Debt
APR (Annual Percentage Rate)
The true annual cost of borrowing, including interest rate and fees, expressed as an annual percentage.
Formula
APR ≈ Nominal Rate + (Total Fees ÷ Loan Amount) ÷ Years
Variables
Nominal Rate- Stated annual interest rate
Total Fees- Origination, appraisal, title, etc.
Loan Amount- Principal borrowed
Years- Loan term in years
Worked Example
Scenario: $200,000 loan, 5% rate, $5,000 fees, 30 years: APR ≈ 5% + (5,000 ÷ 200,000) ÷ 30 ≈ 5.00% + 0.83% = 5.83%.
Steps:
- Identify nominal (stated) rate
- Sum all fees (origination, title, appraisal, insurance, etc.)
- Divide fees by principal
- Divide result by years
- Add to nominal rate
When to Use This Formula
- Compare true cost of loans
- Understand fee impact on effective rate
- Make informed borrowing decisions
Limitations & Assumptions
- Simplified formula; actual APR calculation is more complex
- Does not account for prepayment
- Assumes fees are paid upfront, not rolled into loan
Common Questions
Why is APR higher than the stated rate?
Because fees increase the true cost of borrowing. The interest rate alone does not reflect all charges.
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Reference note: This is an educational mathematical reference. The formula's applicability depends on assumptions, market conditions, and use case. Always verify results independently and consult domain experts for decisions.