Loan APR Calculator

Related Calculators

Table of contents

• How to use
• Common mistakes
• Definitions
• Methodology
• Limitations & assumptions
• Sources

APR with fees: The yearly cost rate after interest and required fees are included. APR can be higher than the stated interest rate when mandatory fees apply [4].

Stated interest rate: The loan rate used to calculate the scheduled payment before required fees are included in the APR.

Required loan fees: Fees required to get the loan, such as lender or origination fees. Optional add-ons should be included only if you want them counted in this estimate.

Paid upfront or taken out of cash: A fee setup where the loan balance is based on the loan amount, but the borrower effectively receives less cash at the start.

Added to the loan balance: A fee setup where the fee increases the balance used to calculate the scheduled payment.

Total finance charge: The dollar cost of the credit in this calculator, including total interest, required fees, and any extra required monthly cost entered.

Percentage points: The direct difference between two percent rates. For example, 14 percent APR minus 12 percent interest is 2 percentage points.

Mistake: Putting the amount you receive after fees into Loan amount before fees ($) .
Fix: Enter the loan amount before fees, then put the fee in Required loan fees ($) .

Mistake: Choosing the wrong answer for How are those fees handled? .
Fix: Choose "Paid upfront or taken out of cash" if the fee lowers the cash you receive, or "Added to the loan balance" if you repay the fee over time.

Mistake: Entering 0.12 in Stated interest rate (percent per year) for a 12 percent loan.
Fix: Enter 12, not 0.12.

Mistake: Adding optional products to Required loan fees ($) when you only want the APR for required credit costs.
Fix: Include only fees required to get the loan unless you intentionally want those optional costs in the estimate.

Mistake: Using Optional payoff check (months) with a month equal to or greater than Loan term (months) .
Fix: Leave it blank for the full-term APR, or enter a whole number from 1 to one less than the loan term.

Mistake: Treating Monthly loan payment as the full monthly cash need when Extra required monthly cost ($ per month) is entered.
Fix: Use Monthly cash outflow with extra costs when extra required monthly costs are included.

• This calculator is for fixed-rate loans with equal monthly payments. It is not for credit cards, variable-rate loans, interest-only loans, or loans with uneven payment schedules.
• The APR is an estimate from monthly cash flows. Official lender disclosures can differ because of legal rounding rules, exact payment dates, prepaid interest, odd first periods, or fees not entered here.
• Required loan fees ($) should include required credit costs only. Taxes, title charges, insurance, or optional products may be treated differently in real disclosures.
• If How are those fees handled? is wrong, the APR and total paid can be wrong because the calculator changes both cash received and the balance repaid.
• Optional payoff check (months) assumes normal scheduled payments through that month, then payoff of the remaining balance at the same time. It does not model prepayment penalties or lender payoff quote fees.
• APR solving can fail when inputs create impossible or unusual cash flows, such as paid-upfront fees equal to or greater than the loan amount.

Calculation method

The calculator first decides which balance is repaid and how much value the borrower effectively receives at the start. APR is then solved from the timing of the amount received and the monthly payments, which matches the actuarial cash-flow idea used for closed-end credit APR computations [3].

balance_for_payment = loan_amount + upfront_fees if fees are added to the loan balance; otherwise balance_for_payment = loan_amount

amount_received = loan_amount - upfront_fees if fees are paid upfront or taken out of cash; otherwise amount_received = loan_amount

The stated yearly interest rate is converted to a monthly note rate by dividing by 12 months per year.

monthly_note_rate = stated_interest_rate_percent / 100 / 12

The scheduled loan payment uses the standard fixed-payment loan formula. If the stated rate is 0 percent, the payment is the repayable balance divided by the number of months.

monthly_payment = balance_for_payment * monthly_note_rate / (1 - (1 + monthly_note_rate)^(-loan_term_months))

if monthly_note_rate = 0, monthly_payment = balance_for_payment / loan_term_months

APR is found by solving for the monthly APR rate that makes the present value of all monthly cash outflows equal the amount received. The calculator then multiplies the monthly APR rate by 12 and by 100 to show a nominal yearly percent.

amount_received = sum from m = 1 to loan_term_months of (monthly_payment + extra_monthly_cost) / (1 + monthly_apr_rate)^m

apr_percent = monthly_apr_rate * 12 * 100

The fee impact is the solved APR minus the stated interest rate. It is not forced to zero because unusual cash flows can produce a lower solved APR.

fee_impact_points = apr_percent - stated_interest_rate_percent

Full-term totals are based on the scheduled payment, the number of months, required fees, and any extra required monthly cost entered.

total_interest = monthly_payment * loan_term_months - balance_for_payment

total_finance_charge = total_interest + upfront_fees + extra_monthly_cost * loan_term_months

total_paid = monthly_payment * loan_term_months + upfront_fees_paid_outside_balance + extra_monthly_cost * loan_term_months

For an early payoff check, the calculator finds the remaining balance after the entered payoff month, then solves a second APR using the scheduled payments through that month plus the payoff amount.

remaining_balance_after_k = balance_for_payment * (1 + monthly_note_rate)^k - monthly_payment * (((1 + monthly_note_rate)^k - 1) / monthly_note_rate)

if monthly_note_rate = 0, remaining_balance_after_k = balance_for_payment - monthly_payment * k

amount_received = sum from m = 1 to k of (monthly_payment + extra_monthly_cost) / (1 + early_monthly_rate)^m + remaining_balance_after_k / (1 + early_monthly_rate)^k

early_apr_percent = early_monthly_rate * 12 * 100

Mini example

For a $10,000 loan, 12 percent stated interest, 36 months, and a $300 fee paid upfront, the scheduled payment is about $332.14 per month. The borrower effectively receives $9,700, so the solved APR is about 14.12 percent. The fee adds about 2.12 percentage points to the stated rate, total interest is about $1,957.17, and total finance charge is about $2,257.17.