Extra Payments on a Loan Calculator: Months and Interest Saved

This calculator shows what an extra amount added to every monthly payment does to a fixed-rate loan. Enter the balance, the APR, the months left and the extra amount; you get the months saved, the new payoff time and the interest saved.

Formula

Regular payment M = P × r ÷ (1 − (1 + r)⁻ⁿ), r = APR ÷ 1200. With the extra x, months to pay off = −ln(1 − r × P ÷ (M + x)) ÷ ln(1 + r), rounded up. Interest saved = (M × n − P) − (interest with the extra), where the last payment with the extra is the balance left plus one month of interest.

Worked Example

A $25,000 balance at 7.5% APR with 60 months left, paying $100 extra a month.

1. M = 25,000 × 0.00625 ÷ (1 − 1.00625⁻⁶⁰) = 500.95
2. With 600.95 a month: −ln(1 − 0.00625 × 25,000 ÷ 600.95) ÷ ln(1.00625) = 48.3, so 49 months
3. Months saved = 60 − 49 = 11
4. Interest without the extra = 5,056.92; with it = 4,043.31; saved = $1,013.61

Assumptions

• Results use the exact level payment before rounding to the cent; a lender’s cent-rounded schedule can differ by a few cents.
• Fixed interest rate for the whole term; payments of equal size at the end of each month.
• Interest compounds monthly at APR ÷ 12.
• No fees, taxes or insurance unless the calculator has a field for them.
• The extra goes entirely to principal every month from now on.
• No prepayment penalty.

How to read the result

Extra principal saves interest because it lowers the balance that every later month’s interest is charged on. The earlier in the loan you pay extra, the more it saves.

Limits and common mistakes

• Check that your lender applies extra payments to principal and does not charge a prepayment fee.
• Use the balance and months left from your latest statement.

Frequently Asked Questions

How much does $100 extra a month save on $25,000 at 7.5% over 5 years?

About $1,013.61 of interest and 11 months.

Is a lump sum better than monthly extras?

A lump sum paid now saves more than the same total spread over later months, because it reduces the balance sooner.

Can I enter 0?

Yes; then nothing is saved and the payoff stays at the months left.

in p | Loan balance | $ | 25000 | 1 | 100000000
in apr | Interest rate (APR) | % | 7.5 | 0.01 | 100
in n | Months left | months | 60 | 1 | 600
in x | Extra each month | $ | 100 | 0 | 100000000
out ms | Months saved | months | n - ceil(round(-ln(1 - (apr / 1200) * p / (p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -n) + x)) / ln(1 + apr / 1200), 6)) | 0
out nn | New payoff time | months | n - ms | 0
out sav | Interest saved | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -n) * n - (p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -n) + x) * (nn - 1) - (p * (1 + apr / 1200) ^ (nn - 1) - (p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -n) + x) * ((1 + apr / 1200) ^ (nn - 1) - 1) / (apr / 1200)) * (1 + apr / 1200) | 2