APR Calculator
Calculate the Annual Percentage Rate (APR) including fees and points. Compare the true cost of borrowing versus the nominal interest rate. See also Loan Calculator and Mortgage Calculator.
How to Calculate APR
APR (Annual Percentage Rate) represents the true annual cost of borrowing, including both the interest rate and any fees or points. While the nominal interest rate only reflects the cost of interest, APR factors in origination fees, discount points, closing costs, and other charges. This makes APR a better tool for comparing loan offers from different lenders, as it provides an apples-to-apples comparison of total borrowing costs.
APR Formula
APR is the rate (r) that satisfies:
(Loan Amount − Fees) = Payment × [(1 − (1 + r)^−n) / r]
Where:
Payment = Monthly payment based on nominal rate
r = Monthly APR rate (APR / 12 / 100)
n = Total number of payments
Solved iteratively using Newton's method
Example
Loan: $200,000 at 6% for 30 years
Fees: $3,000
Monthly Payment = $1,199.10 (based on 6% rate)
Net Amount Received = $200,000 − $3,000 = $197,000
APR = 6.131% (effective annual cost)
Difference: 6.131% − 6.000% = 0.131%
APR vs Interest Rate Reference
| Loan Amount | Rate | Fees | APR | Difference |
|---|---|---|---|---|
| $200,000 | 6% | $2,000 | 6.087% | +0.087% |
| $200,000 | 6% | $3,000 | 6.131% | +0.131% |
| $200,000 | 6% | $5,000 | 6.219% | +0.219% |
| $300,000 | 6.5% | $4,000 | 6.614% | +0.114% |
| $300,000 | 6.5% | $6,000 | 6.671% | +0.171% |
| $400,000 | 7% | $8,000 | 7.172% | +0.172% |
Frequently Asked Questions
What is the difference between APR and interest rate?
The interest rate is the cost of borrowing the principal amount. APR includes the interest rate plus all fees, points, and other costs associated with the loan, expressed as an annual percentage. APR is always equal to or higher than the interest rate and gives a more complete picture of borrowing costs.
Should I compare loans using APR or interest rate?
Use APR to compare loans from different lenders. A loan with a lower interest rate but high fees may have a higher APR than a loan with a slightly higher rate but lower fees. APR provides the true cost comparison. However, if you plan to pay off the loan early, the interest rate may matter more since you won't pay interest for the full term.
What fees are included in APR?
APR typically includes origination fees, discount points, mortgage broker fees, and certain closing costs. It generally does not include title insurance, appraisal fees, or home inspection costs. The exact fees included can vary by lender, so always ask for a detailed breakdown.
What are discount points?
Discount points are upfront fees paid to the lender to reduce the interest rate. One point equals 1% of the loan amount. For example, on a $200,000 loan, one point costs $2,000 and typically reduces the rate by 0.25%. Points increase the APR but lower the long-term interest cost.