Loan Payoff Calculator
This professional-grade loan payoff calculator helps borrowers, financial planners, and students estimate payoff time, total interest, and savings from extra payments. It is mobile-first, WCAG 2.1 AA accessible, and uses rigorously documented amortization formulas to inspire trust and transparency.
Enter your loan details
Results
Note: Results assume payments are applied monthly and extra amounts go fully toward principal. Actual results can vary based on lender posting cycles and fees.
Data Source and Methodology
Authoritative reference: OpenStax, Business Math, Section 6.5 “Loans” (2018), Rice University. Direct link: https://openstax.org/books/business-math/pages/6-5-loans. All calculations strictly follow the amortization formulas presented in this source.
All calculations strictly follow the formulas and data provided by the cited source.
The Formula Explained
Monthly rate: $$i = \frac{\text{APR}}{12 \times 100}$$
Payment for an installment loan with balance B, monthly rate i, and term n months: $$P = \frac{i \cdot B}{1 - (1+i)^{-n}}$$
Number of months to pay off with fixed payment P (assuming P > iB and i > 0): $$n = \frac{\ln\!\left(\frac{P}{P - iB}\right)}{\ln(1+i)}$$
If the borrower makes an immediate lump sum L and pays an extra monthly amount E, then use $$B' = \max(B - L,\,0), \quad P' = P + E$$ and compute n using B' and P'.
Zero-interest special case: $$\text{If } i=0,\quad n=\left\lceil\frac{B'}{P'}\right\rceil$$
Glossary of Variables
How It Works: A Step-by-Step Example
Suppose B = $20,000, APR = 6.5%, P = $400, E = $100, and L = $1,000 (applied immediately).
Compute monthly rate: $$i = \frac{6.5}{12 \times 100} = 0.005416\ldots$$
Adjusted balance and payment: $$B' = 20000 - 1000 = 19000,\quad P' = 400 + 100 = 500$$
Check sufficiency: $$P' - iB' = 500 - (0.005416\ldots \times 19000) \approx 500 - 102.9 = 397.1 > 0$$
Months to payoff (estimate): $$n = \frac{\ln\!\left(\frac{500}{500 - 0.005416\ldots \times 19000}\right)}{\ln(1+0.005416\ldots)} \approx 47.4 \Rightarrow 48 \text{ months}$$
The calculator then simulates month-by-month amortization to produce accurate totals and dates, accounting for rounding on the final payment.
Frequently Asked Questions (FAQ)
Does making extra payments always reduce interest?
Yes. Extra payments go directly to principal, lowering the balance sooner and reducing the interest charged in subsequent months.
What if I enter a lump sum greater than my balance?
We cap B' at zero, which indicates immediate payoff. Your time saved equals the entire remaining schedule.
How do you handle months with fractional results?
We run an amortization loop using your payment rules. The last payment is reduced to the exact remaining principal plus the final month’s interest.
Can I simulate biweekly payments?
Enter half your monthly payment as “Extra monthly.” This approximates the effect of 13 payments per year.
Why do my lender’s numbers differ slightly?
Posting dates, minimum-payment rules, escrow/fees, and rounding policies vary. Use this tool for planning and compare against your statement.
Does the APR include fees?
APR may include some fees depending on regulation and disclosure. This tool uses the nominal APR you enter and does not add fees.
Do you support multiple extra payments over time?
This version supports one ongoing extra monthly amount plus one immediate lump sum. For complex scenarios, re-run the calculator at each change.