APR Calculator Uncover the true cost of borrowing — with fees, compounding, and real 2025 benchmarks. Loan AP...
APR Calculator
Uncover the true cost of borrowing — with fees, compounding, and real 2025 benchmarks.
APR Formula (Loan)**:
APR is the interest rate that makes the **present value of all payments** equal to the **net loan amount (principal − fees)**.
$$ \text{Loan} - \text{Fees} = \sum_{t=1}^{n} \frac{PMT}{(1 + \frac{APR}{12})^t} $$
Example** ($30K auto loan @ 7.2%, 72 mos, $595 fee): • Monthly payment = **$514.85** • Net loan = $30,000 − $595 = **$29,405** • APR = **8.12%** (solve for rate where PV of payments = $29,405)
✅ Pro Tip**: APR includes *upfront* fees but excludes *contingent* fees (late, prepayment). Always verify it on the Loan Estimate (LE) form.
⚠️ Avoid these misleading practices:
- Teaser APRs** — “2.9% for 12 mos” → 19.99% after (common in credit cards)
- “No-cost” refinance traps** — $0 upfront, but +0.5% rate for 10+ years = $15K+ extra interest
- Hidden back-end fees** — $395 “document prep” buried in closing
- APR on balloon loans** — artificially low because payment shock isn’t modeled
✅ Smart Borrower Tips**:
- Compare **APR**, not interest rate — it’s the only apples-to-apples metric
- Ask: “What’s the APR on the Loan Estimate?” — lenders must disclose it
- For credit cards: use effective APR = (1 + r/n)n − 1 for true cost
| Loan | Rate | Fees | APR |
|---|---|---|---|
| $250K Mortgage | 6.80% | $3,500 | 7.03% |
| $30K Auto | 7.20% | $595 | 8.12% |
| $10K Personal | 14.2% | $500 | 15.9% |
| $5K Credit Card | 20.4% | — | 22.53%* (daily) |
*Effective APR due to daily compounding
📉 Mortgage Points Math**:
- 1 point = $2,500 on $250K loan = −0.25% rate
- New rate: 6.55%, new APR: 6.78% (vs. 7.03% without points)
- Break-even: ($3,500 − $2,500) / ($162 savings/mo) = **6.2 months**
➡️ Loan APR
“$30K loan @ 7.2% + $595 fee — what’s the APR?” → **8.12%**
➡️ Credit Card
“20.4% daily — what’s the effective APR?” → **22.53%**
➡️ Mortgage APR
Model points, fees, PMI — see true APR and break-even.
➡️ Effective APR
Compare nominal vs. effective: 20.4% daily = 22.53% effective
Note: Uses Newton-Raphson solver for loan APR. Credit card APR uses exact compounding formula.