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Instrument MI-02-098 · Finance

Car Refinance Calculator

Enter what you still owe, your current rate, and the offer on the table — the instrument holds the term steady and shows exactly what the rate change alone is worth, to the cent.

Instrument MI-02-098
Sheet 1 OF 1
Rev A
Verified
Type 02 — Auto Finance SER. 2026-02098

Monthly savings

$32.92

old PMT = P·r_old(1+r_old)^N ⁄ ((1+r_old)^N − 1)

$572.40 Current payment
$539.48 New payment
The working Every figure verified twice
  1. oldPayment = 18000·(9 ⁄ 100 ⁄ 12)·(1 + 9 ⁄ 100 ⁄ 12)^36 ⁄ ((1 + 9 ⁄ 100 ⁄ 12)^36 − 1) = 572.40
  2. newPayment = 18000·(5 ⁄ 100 ⁄ 12)·(1 + 5 ⁄ 100 ⁄ 12)^36 ⁄ ((1 + 5 ⁄ 100 ⁄ 12)^36 − 1) = 539.48
  3. savings = 18000·(9 ⁄ 100 ⁄ 12)·(1 + 9 ⁄ 100 ⁄ 12)^36 ⁄ ((1 + 9 ⁄ 100 ⁄ 12)^36 − 1) − 18000·(5 ⁄ 100 ⁄ 12)·(1 + 5 ⁄ 100 ⁄ 12)^36 ⁄ ((1 + 5 ⁄ 100 ⁄ 12)^36 − 1) = 32.92
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

Refinancing a car loan means a new lender pays off what remains of the old one and issues a fresh loan for that same outstanding balance, at a new rate, over a term the borrower can choose. This instrument fixes that term to whatever is left on the original loan, so the only thing allowed to change between the two payments is the rate — which is what makes the resulting figure a clean read on the rate's value, rather than a number tangled up with a separate decision about spreading payments out further.

Under the hood it runs the same amortizing-payment formula twice against the identical remaining balance and month count — once at the old rate, once at the new one — and reports the gap. People end up looking at this after a credit score climbs since the original purchase, after a credit union runs a rate-beat offer, or after realizing the loan was arranged through a dealer's finance office at a rate marked up above what the bank behind it would have approved on its own.

The figure excludes anything a new lender charges to originate the swap — a title transfer fee, a lien filing fee, occasionally an application fee — and it says nothing about a prepayment penalty the old loan might carry. It also assumes the new offer keeps the same remaining term; if the offer instead resets the clock to a fresh 60 or 72 months, the payment drops for a second reason that has nothing to do with the rate, and this sheet does not separate that reason out unless you run it twice.

PMTold=Prold(1+rold)N(1+rold)N1\text{PMT}_{old} = \frac{P \cdot r_{old}(1+r_{old})^{N}}{(1+r_{old})^{N} - 1}PMTnew=Prnew(1+rnew)N(1+rnew)N1\text{PMT}_{new} = \frac{P \cdot r_{new}(1+r_{new})^{N}}{(1+r_{new})^{N} - 1}Savings=PMToldPMTnew\text{Savings} = \text{PMT}_{old} - \text{PMT}_{new}
P — Remaining balance, $ · r_old — Current rate, % divided by 12 and by 100 · r_new — New offered rate, % divided by 12 and by 100 · N — Remaining term, months, held fixed for both payments · Old PMT, New PMT — the two payments the formula compares · Savings — Old PMT minus New PMT.
  • Enter what's currently owed under Remaining balance, $ — pull this from your latest loan statement, not the amount you originally borrowed.
  • Set Current rate, % to your existing loan's APR and Remaining term, months to however many payments are left on it.
  • Enter the rate you've been offered under New offered rate, %.
  • Compare Current payment against New payment, and read Monthly savings for the exact difference between them.

Worked example — an $18,000 balance moving from 9% to 5%

Take a remaining balance of $18,000 (Remaining balance, $) with 36 months left (Remaining term, months) at a current rate of 9% (Current rate, %). Running those three figures through the old-rate formula returns a current payment of $572.40 — close to what an existing loan statement would already show for that balance, rate, and length.

A credit union then offers 5% (New offered rate, %). Holding the balance and the remaining term exactly the same and swapping in only the new rate gives a new payment of $539.48 — a Monthly savings of $32.92, or roughly $1,185 recovered across the 36 payments left on the loan, entirely from the lower rate and nothing else.

Questions

Why does the calculator keep the loan term the same when I refinance?

Holding Remaining term, months fixed isolates what the rate change alone is worth. Many refinance offers also reset the clock to a fresh 60 or 72 months, which lowers the payment further but adds months of interest on a slowly shrinking balance. That is a term decision, not a rate saving, and mixing the two hides how much of any lower payment actually came from the better rate.

Does a lower rate always make refinancing worth doing?

Not automatically. Monthly savings shows the rate's value, but most lenders charge something to originate the new loan — a title transfer fee, a lien filing fee, sometimes an application fee — and the old loan may carry a prepayment penalty. Dividing any such cost by Monthly savings shows how many payments it takes to break even; this sheet only supplies the savings side of that comparison.

Why is my Current payment slightly different from what my loan statement shows?

Small gaps are normal. A statement may round differently, fold in a product like gap insurance or an extended warranty, or use a daily-interest accrual instead of the flat monthly rate this formula assumes. Enter Remaining balance, $ exactly as the statement shows it and the gap should stay within a few cents to a few dollars.

What if the new lender's offer also changes my remaining term?

Run it twice. Set Remaining term, months to the new lender's proposed length first to see the payment that offer actually produces, then set it back to your current loan's remaining months to see what the same rate would cost without extending anything. The difference between those two runs is the price of the longer term, kept separate from the rate benefit.

Who typically gets offered a car refinance?

Most often someone whose credit score improved since the original purchase, or whose loan was arranged through a dealer's finance office at a rate marked up above what the lender itself would have approved directly. A credit union or bank that did not write the original loan has no reason to preserve that markup, which is why refinance offers frequently beat a dealer-arranged rate.

Is this the same math as refinancing a mortgage?

The underlying formula is identical — the same fixed-installment amortization used for any loan — but the stakes differ. A car's collateral depreciates fast and the remaining term is short, so a car refinance is usually a same-term rate swap decided in weeks, while a mortgage refinance often resets to a fresh 15- or 30-year term and carries closing costs many times larger than anything an auto lender charges.

References

Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.