Loan Payoff Calculator

Estimate the months and years required to repay a loan from its balance, rate and payment.

InputsChange a value to recalculate instantly

Remaining loan balance

Annual interest

Monthly payment

ResultUpdates as you type

Payoff time58 months

Approx. total paid$29,000

Approx. interest$4,000

FORMULA & STEPSLoan Payoff Calculator — Mathematical Derivation & Steps

3 StepsSequential Calculation Breakdown

Monthly rate

Convert the annual rate to a monthly rate.

Check amortization

A payment below this amount will not repay the loan.

Solve payments

The estimate assumes a constant rate and payment.

λ DooMathWork with this calculation

Local · deterministic · optional

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Quick mathNatural-language-style shortcuts for deterministic arithmetic.

Calculator guide

How to use the Loan Payoff Calculator

Estimate the months and years required to repay a loan from its balance, rate and payment.

01Set inputsChoose values, units and assumptions.

02Apply the modeln = −ln(1 − P×r/payment) ÷ ln(1+r).

03Read the resultCheck the output against the assumptions before using it.

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Solve the fixed-payment amortization equation for the remaining number of payments.

functions

n = −ln(1 − P×r/payment) ÷ ln(1+r).

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