APR Calculator
This APR calculator reveals the true annual cost of a loan once upfront fees are folded in, which is almost always higher than the quoted nominal interest rate. It first computes your monthly payment from the stated rate, then solves for the single rate at which the present value of those payments equals the amount you actually receive after fees are deducted. That solved rate is the APR, the figure lenders must disclose so borrowers can compare loans on an apples-to-apples basis.
Formula
Solve for i: (P − F) = M · (1 − (1 + i)^−n) / i, then APR = i × 12
- P
- Loan amount before fees
- F
- Total upfront fees and closing costs
- M
- Monthly payment based on the nominal rate
- i
- Monthly APR solved so payments discount to the net loan
- n
- Total payments = years × 12
How it works
- Enter the loan amount, the nominal annual interest rate, the term in years, and the total upfront fees or closing costs.
- The calculator derives the monthly payment from the stated rate and term, then treats the net loan (amount minus fees) as the cash you really borrow.
- Using a numeric search, it finds the monthly rate whose present value of payments equals that net loan, multiplies by twelve, and reports the APR alongside the monthly payment and the total cost including fees.
Worked example
A $200,000 loan at a 6% nominal rate over 30 years with $5,000 in fees.
- Monthly payment at 6% over 360 months = $1,199.10.
- Net loan received = 200,000 − 5,000 = $195,000; solve for the rate that makes $1,199.10 for 360 months worth $195,000 today.
- That monthly rate annualizes to about 6.24%, and total cost = 1,199.10 × 360 + 5,000 = $436,676.38.
The APR is about 6.24%, higher than the 6% nominal rate, with a monthly payment of $1,199.10 and a total cost of roughly $436,676.38 including the $5,000 in fees.
Frequently asked questions
- Why is the APR higher than the interest rate?
- Because fees reduce the cash you actually receive while your payments stay the same. Spreading those upfront costs across the loan effectively raises the rate you pay, so the APR exceeds the quoted nominal rate whenever fees are charged.
- What happens if I enter zero fees?
- With no fees, the net loan equals the loan amount and there is nothing extra to amortize, so the APR equals the nominal interest rate you entered. APR and nominal rate diverge only when upfront costs exist.
- Does APR include every possible loan cost?
- Only the upfront fees you enter. Some charges such as certain third-party costs or optional insurance may be excluded by lenders, so always confirm which fees are bundled into a disclosed APR before comparing offers.