Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Reverse-solving for the payoff term from a fixed payment only produces a real answer when that payment actually exceeds the interest accruing each period. A payment set below the periodic interest charge never pays down the balance at all, and the math has no finite term to return in that situation.
Before you rely on it
What to check
Confirm the entered payment is comfortably above the periodic interest on the current balance before trusting a computed payoff term.
The common error
Where people go wrong with loan term calculator
Entering a payment too close to or below the periodic interest charge and expecting a normal payoff term. Under that condition, the balance doesn't shrink in any meaningful way, and the reverse-solved term stops meaning what it normally means.
Sensitivity evidence
How annual interest rate changes the estimated payoff term
| Annual interest rate | Estimated payoff term | Estimated total interest | Estimated final payoff total |
|---|---|---|---|
| 5.5% | 51.1 months | $3,098 | $28,098 |
| 6.5% | 52.3 months | $3,777 | $28,777 |
| 7.5%worked example | 53.6 months | $4,502 | $29,502 |
| 8.5% | 55.1 months | $5,278 | $30,278 |
| 9.5% | 56.6 months | $6,111 | $31,111 |
Every input, tested
Which input moves the estimated payoff term most
| Input | Tested from | To | Estimated payoff term at each end | Swing |
|---|---|---|---|---|
| Monthly payment | $495 | $605 | 60.9 months to 48.0 months | 12.9 months (24%) |
| Amount borrowed | $22,500 | $27,500 | 47.4 months to 60.1 months | 12.7 months (24%) |
| Annual interest rate | 6.5% | 8.5% | 52.3 months to 55.1 months | 2.7 months (5.1%) |
Two variables at once
Estimated payoff term by annual interest rate and amount borrowed
| Annual interest rate \ Amount borrowed | $20,000 | $25,000 | $30,000 |
|---|---|---|---|
| 5.5% | 39.9 months | 51.1 months | 62.9 months |
| 6.5% | 40.6 months | 52.3 months | 64.8 months |
| 7.5% | 41.4 months | 53.6 months | 66.9 months |
| 8.5% | 42.2 months | 55.1 months | 69.2 months |
| 9.5% | 43.1 months | 56.6 months | 71.7 months |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Amount borrowed | $25,000 |
| Annual interest rate | 7.5% |
| Monthly payment | $550 |
| Estimated payoff term | 53.6 months |
| Estimated total interest | $4,502 |
| Estimated final payoff total | $29,502 |
Where the inputs come from
The amount borrowed and annual rate come from the loan terms, and the monthly payment is what you plan to pay. The payment must exceed the first month's interest, or the balance never falls; on $25,000 at 7.5% the first month's interest is about $156, so any payment above that reduces principal. Try more than one payment to see how sensitive the timeline is.
When the result stops applying
It assumes the rate is fixed and that no fees are added to the balance. Lenders that limit how much extra you can pay, or that apply payments to interest first, will produce different results.
What to compare it with
After finding a term, compare it with the loan payoff and extra payment calculators to see the effect of small increases. If the term is longer than you expected, check whether the payment is just above interest, since a tiny extra amount then shortens the loan a great deal. For a vehicle or appliance that loses value, keep the term shorter than the useful life of the asset. Otherwise you may be paying for something you no longer own.
People also ask
Frequently asked questions
What is the minimum payment that pays off the loan?
Any payment above the first month's interest will eventually pay the loan off, but it can take a very long time. At exactly the interest amount the balance never falls, and below it the balance grows, so test several payments.
How does one extra payment a year change the term?
It usually shortens a multi-year loan by several months, because the whole extra payment goes to principal and stops interest accruing on it. The effect is larger the earlier in the loan you make it and the higher the rate.
Does a lower rate shorten the term?
At the same payment, yes. A lower rate means less of each payment goes to interest, so more of it reduces the balance and the loan ends sooner.