APR Calculator: The True Rate of a Loan With Fees

This calculator works out the APR of a loan when fees are paid up front or taken out of the money you receive. Enter the loan amount, the fees, the interest rate on the note and the term in months; you get the APR including the fees, the monthly payment, the cash you actually receive and the total cost of credit.

Formula

The payment M is set on the full amount P at the note rate: M = P × r ÷ (1 − (1 + r)⁻ⁿ). The APR is the yearly rate i that makes the same payments repay only the cash received: P − fees = M × (1 − (1 + i ÷ 12)⁻ⁿ) ÷ (i ÷ 12). It is solved numerically by repeatedly halving the interval that contains the answer.

Worked Example

A $10,000 loan at a 9% note rate for 36 months, with $500 of fees.

1. M = 10,000 × 0.0075 ÷ (1 − 1.0075⁻³⁶) = $318.00
2. Cash received = 10,000 − 500 = $9,500.00
3. Solve 9,500 = 318.00 × (1 − (1 + i ÷ 12)⁻³⁶) ÷ (i ÷ 12): i = 12.542%
4. Total cost of credit = 318.00 × 36 − 10,000 + 500 = $1,948.00

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 rate, 36 equal monthly payments in the example.
• All fees are paid at the start (up front or deducted from the loan).
• The APR here is the actuarial yearly rate (monthly rate × 12). Which fees a lender must include in its disclosed APR is set by law and may differ.

How to read the result

The gap between the note rate and the APR is the cost of the fees spread over the term. The same fee raises the APR more on a short loan than on a long one.

Limits and common mistakes

• Fees must be smaller than the loan amount.
• Compare offers on APR and total cost, not on the note rate alone.
• Your lender’s disclosure is the official APR for your loan.

Frequently Asked Questions

What is the APR of a 9% loan with a $500 fee on $10,000 over 3 years?

About 12.54%.

Why is the APR higher than the interest rate?

You repay on $10,000 but receive only $9,500, so the effective rate on the money you got is higher.

Does the fee matter less on a long loan?

Yes. Spread over more months, it adds less to the yearly rate.

in p | Loan amount | $ | 10000 | 1 | 100000000
in fee | Fees (up front or from the loan) | $ | 500 | 0 | 100000000
in nr | Note interest rate | % | 9 | 0.01 | 100
in n | Term | months | 36 | 1 | 600
out apr | APR including fees | % | rate(n, round(p * (nr / 1200) / (1 - (1 + nr / 1200) ^ -n), 2), p - fee) * 1200 | 3
out pmt | Monthly payment | $ | round(p * (nr / 1200) / (1 - (1 + nr / 1200) ^ -n), 2) | 2
out cash | Cash you receive | $ | p - fee | 2
out cost | Total cost of credit (interest + fees) | $ | pmt * n - p + fee | 2