calculate-loan

04 Payoff, extra payments and refinance

Refinance Calculator: New Payment, Monthly Saving and Break-Even

Calculator No. 04-0030 · Updated · Formula and assumptions shown below

Monthly saving $28.00
New monthly payment
$469.70
Level-payment formula, rounded to the cent
Months to recover the fees
11 months
Whole months, rounded up
Total saved over the life of the loans
$1,044.00
From the formula below, to the cent
You enter
Current balance ($), Current APR (%), Months left on the current loan (months), New APR (%), New term (months), Refinance fees ($)
You get
Monthly saving ($), New monthly payment ($), Months to recover the fees (months), Total saved over the life of the loans ($)
Rounding
2 dp · 0 dp

Estimate for education, not financial advice. The result follows from the numbers you enter and the formula shown. It is not a quote or an offer, and it does not include fees, taxes or insurance unless the calculator asks for them. Ask your lender for the exact figures.

This calculator compares keeping a loan with refinancing it. Enter the current balance, its APR and months left, the new APR and term, and the fees to refinance; you get the monthly saving, the new payment, how many months the saving takes to pay back the fees, and the difference in the total you would pay.

Formula

Each payment uses M = B × r ÷ (1 − (1 + r)−n) with its own rate and term. Monthly saving = old payment − new payment. Break-even = fees ÷ monthly saving, rounded up. Total saved = old payment × months left − (new payment × new term + fees).

Worked Example

$20,000 left at 9% with 48 months to go; refinance at 6% for 48 months with $300 of fees.

  1. Old payment = 20,000 × 0.0075 ÷ (1 − 1.0075−48) = 497.70
  2. New payment = 20,000 × 0.005 ÷ (1 − 1.005−48) = $469.70
  3. Monthly saving = 497.70 − 469.70 = $28.00
  4. Break-even = 300 ÷ 28.00 = 11 months
  5. Total saved = 497.70 × 48 − (469.70 × 48 + 300) = $1,044.00

Assumptions

  • The payment is rounded to the cent and totals use the rounded payment; a lender’s final payment 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 balance refinanced equals the current balance; fees are paid in cash, not added to the loan.
  • No prepayment penalty on the old loan.

How to read the result

If the new term is longer than the months left, the payment can fall while the total paid rises: look at the last result as well as the monthly saving. If the saving is zero or negative, the break-even shows “Cannot compute”.

Limits and common mistakes

  • Fees rolled into the new loan raise its balance; add them to the balance and set fees to 0 to see that case.
  • Your lender’s quote and disclosure are the source of the new rate and fees.

Frequently Asked Questions

When does a refinance pay off its fees?

When the monthly savings have added up to the fees: here after 11 months ($28.00 a month against $300).

Can a lower payment cost more overall?

Yes, if the new term is much longer than the time left on the old loan.

Does this work for a mortgage?

Yes, the arithmetic is the same; enter months (for example 300 for 25 years).

Formula used
in b | Current balance | $ | 20000 | 1 | 100000000
in r1 | Current APR | % | 9 | 0.01 | 100
in m1 | Months left on the current loan | months | 48 | 1 | 600
in r2 | New APR | % | 6 | 0.01 | 100
in m2 | New term | months | 48 | 1 | 600
in c | Refinance fees | $ | 300 | 0 | 100000000
out sv | Monthly saving | $ | round(b * (r1 / 1200) / (1 - (1 + r1 / 1200) ^ -m1), 2) - round(b * (r2 / 1200) / (1 - (1 + r2 / 1200) ^ -m2), 2) | 2
out p2 | New monthly payment | $ | round(b * (r2 / 1200) / (1 - (1 + r2 / 1200) ^ -m2), 2) | 2
out be | Months to recover the fees | months | ceil(round(c / sv, 6)) + 0 * sqrt(sv) | 0
out td | Total saved over the life of the loans | $ | (p2 + sv) * m1 - p2 * m2 - c | 2

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Photo collage: two plain envelopes side by side on a wooden table, and a close-up of a fountain pen.
Save this page: a 1000 × 1500 image of Refinance Calculator: New Payment, Monthly Saving and Break-Even.

Method: the standard loan formula for this calculation, fixed rate and monthly compounding unless stated, rounded as each result states. Not financial advice; no lender, rate or product is recommended. See formulas and assumptions, the disclaimer or report an error.

More in this section

The whole Payoff, extra payments and refinance section →