Annual percentage rate including fees.
PV_net = PMT × [1 − (1 + r)^(−n)] / r APR = r × m
APR is derived by solving for the interest rate r in the standard present-value-of-annuity equation where the present value equals the net loan proceeds (loan amount minus fees) rather than the full principal. Once the periodic rate is found, it is multiplied by the number of periods per year to obtain the nominal APR.
Because there is no closed-form algebraic solution, the calculator uses an iterative numerical method (Newton-Raphson or bisection) to solve for r. The resulting periodic rate is then annualized.
Note: Results are estimates based on inputs provided and may differ from the APR disclosed by a lender, which can vary depending on jurisdiction-specific rules and which fees are legally required to be included.
Step 1 — Monthly payment at 6.50% nominal rate: Monthly rate = 6.50% / 12 = 0.541667% PMT = 200,000 × [0.005417 / (1 − (1.005417)^(−360))] PMT = 200,000 × [0.005417 / 0.857981] ≈ $1,264.14 Step 2 — Net proceeds to borrower: PV_net = $200,000 − $3,000 = $197,000 Step 3 — Solve iteratively for periodic rate r such that: 197,000 = 1,264.14 × [1 − (1 + r)^(−360)] / r Iterative solution yields r ≈ 0.55036% per month Step 4 — Annualize: APR = 0.55036% × 12 ≈ 6.604%
Result: APR ≈ **6.60%** (compared to the nominal rate of 6.50%)
The APR of 6.60% is higher than the stated nominal rate of 6.50% because the $3,000 in fees effectively reduces the money you receive while keeping your payments the same. A higher APR relative to the interest rate signals greater fee costs. When comparing two loans, always choose the one with the lower APR — it represents the cheaper borrowing option over the full loan term, assuming you keep the loan to maturity.
The interest rate (also called the nominal rate) only accounts for the cost of borrowing the principal. The APR layers in mandatory lender fees, giving you a standardized measure to compare loans from different lenders on equal footing.
In the United States, lenders are required by the Truth in Lending Act (TILA) and Regulation Z to disclose the APR on consumer loans. The European Union uses APRC (Annual Percentage Rate of Charge) under the Mortgage Credit Directive, which follows a similar but not identical methodology.
Simply select the loan with the lower APR, assuming you will hold both loans to their full term. If you plan to pay off early, calculate the total interest and fees paid over your expected holding period for each loan instead, as APR assumes full-term repayment.
Personal loan APRs vary widely by credit score and lender. Borrowers with excellent credit (720+) may qualify for APRs of 7–12%, while those with fair credit may see APRs of 20–36% or higher. Always compare multiple lenders' APRs, not just their stated rates.
Paying discount points lowers your interest rate but increases upfront costs. This raises the APR relative to a no-point loan with a higher rate. Whether paying points is worthwhile depends on your break-even horizon — divide the upfront cost of points by the monthly savings to find how many months until you recoup the cost.
Credit card APR is calculated differently because there is no fixed loan term or amortizing payment schedule. Card APR is typically a daily periodic rate multiplied by 365. Our APR calculator is designed for installment loans (mortgages, auto, personal) with fixed payment schedules, not revolving credit.
APR (Annual Percentage Rate) is a nominal rate — it multiplies the periodic rate by the number of periods without compounding. APY (Annual Percentage Yield) accounts for the effect of compounding within the year. For loans, APR is the standard disclosure; for savings accounts, APY is used. APY will always be equal to or greater than APR for the same periodic rate.
Not necessarily. In the U.S., TILA/Regulation Z specifies which fees must be included in the disclosed APR. Certain third-party fees (appraisal, title insurance) are often excluded. The fees included can vary by loan type and jurisdiction, so our calculator lets you enter only the fees relevant to your comparison.
For large, long-term loans like mortgages, fees are spread across hundreds of payments. A $3,000 fee on a 30-year, $200,000 mortgage adds only about 0.10–0.15 percentage points to the APR. For short-term loans or smaller loan amounts, the same dollar fee can raise APR dramatically.
Generally yes — if you hold the loan to maturity. However, if you expect to refinance or sell within a few years, a loan with a slightly higher rate but fewer upfront fees (lower break-even period) may cost less overall. Use our calculator alongside a break-even analysis for the most informed decision.
In rare cases, yes — for example, if a lender pays borrower closing costs (lender credits). In such cases, the net proceeds are higher than the face loan amount, which mathematically lowers the APR below the nominal rate.
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