Method
Equal-cash comparison and estimated APR
Used by Which offer really costs less?. The worked example is the same fixture our tests check on every release.
Why equal cash
Two offers with the same amount on the note are not the same loan if one deducts a fee from the money you receive. The fair comparison fixes the cash in hand and asks what each offer costs to deliver it. So an offer with a deducted fee is grossed up:
note principal = (cash needed + flat fee) ÷ (1 − fee percent) fee deducted from proceeds note principal = cash needed × (1 + fee percent) + flat fee fee added to the balance
The payment and total of payments then follow the amortization method, and the cost of borrowing is the total of payments minus the cash received.
Worked example
You need $10,000.00 over 36 months. Offer A: 12% with a 5% fee deducted. Offer B: 14% with no fee.
| A | B | |
|---|---|---|
| Note principal | $10,526.32 | $10,000.00 |
| Cash received | $10,000.00 | $10,000.00 |
| Monthly payment | $349.62 | $341.78 |
| Total of payments | $12,586.48 | $12,303.95 |
| Estimated APR | 15.61% | 14.00% |
| Cost of borrowing | $2,586.48 | $2,303.95 |
B costs $282.53 less over the full term, even though its rate is two points higher.
B costs about $282.53 less over the full term. Estimated APR uses a regular-period cash-flow calculation and is not a legally authoritative disclosure.
Estimated APR
The estimated APR is the annual rate at which the present value of all the payments equals the cash received. We solve for the monthly rate by bisection and multiply by twelve. It is the same idea as the APR on a Truth in Lending disclosure, but the disclosure is computed by the lender under Regulation Z on the actual contract dates and fees, so it is the authoritative figure. Ours is for comparison.
Cost of leaving early
Most loans are paid off or refinanced before the last payment. After m payments, the cost of borrowing so far is the payments made plus the balance still owed minus the cash received. A deducted fee is sunk on day one, which is why a fee-plus-low-rate offer is often more expensive if you leave in the first year or two even when it is cheaper over the full term. The tool shows this at months 6, 12 and 24 and as a curve.
Reviewed 5 September 2026. No corrections since. Any change to this method is dated here and in the corrections log.