Loan Calculator: Solve for Rate, Term, Payment or Amount
Know three of four? Solve for payment, rate, term, or amount.
Your Missing Loan Variable Calculator Result
Generated from the inputs below — a record you can revisit, or share with anyone helping you plan.
Your detailsInput Parameters
What's Missing?
Known Values
Example rate, not current market data. Enter the rate on your loan or quote.
To repay $20,000 at 8% over 60 months.
Share of everything you pay that goes to interest rather than principal.
Analysis
Amortization schedule
Yearly view| Year | Interest | Principal | Balance |
|---|---|---|---|
| 1 | $113 | $293 | $16611 |
| 2 | $88 | $317 | $12941 |
| 3 | $62 | $343 | $8966 |
| 4 | $34 | $372 | $4662 |
| 5 | $3 | $403 | $0 |
| Period | Interest | Principal | Balance |
|---|---|---|---|
| 1 | $133 | $272 | $19728 |
| 5 | $126 | $280 | $18621 |
| 9 | $118 | $287 | $17484 |
| 13 | $111 | $295 | $16316 |
| 17 | $103 | $303 | $15117 |
| 21 | $95 | $311 | $13886 |
| 25 | $86 | $319 | $12622 |
| 29 | $78 | $328 | $11323 |
| 33 | $69 | $337 | $9990 |
| 37 | $60 | $346 | $8621 |
| 41 | $50 | $355 | $7214 |
| 45 | $41 | $365 | $5770 |
| 49 | $31 | $374 | $4287 |
| 53 | $21 | $385 | $2764 |
| 60 | $3 | $403 | $0 |
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Open calculatorEvery Loan Is Four Numbers — Give Three, Get the Fourth
A fixed-rate loan is fully described by four values: the principal borrowed, the interest rate, the term, and the payment. They are locked together by a single equation, which means any three determine the fourth exactly. There is nothing to estimate.
Solving for payment or principal is straightforward algebra. Solving for the term requires logarithms:
Solving for the rate is the interesting case: the equation cannot be rearranged to isolate r. No closed-form solution exists. Calculators find it numerically instead, converging on the rate that reproduces the known payment — this tool uses bisection to about twelve decimal places.
When You Actually Need to Solve Backwards
Four situations account for nearly all real use of this calculation.
- A quote with no stated rate. Dealers and some lenders quote "$389 a month for 60 months" without disclosing the APR. Solve for the rate and you can compare the offer against anything else. This is the most valuable use of the tool, and it is why we built the Interest Rate Analyzer as a dedicated version.
- Budgeting from the payment down. If you know you can afford $450 a month, solving for principal tells you what you can actually borrow at current rates. For a full affordability picture including your other debts, use the Personal Loan Affordability Calculator.
- Finding out when a loan ends. Given your balance, rate and what you actually pay, solving for term tells you your real payoff date — which is often earlier than the contract says if you have been overpaying.
- Coursework. Finance and personal-finance classes routinely set problems in exactly this shape. The formulas above are the ones you are expected to apply.
One check worth internalising: if your payment does not exceed the first month's interest, the balance grows rather than shrinks and no valid term exists. This calculator flags that case explicitly instead of returning a nonsense number.