Interest Rate Calculator

What this calculator tells you

When a lender quotes a monthly payment, the rate is not always stated clearly, and sometimes it is hidden inside fees or the way the loan is described. This calculator works backwards from the loan amount, the monthly payment and the term to find the annual interest rate that the payments imply.

It is useful for checking a quote, comparing a loan with the price of a financed purchase, or understanding what a payment really costs. The result is the nominal annual rate, compounded monthly, which is the standard basis for most consumer loans.

How the rate is found

A loan payment depends on the amount, the monthly rate and the number of payments. Given the other three, the rate cannot be rearranged into a simple formula, so the calculator searches for the monthly rate that makes the payment schedule land exactly on zero at the end of the term. It then multiplies that monthly rate by twelve to give the annual figure.

A worked example

Suppose you borrow 10,000 over 60 months and the lender quotes a monthly payment of about 193.33. Working back through the search gives a monthly rate of about 0.5%, which is an annual rate of about 6%. If the same loan were quoted at a payment of 212.47, the implied rate would be about 10%, which shows how sensitive the rate is to the payment.

Why the implied rate can differ from the quote

The rate found here includes only the payments on the loan amount. Arrangement fees, insurance added to the loan, and any balloon payment at the end all change the true cost. If a fee is deducted from the amount you receive, the effective rate is higher than the rate implied by the payments on the full amount. Ask the lender for the annual percentage rate, which is designed to include most of these costs, and compare it with the figure from this calculator.

Limits of the calculation

The calculator assumes equal monthly payments and a term of whole months. It also assumes the rate is constant for the full term. Loans with variable rates, introductory periods or irregular payments will not match the simple result. If no rate exists that fits the payment you enter, the calculator reports that the inputs are not consistent, for example when the payment is too small to repay the amount at any positive rate.

What to ask the lender

If the implied rate differs from the quoted rate, ask for a full illustration of the repayments, including every fee and any change in the rate over the term. A written breakdown lets you compare offers on the same basis and shows whether the quoted rate applies only to an introductory period.

Also ask how early repayment is treated. Some loans charge a fee if the balance is repaid before the end of the term, which changes the true cost if you expect to repay early.

Using the result

Use the implied rate to compare offers on the same basis, and to check whether a quoted rate matches the payment in the contract. If the implied rate is higher than you were told, ask why, and request a full breakdown of the cost before you sign. Comparing several quotes at the same amount and term is the clearest way to see which is cheapest.

Comparing loan offers on the same basis

To compare two loan offers, use the same amount and the same term, then compare the implied rates and the total repayable. A loan with a lower monthly payment can have a higher implied rate if its term is longer, so the monthly figure alone is misleading. Keep a simple table with the amount, term, fees, payment, implied rate and total cost for each offer, and choose on the total cost unless other features matter more.