Estimate nominal APR for one advance and equal monthly payments, or estimate a prepaid-fee allowance at a target APR. The first payment is exactly one month after the advance. This simplified model does not certify a lending disclosure or classify fees; balloons and irregular cash flows are excluded.
Loan APR Formula
APR relates the amount the borrower actually receives to the timing and amount of the required payments. For equal monthly payments, the periodic rate is the value of r that satisfies:
N = M * [1 - (1 + r)^(-n)] / r APR = 12 * r * 100
Variables:
- N is the net amount received after prepaid finance charges
- M is the monthly payment
- r is the monthly actuarial rate
- n is the number of monthly payments
- APR is the annual percentage rate
The calculator first determines the payment from the note rate unless an actual lender-quoted payment is entered. It then solves the present-value equation for r. In target-APR mode, the same equation is rearranged to find the amount of prepaid fees that produces the selected APR.
How Fees Affect Loan APR
Fees have the greatest APR impact when they are large relative to the amount borrowed or when the loan term is short.
| Loan amount | Note rate | Term | Prepaid fees | Estimated effect |
|---|---|---|---|---|
| $20,000 | 8% | 60 months | $0 | APR is close to the note rate |
| $20,000 | 8% | 60 months | $500 | APR rises because net proceeds fall |
| $20,000 | 8% | 36 months | $500 | Fee has a larger annualized effect |
| $20,000 | 8% | 84 months | $500 | Fee is spread across more periods |
Example Problems
Example 1: Estimate APR with an origination fee.
A $20,000 loan has an 8% note rate, a 60-month term, and $500 in prepaid finance charges. The scheduled payment is calculated on $20,000, but the borrower receives only $19,500. The calculator solves for the monthly rate that makes the present value of the payments equal $19,500, then multiplies that rate by 12.
Example 2: Find the fee limit for a target APR.
Enter the amount, note rate, payment, term, and a target APR of 10%. The calculator discounts the payment stream at the target monthly rate. The difference between the face amount and that present value is the estimated maximum prepaid fee.
Frequently Asked Questions
Why is APR higher than the interest rate?
The note rate measures interest on the loan balance. APR is broader and can include certain fees or charges required to obtain the credit, so the amount received is lower relative to the payments made.
Is this the same as the lender’s disclosed APR?
It is an actuarial estimate for equal monthly periods. Official disclosures follow legal classification and timing rules for particular charges, so use the lender’s Truth in Lending disclosure as the controlling figure.
What is the effective annual rate?
The effective annual rate compounds the solved monthly rate for 12 periods. APR normally annualizes the periodic rate without that compounding, which is why the two figures can differ.
