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How to find a loan’s interest rate from its payment

Dealers and lenders often quote a payment, not a rate. The rate is one keystroke away.

Problem

You’re offered $25,000 for 60 months at $495 a month. What annual interest rate is that?

Keystrokes

  1. fFINx≷y
    0.00

    Start clean.

  2. 60n
    60.00

    The number of monthly payments.

  3. 25000PV
    25,000.00

    The amount you receive.

  4. 495CHSPMT
    −495.00

    The payment you make.

  5. i
    0.58

    Solves for the rate per period, here per month.

  6. 12×
    7.00

    Turns the monthly rate into an annual rate.

Answer

The loan charges 7.00% a year (0.58% a month).

Why it works

There’s no formula for the rate in a loan, so the calculator finds it by iteration: it tries rates until the payments exactly repay the loan. That’s why i can take a moment longer than the other keys.

The rate comes out per period because n counts months. Multiplying by 12 gives the nominal annual rate, the APR that loan disclosures quote.

Questions

What about fees?

Fees raise the real cost of a loan. See the guide on APR with fees.

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