Interest Rate Calculator

Why Reverse-Calculate the Rate?

Lenders and car dealers sometimes advertise a monthly payment and purchase price without stating the interest rate. This calculator reveals the actual rate implied by those numbers, letting you compare it to what you were quoted or what competing lenders offer.

APR vs Interest Rate

The annual percentage rate (APR) includes fees and costs beyond the base interest rate. This calculator finds the nominal interest rate from the payment stream — the APR will be higher if origination fees or other charges are rolled into the loan.

Always ask lenders for the APR to make true cost comparisons. The finance calculator models overall loan cost including APR effects.

How the Math Works

The monthly payment formula for a fixed-rate loan is: PMT = P × r(1+r)ⁿ / ((1+r)ⁿ − 1), where P is the principal, r is the monthly rate, and n is the number of months. Given PMT, P, and n, solving for r requires numerical iteration (Newton-Raphson method) since r appears non-linearly.

Common Use Cases

Auto loans: Dealers often present "you pay $450/month for 60 months" — find out if the implied rate matches your agreement — or use the auto loan calculator to model the payment first.

Personal loans: Compare rates across lenders who quote different payment amounts for the same term.

Mortgages: Verify the rate being applied to your quoted payment matches your loan documents. The mortgage calculator gives the expected payment to compare against.

Worked example

You borrow £20,000 and are quoted repayments of £432/month over 48 months. Total repaid = £432 × 48 = £20,736, so total interest is £736. Entering these values into the calculator reveals the implied annual rate is approximately 3.6% — useful for verifying a lender's quoted rate before signing.

Related calculations

To compare rates and terms in one view, use the loan payment table. For the full payment-by-payment picture on one loan, the amortization schedule shows how each payment splits.

How do I find the interest rate on a loan from monthly payments?

Enter the loan amount, monthly payment, and loan term, then click Calculate. The calculator uses numerical iteration (Newton-Raphson method) to solve the amortisation formula in reverse, finding the rate that produces your payment. Useful when a lender quotes a payment without clearly stating the rate.

Why would I need to reverse-calculate an interest rate?

Car dealers sometimes advertise '£450/month for 60 months' without prominently disclosing the rate. Reverse-calculating reveals the actual APR being charged, letting you compare it to rates from other lenders or verify it matches your loan agreement.

What is the difference between APR and the nominal interest rate?

The nominal rate is the base rate used to calculate payments. APR includes the nominal rate plus origination fees and other costs — giving the true annual cost. This calculator finds the nominal rate; the APR will be higher if fees are involved.

How accurate is the interest rate calculation?

The calculator iterates to a precision of 0.0001% using the Newton-Raphson method, typically accurate to several decimal places. Small discrepancies may appear if the lender rounds payment amounts or uses a different day-count convention.