APR Calculator: Effective Rate & Cost Model

• Worked example:
  Borrow $300,000 with $8,000 in fees paid from proceeds → amount financed is $292,000. The payment still prices off the full $300,000 at 6.5%, but the equivalent annual cost on $292,000 lands near 6.78%. That 0.28% spread is what fees did.
• What this misses:
  Appraisal, title insurance, recording fees, and taxes (excluded from APR under TILA). Short hold periods where upfront fees matter more than long-run APR. This is a comparison tool, not a substitute for the official Loan Estimate.
• Comparing fairly:
  Same product and term only: 30-year fixed against 30-year fixed. Pull Loan Estimates from three or more lenders on the same day; rates move daily and a 24-hour gap can scramble the comparison. Spread under ~0.25% is usually clean on mortgages; above ~0.8% deserves a second quote.

Amount financed and iteration

• Amount Financed:
  Loan Principal minus Prepaid Finance Charges. If you borrow $300,000 but pay $8,000 in fees from proceeds, your Amount Financed is $292,000. This is the "real" loan amount for APR purposes.
• The Iterative Solution:
  APR solves for: What rate (r) makes the present value of all payments equal the Amount Financed?

  $$\text{Amount Financed} = \text{Payment} \times \frac{1 - (1+r)^{-n}}{r}$$

  This requires numerical methods (bisection, Newton-Raphson) since there's no closed-form solution.
• Why Fees Increase APR:
  By reducing Amount Financed while keeping Payment the same, fees force a higher rate to balance the equation. $300K loan at 6.5% = $1,896/month. But if Amount Financed is $292K (after fees), the rate that produces $1,896/month is ~6.78%, that's your APR.
• Term Sensitivity:
  Shorter loans have higher APR impact from fees because the same fees are spread over fewer payments. $8,000 in fees on a 30-year loan adds ~0.25% to APR. On a 15-year loan, the same fees add ~0.45% to APR.
• Scope & Limits:
  Uses iterative numerical methods to solve for APR from loan amount, payment, term, and fees. Standard formulas; results are estimates. All calculations run in your browser; no data is sent to servers. Verify with a qualified professional before making significant borrowing decisions.

Included vs excluded (TILA)

• Origination Fees (Included):
  Lender profit for processing your loan. Typically 0.5-1% of loan amount. On $300,000: $1,500-$3,000. This is pure lender revenue and often negotiable, especially with strong credit or competing offers.
• Discount Points (Included):
  Prepaid interest to "buy down" your rate. Each point = 1% of loan amount = approximately 0.25% rate reduction. Points make sense if you'll keep the loan past break-even (typically 5-7 years for 1-2 points).
• PMI Premiums (Included):
  Required with less than 20% down payment. Monthly PMI of $150 on a 30-year loan adds ~0.3% to APR. Upfront PMI premium (common with FHA) has even larger APR impact. PMI drops off at 20% equity. APR assumes full-term PMI.
• Mortgage Broker Fees (Included):
  If using a broker, their compensation is a finance charge. Can be paid by borrower, lender, or split. "No-cost" broker loans often have higher rates, the broker fee is built in.
• NOT Included in APR:
  Appraisal ($400-700), title insurance ($1,000-3,000), attorney/settlement fees, recording fees, property taxes, homeowner's insurance. These costs exist whether you finance or pay cash, so they're excluded from APR.

Same product, same day

• Same Loan Type Only:
  Compare 30-year fixed APR to 30-year fixed APR. A 15-year loan will always have lower APR than a 30-year (same fees, shorter term = less interest). ARM APRs use initial rate only, not comparable to fixed rates.
• The Short-Term Exception:
  If you'll refinance or sell within 5 years, minimize upfront fees even if the rate is higher. A 6.75% rate with $2,000 in fees beats 6.25% with $8,000 in fees if you're moving in 3 years.
• The Loan Estimate Document:
  Within 3 days of application, lenders must provide a Loan Estimate with standardized APR disclosure. Get Loan Estimates from 3+ lenders on the same day for accurate comparison (rates change daily).
• Beware "No Closing Cost" Loans:
  These roll fees into the loan balance or increase the rate. A "no cost" loan at 6.75% might have higher APR than a "normal" loan at 6.25% with $5,000 in fees. Calculate both scenarios.

Typical spreads

• Mortgages:
  Typical spread: 0.1-0.5% above rate. Highest fee complexity (points, PMI, origination). Most regulated and standardized APR disclosure. 30-year conventional: expect 6.5-7.5% APR in current market.
• Auto Loans:
  Typical spread: 0-0.3% for direct lenders, 1-2% for dealer financing. Dealers often mark up "buy rate" from banks. A credit union at 6.5% APR vs. dealer at 8.5% APR on a $35,000 car = $2,400 savings over 5 years.
• Personal Loans:
  Typical spread: 0-1% (origination fees common). No collateral means higher base rates (8-20%+ depending on credit). APR is usually close to stated rate unless there's an origination fee (often 1-5% of loan amount).
• Credit Cards:
  APR equals stated rate for purchases (no additional fees). But cash advance APR is higher, and balance transfer APR may be promotional. Watch for "penalty APR" (25-29%) triggered by late payments.