What this calculator does
See how much interest and time you save by paying a little extra on your loan. Think of a loan you pay down in fixed monthly payments, like a mortgage or car loan. Any extra money goes straight to the principal, the amount you still owe. A smaller balance means less interest next month. So more of every later payment goes to the balance too. The savings build on each other, and the loan ends early.
Enter your balance, rate and the time left. Then try a regular extra amount, a one-time lump sum, or both. The calculator runs your payment schedule with and without the extras. It shows the interest saved, the time saved and how the two balances compare year by year.
Where it's used
Why this math matters outside the classroom:
- Paying a loan early. Adding $100 a month to a $200,000, 30-year loan at 6% pays it off in 295 months instead of 360.
- Interest saved. Borrowers compare total interest with and without extra principal to see what the extra payments save.
- Yearly lump sums. Homeowners model one extra payment a year, such as a tax refund or bonus, applied directly to principal.
- Student loans. Graduates see how a small extra amount each month shortens the repayment period on a student loan.
Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter your current loan balance, the interest rate and how long is left on the loan.
- Enter the extra amount you plan to add each month. Use 0 to test a lump sum on its own.
- If you like, enter a one-time payment and the payment number when you'll make it.
- Read the interest saved and your new payoff time. Then compare the balances in the yearly table.
What the inputs mean
- Time left on the loan
- The calculator works out your regular payment from the balance, rate and time left. That way it matches a loan that is on schedule.
- Extra payment each month
- Added every month starting with the first payment, on top of the regular payment.
- One-time extra payment
- A single extra payment toward the balance, such as a bonus or tax refund. If it's more than you owe, only the remaining balance is used.
- Make the one-time payment with payment number
- Counted from your next payment. 1 means along with your next payment, and 12 means a year from now.
Formula and method
i = rate ÷ 100 ÷ 12; regular payment = B × i ÷ (1 − (1 + i)^(−n)) each month: interest = balance × i principal = regular payment − interest + extra (+ lump sum in its month) interest saved = interest on the regular schedule − interest with extras without a lump sum: months to payoff = −ln(1 − B × i ÷ (payment + extra)) ÷ ln(1 + i), rounded up
In the formulas, B is your loan balance, i is the monthly interest rate and n is the number of months left. ln is the natural logarithm, a calculator key used here to solve for the number of months.
The regular schedule and the faster one start from the same balance and the same required payment. The only difference is the extra money toward the balance. So the gap in total interest is exactly what the extras save.
The last formula is a one-line shortcut that checks the answer when the extra is the same every month. The calculator itself goes month by month, so it can handle a lump sum too.
Worked example
A $300,000 balance at 6.5% with 30 years left, adding $200 a month.
- Regular payment: $300,000 × 0.00541667 ÷ (1 − 1.00541667^(−360)) ≈ $1,896.20.
- Interest on the regular schedule: $1,896.20 × 360 − $300,000 ≈ $382,633.47.
- Paying $2,096.20 a month clears the loan in 277 payments, or 23 years 1 month.
- Interest with the extra: $279,184.67. Saved: $382,633.47 − $279,184.67 = $103,448.79.
Result: An extra $200 a month saves about $103,448.79 in interest and ends the loan 83 months (6 years 11 months) early. Adding a one-time $10,000 at payment 12 raises the saving to about $133,152.94.
Understanding the result
Extra payments save the most when you make them early, while the balance and the interest on it are largest. The same $10,000 lump sum saves far more in year one than in year twenty.
Compare the interest saved with what the same money could earn elsewhere. Paying down a loan gives you a guaranteed return equal to the loan's rate.
Assumptions and limitations
- The rate is fixed, and interest is charged monthly at the yearly rate ÷ 12. Payments are made at the end of each month.
- All extra money goes to the balance right away, and the required payment stays the same.
- The last payment is made smaller so it clears the balance exactly. Amounts aren't rounded to the cent.
- It doesn't model prepayment penalties (fees some lenders charge for paying early), recasting or biweekly payment plans.
- Some lenders put extra money toward future payments instead of the balance, unless you tell them otherwise. Check how yours handles it.
- Escrow amounts for tax and insurance (the extra your lender collects to pay those bills) aren't included.
Frequently asked questions
Does an extra payment lower my monthly payment?
Not on a standard fixed-rate loan. The required payment stays the same, and the loan ends sooner. Some lenders offer a recast, which lowers the payment after a large lump sum. This calculator doesn't model that.
Is a lump sum or a monthly extra better?
Money paid sooner saves more interest. So a lump sum today beats the same total spread over several years. But a steady monthly extra is often easier to keep up. Try both here with your own numbers.
How do I make sure the extra goes to principal?
Many lenders let you mark an extra amount as principal when you pay online. If you're not sure, ask your servicer (the company that collects your payments) how it applies extra money.
What if I can only pay extra sometimes?
Use the one-time payment for an occasional amount. Or enter a smaller monthly extra that averages out to what you expect to add over a year.
How this calculator is checked
Method: Month-by-month amortization with the standard level payment plus extra principal; checked against the closed-form payoff period for a constant payment. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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