Loan Payoff Formula
This formula helps you accurately determine the exact number of months required to completely pay off a loan, given your current loan amount, interest rate, and consistent monthly payments. It's a powerful tool for strategic debt management and financial planning.
Formula
Copy the exact expression or work through it step by step below.
Months To Pay Off = -ln(1 - Monthly Rate x Loan Amount / Monthly Payment) / ln(1 + Monthly Rate) Variables
MPO
Months To Pay Off
The months to pay off value plugged into the loan payoff calculation.
MR
Monthly Rate
The monthly rate assumption used in the loan payoff calculation.
LA
Loan Amount
The loan amount value plugged into the loan payoff calculation.
MP
Monthly Payment
The recurring amount that changes the loan payoff result over time.
Step By Step
- 1
Set the baseline case with the real calculator inputs.
Principal = $35,000, Annual Rate Percent = 7.20%, Monthly Payment = $650, Extra Monthly Payment = $100
- 2
Translate rates, periods, and cash values onto the same footing before combining them.
Keep the loan payoff assumptions consistent instead of mixing monthly and annual views.
- 3
Apply the formula and read the first calculator outputs, not just the headline assumption.
The calculator lands with interest saved at $1,212 and months saved at 11.
- 4
Run one changed scenario so the formula is stress-tested before it is trusted.
The loan payoff calculator page is the fastest way to compare that second case.
Worked Example
Loan Payoff sample case
Principal
$35,000
Annual Rate Percent
7.20%
Monthly Payment
$650
Extra Monthly Payment
$100
Months To Pay Off = -ln(1 - Monthly Rate x Loan Amount / Monthly Payment) / ln(1 + Monthly Rate) using principal $35,000, annual rate percent 7.20%, monthly payment $650, extra monthly payment $100.
The calculator lands with interest saved at $1,212 and months saved at 11.
Common Variations
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Sources & References
- Loan Amortization: How It Works — Investopedia
- Loan Payment Calculator — Calculator.net
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