True APR Calculator

Reviewed by: Charles Kim, Senior Lending Analyst
Expert in regulatory compliance (TILA) and analyzing the true cost of consumer debt.

The Annual Percentage Rate (APR) is the true cost of borrowing, which includes the nominal interest rate plus any mandatory loan fees. Use this calculator to see how much your lender’s upfront fees (like origination or documentation fees) increase your actual borrowing cost.

The calculation is complex because it requires finding the interest rate that makes the loan’s stated monthly payment equal to the loan principal minus the fees.

True APR (Annual Percentage Rate) Calculator

Understanding the APR Calculation

The APR is calculated by finding the discount rate that equates the present value of the stream of loan payments to the actual amount of loan proceeds received by the borrower. Because this calculation cannot be solved algebraically, it requires iterative approximation (trial and error) to find the correct rate.

$$ \text{Payment} = (\text{Principal} – \text{Fees}) \frac{r(1+r)^n}{(1+r)^n – 1} $$
Where $\text{r}$ is the True Monthly Rate (APR / 12 / 100) that must be solved for.
Source: Federal Reserve (Regulation Z – Truth in Lending Act)
  • Principal: The amount you initially applied for.
  • Fees: Upfront, mandatory charges (e.g., origination fees) that you pay or that are deducted from the loan amount.
  • True APR: The annual rate that reflects the true cost of the loan proceeds you actually receive.

Related Calculators for Loan Cost

Why APR is Higher Than the Interest Rate

The core difference is that the interest rate only accounts for the percentage charged on the principal. The APR, by contrast, includes all mandatory fees. When a lender deducts fees upfront, you receive less cash, but you are still making payments based on the full initial loan amount. This mathematical reality forces the effective interest rate (the APR) to be higher than the stated rate.

The higher the fees or the shorter the loan term, the greater the difference between the APR and the stated interest rate. For consumers, the APR is the single most important number to compare when shopping for credit.

Frequently Asked Questions (FAQ)

Which fees must be included in the APR?

Generally, all fees required by the creditor and paid by the consumer to get the loan (like origination, closing fees, or discount points) must be included. Fees for optional services (like optional credit life insurance) are not included.

Why is the calculation so complex?

Because the true interest rate ($r_{true}$) is buried deep inside the amortization formula. To solve for it, the computer must essentially try hundreds of different rates until it finds the one that exactly matches the monthly payment derived from the stated interest rate, but applied to the net loan amount received.

If the fee is zero, will the APR equal the interest rate?

Yes, if there are absolutely no mandatory fees (including closing costs or origination charges), then the APR will be equal to the stated nominal interest rate.

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