Loan & credit tools
Turn a loan amount, a term, and a monthly payment into the annual interest rate you are actually being charged — or work out exactly what an advertised rate will cost you every month.
Most loan offers are presented as a monthly figure, not a rate. A dealership quotes “$489 a month,” a store card advertises a weekly instalment, and an online lender leads with a repayment schedule rather than a percentage. This calculator reverses that presentation. Give it the amount borrowed, the number of months, and the payment, and it solves for the nominal annual interest rate that makes those three numbers consistent.
It also works in the opposite direction. Switch to payment mode, enter an advertised rate, and the calculator returns the monthly repayment together with the total cost of borrowing — the sum of all payments and the total interest over the life of the loan. Both directions use the standard amortising-loan formula, the same mathematics behind mortgages, auto loans, student loans, and personal instalments.
Fill in three values. The fourth is what we solve for.
Result
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Enter your loan details and select Calculate.
Six steps, in the order you will actually do them.
Use the toggle at the top of the calculator. Select Solve for interest rate when you know the loan amount, the term, and the monthly payment. Select Solve for monthly payment when you know the loan amount, the term, and the advertised rate.
Type the full amount borrowed, before any interest. Do not include a down payment, a trade-in, or anything you are paying upfront — this field is the principal the lender actually advances.
Use the two fields to give the term in years and months. A five-year loan is 5 years and 0 months; a 42-month loan is 3 years and 6 months. The total term must be between one month and 100 years.
In rate mode, enter the fixed monthly payment you have been quoted, including principal and interest. In payment mode, enter the nominal annual interest rate as a percentage.
The large figure at the top of the results panel is the answer. The four tiles beneath it show the total of all payments, the total interest, the payoff time, and interest as a proportion of the amount borrowed.
Change any field and the results refresh automatically once you have calculated once. Press Calculate at any time to run the numbers again, or Reset to clear every field and start over.
It solves the standard amortising loan equation for whichever variable you leave out. In rate mode it finds the interest rate; in payment mode it finds the monthly payment. Everything else — the total of payments, the total interest, and the payoff time — is derived from those two results.
Every result comes from the level-payment amortisation formula shown below. Solving for the monthly payment is direct arithmetic. Solving for the rate is not, because the rate appears on both sides of the equation — so the calculator narrows in on it numerically, repeatedly halving the search range until the payment implied by a candidate rate matches the payment you entered to within a fraction of a cent.
The formula behind every result
M = P × i ÷ (1 − (1 + i)−n)
M = monthly payment · P = principal · i = monthly interest rate (annual rate ÷ 12) · n = total number of monthly payments
The rate returned in rate mode is the nominal annual rate that exactly reconciles the amount borrowed, the term, and the payment you entered. Because it is derived from a payment rather than quoted by a lender, it is effectively the annualised cost of the credit you were offered.
A result noticeably above the rates you see advertised usually means one of three things: fees have been folded into the payment, the term is shorter than you assumed, or the payment includes add-ons such as insurance or a service contract.
Because interest is compounded monthly, the effective annual rate is slightly higher than the nominal rate shown. Converting is straightforward: take the monthly rate, add one, raise it to the twelfth power, and subtract one. A nominal 7.432% becomes an effective annual rate of roughly 7.69%.
This tool models a single, fixed-rate, fully amortising loan with monthly payments. It does not handle interest-only periods, biweekly schedules, variable rates, or compounding conventions other than monthly.
Regulated credit agreements quote an annual percentage rate (APR) that also includes mandatory fees, so the APR will normally be higher than the nominal rate shown here. Treat this calculator as a precise guide to the interest cost of a loan, not as a replacement for the disclosure documents your lender is required to provide.
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