APR Calculator

What this calculator answers

What a fixed-rate installment loan costs as a yearly rate once its fees are counted: the annual percentage rate (APR). It also gives the four other figures a Truth in Lending disclosure shows, the payment, finance charge, amount financed and total of payments, so you can check a lender’s numbers line by line. Use it for personal loans, car loans and fixed-rate mortgages with origination fees, points or broker fees. For the APR on a credit card balance, use a credit card payoff calculator instead.

How to use it

• Loan amount: the cash you ask for, before any fee is added. With no fees taken out, it is the cash you receive. 25,000, $25,000 and 25k all work.
• Interest rate: the note rate from the offer, in percent a year. Type 10.99 for 10.99%. This is not the APR.
• Loan term: the number of monthly payments, such as 60 for five years.
• Fees: press Add fee for each charge that counts toward the APR (see the list below). Enter it in dollars, or switch to % for points and fees quoted as a percent of the loan; the line under the amount shows it the other way. Then choose Paid at closing (withheld from the money you receive, or paid in cash) or Added to the loan (borrowed).
• Days to first payment (optional): leave it blank when the first payment is due one month after the loan starts. Enter the days for a shorter or longer first period.

Results update as you type. The Try buttons load the cases below: the same fee added to the loan, no fees, a first payment 45 days out, a 0% rate for 12 months and a 30-year mortgage with a point. To compare offers, press Save for comparison after each one; later offers show how far their APR and costs differ from the first. Continue in the Loan Payment Calculator carries the loan you sign for, the rate and the term over for a full amortization schedule.

How APR is calculated

The APR is 12 times the monthly rate $i$ at which the loan’s payments, discounted back to the day the loan starts, add up to the amount financed. This is the actuarial method of Regulation Z, Appendix J:

$$A = \sum_{k=1}^{n} \frac{P_k}{(1 + f\,i)(1 + i)^{t_k}} \qquad \text{APR} = 12\,i$$

• $A$ is the amount financed: the loan amount minus any fees paid at closing.
• $P_k$ is the $k$-th payment. The lender sets the payment on the loan you sign for at the interest rate, so fees paid at closing don’t change the payments; they lower $A$.
• $n$ is the number of payments.
• $t_k$ is the number of whole months from the start of the loan to payment $k$, and $f$ is the extra fraction of a month before the first payment (0 for a regular first month).

There is no closed-form formula for $i$, so the calculator solves the equation numerically. The payment itself comes from the usual installment formula, rounded to the cent: $M = N\,r \div (1 - (1 + r)^{-n})$, where $N$ is the loan you sign for and $r$ is the interest rate ÷ 12.

Worked example: $25,000 over 60 months with a 3% origination fee

A personal loan of $25,000 at a 10.99% interest rate for 60 months, with a 3% origination fee taken out of the money you receive:

1. Fee: 3% × $25,000 = $750.00. You receive $24,250.00, so the amount financed is $24,250.00.
2. Monthly rate: 10.99% ÷ 12 = 0.00915833.
3. Payment: $25,000 × 0.00915833 ÷ (1 − 1.00915833⁻⁶⁰) = $543.4359, so $543.44. With interest charged on the balance each month and rounded to the cent, the 60th payment is $543.15.
4. Total of payments: 59 × $543.44 + $543.15 = $32,606.11.
5. Finance charge: $32,606.11 − $24,250.00 = $8,356.11, which is $7,606.11 of interest plus the $750.00 fee.
6. Solve $24,250.00 = Σ P_k ÷ (1 + i)^k for the monthly rate: i = 1.027202%.
7. APR = 12 × 1.027202% = 12.3264%, shown as 12.33%.

Check: the same payments repay the full $25,000 at 10.9900% a year, the interest rate, so the fee adds 1.34 percentage points. In a spreadsheet, =12*RATE(60,-543.44,24250,0.29) gives the same APR; the last argument accounts for the smaller final payment.

APR vs. interest rate: why the APR is higher

The interest rate prices only the money you owe. The APR also counts the fees you pay to get the loan, so it is higher whenever there are fees that count as finance charges, and equal to the rate when there are none. In the example, the 10.99% rate becomes a 12.33% APR because you pay back a $25,000 loan but have the use of only $24,250. With the No fees preset, the APR is 10.99%, the interest rate.

A 0% rate with a fee is not free credit. The 0% for 12 months preset keeps the 3% fee: you repay $25,000 in 12 payments of $2,083.33 (the last $2,083.37) after receiving $24,250, so the finance charge is $750.00 and the APR is 5.66%.

Which fees count toward the APR

Regulation Z counts a charge in the finance charge when the lender requires it or imposes it because you are borrowing. List these as fees:

• Points (discount points) and loan or origination fees. One point is 1% of the loan amount.
• Mortgage broker fees, even when paid directly to the broker.
• Charges for services the lender requires from a third party, and premiums for insurance that protects the lender if you don’t pay.
• Prepaid interest collected at closing.

Leave these out:

• Application fees charged to every applicant, whether or not they get the loan.
• Late fees and other charges for a default.
• On loans secured by real estate, reasonable fees for title examination and title insurance, surveys, document preparation, notaries, credit reports and appraisals.
• Charges you would also pay in a cash purchase, such as sales tax on a car.

If you borrow a cost that is not a finance charge, such as title insurance rolled into a mortgage, add it to the loan amount rather than listing it as a fee. It raises the amount financed, not the finance charge. The rules have more detail for specific loan types, so the fee list on your disclosure is the final word.

Fees paid at closing or added to the loan

A fee paid at closing is taken out of the money you receive, or paid from your own cash; both lower the amount financed by the same amount. A fee added to the loan is borrowed: you sign for the loan amount plus the fee, receive the full loan amount, and pay interest on the fee too.

Try Fee added to loan on the example. A percent fee is a percent of the loan you sign for, so to receive $25,000 with a 3% fee you sign for $25,000 ÷ (1 − 0.03) = $25,773.20 and the fee is $773.20. The payment rises to $560.24 (last $560.52) and the finance charge to $8,614.68, but the APR stays 12.33%, because the fee is still 3% of the loan. Paying the fee at closing costs less in dollars; the APR can’t tell the two apart.

The first payment date and odd days

The APR also depends on when the payments come. Appendix J counts the extra days before a first payment as 30ths of a month, so 45 days is one month plus 15/30. The 45-day first period preset keeps the same payments but moves them 15 days later, and the APR falls to 12.10%.

A loan repaid in one payment is the exception. Appendix J then treats the whole term as a single period: a payment due 45 days out counts as 365 ÷ 45 periods a year, and the APR is the finance charge ÷ the amount financed × 365 ÷ 45. For a whole number of months, it is × 12 ÷ the months instead.

In practice, lenders usually charge interest for the extra days, which raises the finance charge. At 10.99% on $25,000, 15 days of interest is about $114.48. Add it as a second fee paid at closing and the APR is 12.31%, close to the 12.33% of a regular first month. If your lender adds that interest to the first payment instead, your disclosure will show a larger first payment than this schedule.

Reading the result

• APR is the headline, to two decimals as disclosures show it. Below it are the payment, the finance charge (interest plus fees), the amount financed (the credit you actually get), the total of payments, the loan you sign for and how many percentage points the fees add.
• Notes appear for the cases that surprise people: a 0% rate with fees, a single payment and a first period longer or shorter than a month.
• Where your payments go splits the total of payments into the amount financed, the fees and the interest.
• How this was calculated shows every figure with your numbers, the equation solved for the monthly rate, a check against the interest rate and the spreadsheet formula.
• If you repay early gives the yearly cost and the cost of borrowing if you repay after each year (after every payment, or every six months, on short loans), with what you have paid and the balance still owed. In the example, repaying after 12 months costs $3,301.51, which is 14.47% a year; after 24 months it is 13.00%, and kept to the end it is the APR. The chart shows the same fall month by month.
• APR by loan term reruns the loan with the same amount, rate and fees at shorter and longer terms. Spread over fewer months, the fees raise the APR more.

Why your lender’s APR may differ slightly

• Which charges count. The lender applies the finance-charge rules to its own fee list, which may include charges you didn’t enter.
• Dates. Appendix J counts whole months on the calendar from the actual loan and payment dates. This calculator counts days in 30-day months.
• Odd-days interest added to the first payment or collected at closing (see above).
• Tolerance. A disclosed APR counts as accurate within 1/8 of a percentage point of the exact figure for a loan like this, and within 1/4 point for irregular loans such as those with several advances. Lenders may also use the United States Rule method instead of the actuarial one.

When comparing APRs can mislead

• Repaying early. The APR assumes every payment is made. Fees paid upfront cost more per year the sooner the loan ends, as the early-repayment table shows. The CFPB suggests asking lenders for total costs over a few time frames: the shortest, longest and most likely time you’ll keep the loan.
• Different terms. A longer loan can have a lower APR and still cost more in dollars, because you pay interest for more months. Compare offers at the same term, and compare the finance charges too.
• Adjustable rates. The APR of an adjustable-rate loan does not reflect the highest rate the loan could reach.
• Compare like with like. Compare an APR with another APR, never with an interest rate.

The Mortgage with 1 point preset shows how much repaying early matters: $350,000 at 6.5% with a $3,500 point and a $1,200 origination fee has an APR of 6.63% over 30 years, but repaid after 12 months it costs 7.91% a year.

APR vs. APY

A loan’s APR is a nominal rate: 12 times the monthly rate, with no compounding, so a 12% APR is 1% a month. The APY on a savings account includes compounding, and 1% a month compounds to 12.68% a year; an APY calculator converts between the two.

Assumptions and limitations

• Fixed interest rate, monthly payments, payment and interest rounded to the cent, and a final payment that clears the balance. Other lenders may round differently.
• Every fee you list is treated as a finance charge. Lender credits, variable rates, balloon payments and payment holidays are not modeled.
• The first payment date changes the timing only; the payments stay the same.
• The early-repayment figures assume payoff right after a payment, with no prepayment penalty.
• The result is an educational estimate, not a lender’s disclosure or financial advice.

Common mistakes

• Entering the loan you sign for as the loan amount when a fee is added. If your contract’s loan already includes a financed fee, enter the cash you receive as the loan amount and the fee as added to the loan. Entering both counts the fee twice.
• Typing the APR into the interest rate field. The calculator would add the fees a second time. Use the note rate from the offer.
• Leaving a percent fee in dollars. A 3% fee typed as 3 with $ selected is a $3 fee. The line under the amount shows what it was read as.
• Listing charges that are not finance charges, such as title insurance or an appraisal on a mortgage. They make the APR look higher than the lender’s.
• Entering the term in years. The term is in months: a five-year loan is 60.