APR Calculator

Calculate the effective Annual Percentage Rate (APR) including origination and other fees to understand the true cost of your loan.

About this Calculator

Calculate the effective Annual Percentage Rate (APR) including origination and other fees to understand the true cost of your loan.

Formula & Calculations

Formula

Nominal Payment = P × [i(1+i)^n] / [(1+i)^n - 1]; Effective APR solves for rate where PV of payments equals Loan Amount minus Fees

Where:

P=Loan principal amount
r=Nominal annual interest rate
n=Loan term in years
OF=Origination fee charged by the lender
OF_other=Other miscellaneous fees
NP=Net proceeds = Loan Amount minus total fees
APR=Effective annual percentage rate accounting for all fees

Assumptions

APR calculation uses an iterative binary search to find the rate that equates loan payments to net proceeds.
All fees are deducted from the loan amount at origination.
Monthly compounding is assumed in the payment calculation.
The Truth in Lending Act requires lenders to disclose APR alongside the nominal rate.

Calculation Examples

Example 1

Inputs:Loan: $25,000, Nominal Rate: 5%, Term: 5yr, Origination: $250, Other Fees: $150

Result:Monthly: $471.78, Effective APR: 5.66%, Total Cost: $28,306.80

Fees of $400 add about 0.66% to the effective APR. You receive $24,600 but repay based on the full $25,000.

Example 2

Inputs:Loan: $10,000, Nominal Rate: 7%, Term: 3yr, Origination: $500, Other Fees: $100

Result:Monthly: $308.77, Effective APR: 11.20%, Total Cost: $11,115.72

High fees relative to a smaller loan amount dramatically increase the effective APR from 7% to over 11%.

Example 3

Inputs:Loan: $300,000, Nominal Rate: 6.5%, Term: 30yr, Origination: $3,000, Other Fees: $2,000

Result:Monthly: $1,896.20, Effective APR: 6.68%, Total Cost: $682,632

On a large mortgage, $5,000 in fees only adds about 0.18% to the effective APR due to the long amortization period.

Frequently Asked Questions

What is the difference between APR and interest rate?

The interest rate (nominal rate) is the cost of borrowing the principal. The APR (Annual Percentage Rate) includes the interest rate plus lender fees and other charges, giving a more complete picture of the loan's true annual cost. Federal law requires lenders to disclose both rates.

Why would a loan's APR be significantly higher than its interest rate?

When fees are high relative to the loan amount, the APR will be noticeably higher. This is common with small loans, short-term loans, or loans with high origination fees. On large, long-term loans like mortgages, the APR is usually only slightly above the nominal rate.