APR Calculator

This APR calculator (also called an annual percentage rate calculator) converts a loan's sticker interest rate into its true yearly cost once fees are baked in. The two numbers are not the same, and lenders know most borrowers confuse them. The interest rate prices only the borrowed principal. The APR prices the interest plus origination fees, discount points, mortgage insurance, and other lender charges spread across the life of the loan. If you only compare interest rates when shopping lenders, you will routinely pick the more expensive offer.

1. Enter the loan amount. Use the amount financed, which is the principal written on the note before any fees are deducted. For a $200,000 mortgage, enter 200,000 even if the lender will net you less after closing costs.
2. Enter the nominal interest rate. This is the rate advertised in the ad, quote sheet, or Loan Estimate. It is the number used to calculate your monthly payment. Do not enter the APR here, that is what the calculator solves for.
3. Enter the loan term in months. 60 months for a typical auto loan, 360 months for a 30-year mortgage, 36 or 48 months for most personal loans.
4. Add the origination fee. Lenders charge 0.5% to 1% of the loan amount as an origination fee on mortgages and personal loans. On a $200,000 loan, that is $1,000 to $2,000.
5. Add other fees paid at closing. Application fees, underwriting fees, document prep, and lender-required third-party fees (credit report, flood certification) all belong here. Skip recurring costs like homeowner's insurance, property taxes, and optional items like extended warranties. Those are not included in APR by law.
6. Enter discount points. Each point costs 1% of the loan amount and usually buys down the rate by 0.25%. One point on $200,000 is $2,000 prepaid.

The result panel shows the nominal rate next to the APR, the gap between them (the "fee drag"), and your monthly payment, total interest, total fees, and total cost over the life of the loan. Use the APR, not the nominal rate, to compare loan offers from different lenders. A 6.5% loan with $6,000 in fees costs more over 30 years than a 6.75% loan with $500 in fees, and only the APR shows you that.

The exact APR formula has no closed-form algebraic solution, so lenders and calculators solve it iteratively. The calculator above uses Newton's method. Here is the underlying math, plus a simplified version you can do on paper.

1. Exact APR (what this calculator solves)

APR is the interest rate r where:

(Principal − Fees) = Payment × [1 − (1+r)^(−n)] ÷ r

Where:
r = monthly APR (APR ÷ 12)
n = number of payments
Payment = based on nominal interest rate

Solved numerically (Newton's method)
since r cannot be isolated algebraically.

2. Simplified APR (quick back-of-envelope)

APR ≈ (Total Finance Charges ÷ Loan Amount) ÷ Years × 100

Example: $25,000 auto loan, 5 years, 6.5% nominal,
         $500 origination fee
Monthly payment at 6.5% = $489.15
Total paid = 489.15 × 60 = $29,349
Total interest = 29,349 − 25,000 = $4,349
Total finance charges = 4,349 + 500 = $4,849

APR ≈ (4,849 ÷ 25,000) ÷ 5 × 100 = 3.88% per year added
Rough APR ≈ 6.5% + 0.38% = 6.88%

Exact APR (Newton's method) = 6.915%

The simplified formula is close on short-term loans but drifts on long mortgages because it ignores that fees are paid upfront while interest accrues over decades.

3. Effective APR with Monthly Compounding

Effective APR = (1 + nominal APR ÷ 12)^12 − 1

Example: 6.5% nominal APR, compounded monthly
Effective APR = (1 + 0.065 ÷ 12)^12 − 1
              = 1.06697 − 1
              = 6.697%

This is the rate you actually pay once compounding
is accounted for. Most loans quote the nominal APR,
not the effective one.

4. APY vs APR

APY = (1 + APR ÷ n)^n − 1

Where n = compounding periods per year.

A credit card with 24% APR compounded daily (n = 365):
APY = (1 + 0.24 ÷ 365)^365 − 1 = 27.11%

A savings account with 4.5% APR compounded monthly:
APY = (1 + 0.045 ÷ 12)^12 − 1 = 4.59%

Banks advertise APY on savings (higher number, looks
generous) and APR on loans (lower number, looks cheap).

Quick Reference: Nominal Rate vs APR on a $200,000 Mortgage

Same loan, same rate, different fee structures. The nominal rate is 6.5% in every row. The APR shifts with the closing costs the lender charges. This is why lender A at 6.5% can be more expensive than lender B at 6.6%.

A $200,000 mortgage at 6.5% with $3,000 origination and $2,000 in closing costs gives an APR of roughly 6.72%. The 0.22% APR bump does not sound dramatic, but over 30 years it translates to about $10,400 in extra cost compared to a fee-free loan at the same rate. Multiply that by larger loan sizes and the dollar difference grows proportionally.

The APR is a regulated disclosure, not a marketing number. It exists because without it, lenders could advertise a rock-bottom interest rate and bury the real cost in fees. This section covers why the APR was invented, how it differs from APY, what ranges are typical for different loan products, and the cases where the APR still fails to tell the full story.

Why APR Exists: The Truth in Lending Act of 1968

Before 1968, lenders advertised interest rates without disclosing fees, and two loans with the same rate could cost wildly different amounts. Congress passed the Truth in Lending Act (TILA, Regulation Z) in 1968 to force a standardized disclosure so shoppers could compare offers apples-to-apples. TILA requires every consumer loan to show the APR next to the nominal rate on the Loan Estimate and Closing Disclosure for mortgages, the Schumer Box for credit cards, and the finance charge disclosure for auto and personal loans. The APR is the single most important number for comparing lenders because it rolls the rate and most of the fees into one figure.

APR vs APY: One You Pay, One You Earn

APR and APY both express yearly rates, but they are used on opposite sides of the balance sheet and calculated differently.

On a 24% credit card APR compounded daily, the APY is 27.1%. That 3.1% gap is what the bank actually collects, and it is why banks quote APR on cards (looks lower) and APY on savings (looks higher). Same math, opposite marketing.

Typical APR Ranges by Loan Type

Use these ranges as a sniff test before you sign anything. Numbers reflect the US market in 2024 to 2026.

A 6.8% APR on a 30-year mortgage is unremarkable. A 6.8% APR on a credit card would be historically cheap and almost certainly an introductory teaser. Context matters more than the absolute number.

Where APR Misleads: Teaser Rates, ARMs, and Revolving Credit

The APR is designed for fixed-rate, fully-amortizing installment loans. It gets less accurate in three cases:

• Credit cards with 0% introductory APR. The Schumer Box shows both the intro APR (0% for 12 to 18 months) and the go-to APR (often 24%+). If you carry a balance past the intro period, deferred interest can kick in retroactively on some promos, so the effective APR over 2 years is much higher than the average of the two quoted numbers.
• Adjustable-rate mortgages (ARMs). The APR on a 5/1 ARM assumes the fully-indexed rate after the fixed period, but nobody knows what the index will actually be in year 6. The quoted APR is a snapshot based on today's index and can understate or overstate the real cost by a full percentage point or more.
• Payday and installment loans with balloon structures. APR annualizes a 14-day finance charge, producing the eye-popping 400% numbers. The math is correct, but the APR disclosure does not capture rollover behavior, which is how most payday borrowers end up paying 3x to 5x the original principal.

For straightforward fixed-rate loans, the APR is the most honest single number you will see. For revolving credit and adjustable products, treat it as a starting point, not the last word.