.
- Caps limit the change in rate, in percentage points. The floor and ceiling are applied last.
- It doesn't handle interest-only ARMs, payment caps or negative amortization (when unpaid interest is added to what you owe).
- It doesn't handle lookback periods (how far back the lender reads the index) or the exact index dates in your loan papers.
- Taxes, insurance and mortgage insurance aren't included.
- This is an example based on your guesses. It isn't a lender's official disclosure or quote.
Frequently asked questions
What do ARM names like 5/6 and 7/1 mean?
The first number is the fixed-rate period in years. The second is how often the rate changes after that. 6 means every six months, and 1 means every year. A 10/1 ARM is fixed for ten years and then adjusts yearly.
What do caps like 2/1/5 mean?
They limit rate changes, in percentage points. The first number caps the first reset, and the second caps each later reset. The third caps the total rise over the starting rate, for the life of the loan. Caps of 2/2/5 are common on loans that adjust yearly.
Why does my payment change slightly even when the rate does not?
Here it doesn't change, apart from rounding. Each new payment repays the same balance over the same months left at the same rate. On a real statement, small differences can come from rounding the payment to the cent, or from extra payments.
Is an ARM cheaper than a fixed-rate mortgage?
At the start it usually is, because the starting rate is lower. Over the full term, it depends on where rates go. Compare the worst-case payment here with a fixed-rate payment. That shows how much risk you'd take on for the lower start.
How this calculator is checked
Method: Standard ARM mechanics: fully indexed rate = index + margin, limited by initial, periodic and lifetime caps and a floor, with the level payment recast over the remaining term at each adjustment. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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