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.
Solved Examples
Example 1: Calculating APR on a mortgage with fees
Solution:
Loan Amount = $300,000, Nominal Rate = 6.5%, Term = 30 years
Fees: Origination = $3,000, Appraisal = $500, Title = $1,200, Other = $800
Total Fees = $5,500
Effective Loan Amount received = $300,000 − $5,500 = $294,500
Monthly Payment (based on $300,000 at 6.5%) = $1,896.20
APR = rate that makes $294,500 = PV of $1,896.20/month for 360 months
Using iterative calculation: APR ≈ 6.66%
Answer: APR = 6.66% vs nominal 6.5% — fees add 0.16% to true cost
Example 2: Comparing two loan offers using APR
Solution:
Loan needed: $200,000 for 30 years
Offer A: 6.25% rate, $8,000 in fees → Monthly = $1,231.43, APR = 6.49%
Offer B: 6.75% rate, $2,500 in fees → Monthly = $1,297.20, APR = 6.86%
Offer A total cost = $1,231.43 × 360 + $8,000 = $451,315
Offer B total cost = $1,297.20 × 360 + $2,500 = $469,492
Offer A saves $18,177 over the full term despite higher upfront fees
Answer: Offer A (APR 6.49%) is cheaper long-term, but Offer B wins if selling within 5 years
Example 3: APR for a personal loan with origination fee
Solution:
Loan = $15,000, Nominal Rate = 9%, Term = 3 years (36 months)
Origination Fee = 3% = $450, deducted from disbursement
You actually receive: $15,000 − $450 = $14,550
Monthly Payment (based on $15,000 at 9%) = $477.00
APR: solve for rate where PV of $477 × 36 = $14,550 → APR ≈ 10.12%
Answer: APR = 10.12% — significantly higher than the advertised 9% rate
Practice Questions
Try these on your own:
- A $250,000 mortgage at 6% with $4,000 in fees for 30 years. What is the APR? (Answer: ≈6.14%)
- Loan A: 5.5% + $6,000 fees vs Loan B: 6.0% + $1,500 fees on $200,000 for 30 years. Which has lower APR? (Answer: Loan A ≈ 5.72%; Loan B ≈ 6.07%)
- A credit card charges 1.5% per month. What is the APR and effective APY? (Answer: APR = 18%; APY = 19.56%)
- A $10,000 loan at 8% for 2 years with a $500 origination fee. What is the APR? (Answer: ≈10.43%)
- You pay 2 discount points ($4,000) on a $200,000 loan at 5.75% for 15 years. What is the APR? (Answer: ≈6.01%)
Common Mistakes to Avoid
The most common mistake is comparing the nominal interest rate instead of APR when shopping for loans. Two loans with the same rate can have very different APRs due to fee differences. Another frequent error is confusing APR with APY (Annual Percentage Yield) — APR does not account for compounding within the year, while APY does. For example, a 12% APR compounded monthly has an APY of 12.68%. Many borrowers fail to realize that APR assumes you keep the loan for its full term — if you pay off early, a loan with higher fees but lower rate may cost more. Additionally, some advertised APRs exclude fees like title insurance or escrow. Finally, variable-rate loans show APR based on current rates, but your actual cost changes as rates fluctuate.
Key Takeaways
- APR includes interest rate PLUS fees and points, giving the true annual cost of borrowing.
- Always compare APR (not just interest rate) when choosing between loan offers.
- Higher fees increase APR even when the nominal rate is low — evaluate total cost over your expected holding period.
- APR assumes full-term holding — shorter periods favor low-fee, higher-rate loans.
- APR ≠ APY: APR ignores intra-year compounding, APY accounts for it (APY is always ≥ APR).
- Federal law (Truth in Lending Act) requires lenders to disclose APR for easier comparison shopping.