Loan Payment Calculator

What this calculator answers

What each payment on a fixed-rate installment loan will be, how much interest the loan costs in total, and when it is paid off, with every payment laid out in an amortization schedule you can download. It also answers the two reverse questions: how much you can borrow for a payment you can afford, and how long a payment you choose takes to clear a loan. It fits personal, auto and student loans and the principal-and-interest part of a mortgage.

How to use it

• Solve for: Payment (the usual question), Loan size (the most a payment repays over a term) or Payoff time (how long a payment takes).
• Loan amount: the amount you borrow, in dollars, from the loan offer. 20,000, $20,000 and 20k all work.
• Payment amount (loan size and payoff time only): what you pay each period.
• Annual interest rate: the interest rate from the offer, in percent. Type 8.25 for 8.25%. See below for why the APR is the wrong number here.
• Loan term and term unit: years or months. The line under the box converts between them (60 months = 5 years). A term that isn’t a whole number of payments is rounded to the nearest one, and the result says so.
• Payment frequency: monthly unless your loan says otherwise; also every 2 weeks, weekly, quarterly or yearly.
• First payment date (optional): adds a date to every row, gives the payoff date, and groups the yearly table by calendar year.

Results update as you type. The Try buttons load the bi-weekly, 0%, loan size and payoff time cases worked through below. The What if tabs repeat your loan with other terms, rates and payment frequencies. To compare two offers, press Save for comparison, change the inputs and save again: each saved scenario shows how its interest and total differ from the first. Under a monthly result, the Continue in links carry the loan to the APR calculator, where you add the lender’s fees, or to the extra payment calculator.

How is a loan payment calculated?

The payment is the level amount that covers each period’s interest and repays the loan exactly with the last payment. For a loan of $P$ repaid in $n$ equal payments at a rate $i$ per payment:

$$M = \frac{P \times i}{1 - (1 + i)^{-n}} \qquad \text{with no interest: } M = \frac{P}{n}$$

• $M$ is the payment per period.
• $P$ is the loan amount.
• $i$ is the annual rate as a decimal divided by the payments per year: 8.25% paid monthly is 0.0825 ÷ 12 = 0.006875.
• $n$ is the number of payments: years × payments per year, so 5 years of monthly payments is 60.

Each period, the interest is the balance times $i$. The payment pays that interest first, and the rest reduces the balance. The same formula, rearranged, gives the other two answers: the loan size is $P = M \times (1 - (1 + i)^{-n}) \div i$, and the number of payments is $n = -\ln(1 - P \times i \div M) \div \ln(1 + i)$, rounded up to a whole payment.

Worked example: $20,000 over 5 years at 8.25%

1. Rate per payment: i = 8.25% ÷ 12 = 0.006875.
2. Number of payments: n = 5 × 12 = 60.
3. Payment: $20,000 × 0.006875 ÷ (1 − 1.006875⁻⁶⁰) = $137.50 ÷ (1 − 0.662928) = $407.925…, which rounds to $407.93 a month.
4. First payment: interest $20,000 × 0.006875 = $137.50, so $407.93 − $137.50 = $270.43 goes to principal, leaving $19,729.57.
5. Final payment: after 59 payments $404.81 is left, and its interest is $2.78, so payment 60 is $407.59, which is $0.34 less than the others.
6. Totals: 59 × $407.93 + $407.59 = $24,475.46 paid, of which $4,475.46 is interest.

In a spreadsheet, =PMT(8.25%/12, 60, -20000) returns 407.925…, the payment before rounding to the cent.

What an amortization schedule shows

An amortization schedule lists every payment with its interest, the principal it repays and the balance left after it. In the example, the first year’s twelve payments include $1,524.43 of interest and repay $3,370.73 of principal. In year 5 the same payments include only $211.90 of interest and repay $4,682.92. Half the loan is repaid after payment 34 of 60, not payment 30, because early payments are mostly interest.

The Every payment tab shows each payment; By year adds them up by loan year (or by calendar year once you enter a first payment date). The principal column of both adds up to the loan amount to the cent, and the total row shows it. Both tables download as CSV with plain numbers, so they open cleanly in a spreadsheet.

Why the last payment is slightly different

The exact payment in the example is $407.925…, but you can only pay whole cents, and each month’s interest is rounded to the cent as well. Those fractions of a cent add up over 60 payments, so the last payment is whatever clears the balance: here $0.34 less than the others. It happens at 0% too: $20,000 ÷ 60 is $333.333…, so the schedule has 59 payments of $333.33 and a last one of $333.53. This calculator rounds the payment and each period’s interest to the nearest cent. Some lenders and textbooks round up to the next cent instead, which can move the final payment by a few cents; your loan statement’s figure wins.

How the loan term changes your payment and total interest

A longer term lowers the payment but charges interest on the balance for longer. The same $20,000 at 8.25%, paid monthly:

Going from 5 years to 7 cuts the payment by $93.71 a month and adds $1,919.19 of interest. The Term tab under What if builds this table for your own loan.

Monthly vs. bi-weekly payments

A bi-weekly loan takes 26 payments a year at the annual rate ÷ 26. For the example that is 130 payments of $187.99, and the interest comes to $4,439.13, which is $36.33 less than monthly. Paying more often knocks the balance down a little sooner in each month, so slightly less interest builds up. Weekly payments of $93.94 bring the interest to $4,423.26.

A “bi-weekly plan” that takes half of a monthly payment every two weeks is different. Twenty-six half payments make 13 monthly payments a year instead of 12, so that plan is really an extra payment each year, and the savings come mostly from that extra money.

Loan size and payoff time

Solving for Loan size answers “how much can I borrow for $450 a month?”. Over 5 years at 8.25% the payments are worth $22,062.877…, so the loan is $22,062.87, rounded down to the cent so the payment covers it. Its final payment is $449.97.

Solving for Payoff time answers “how long will $450 a month take?”. On the $20,000 loan it takes 54 payments: 53 of $450.00 and a last one of $99.79. Interest comes to $3,949.79, which is $525.67 less than the 5-year schedule.

A payment has to be larger than one period’s interest to reduce the balance. On $20,000 at 8.25%, the first month’s interest is $137.50, so $130 a month never repays the loan, and the calculator says so instead of showing an endless schedule. It also gives the smallest payment that makes progress ($137.51) and the smallest that repays within 1,200 payments, 100 years of monthly payments ($137.54).

Interest rate vs. APR: which to enter

Enter the interest rate. The APR adds the lender’s fees to the interest rate, so it is higher whenever there are fees, and entering it here gives a payment a little above the lender’s. The APR is the better number for comparing offers, as long as you compare APR with APR. If fees are added to the loan instead of paid upfront, include them in the loan amount.

Reading the result

• The headline is the answer to what you solved for: the payment, the loan size or the payoff time.
• Total interest and total paid are for the whole schedule, including the adjusted final payment.
• First payment’s interest shows how much of the first payment is interest and how little is left by the last one.
• Half the loan repaid after (or the payoff date, when you give a first payment date) shows how the balance falls.
• How this was calculated repeats the formula with your numbers and the spreadsheet function that gives the same result.
• The charts show the balance after each payment and how each year splits between principal and interest; Chart data lists the numbers.
• What if reruns the calculation with the term, the rate or the payment frequency changed and everything else kept. In the example, 7.25% would make the payment $398.39 and 9.25% would make it $417.60.

Assumptions and limitations

• The rate is fixed for the whole loan, and each period’s interest is the balance × the annual rate ÷ payments per year. There is no separate compounding setting: this is the textbook formula and the one spreadsheet PMT uses.
• The first payment is one full period after the loan starts and carries a full period’s interest, whatever the number of days. A lender that counts the actual days in each period will show slightly different interest.
• Payments and interest are rounded to the nearest cent, and the final payment absorbs the difference.
• No fees, insurance, taxes, late charges or extra payments are included.
• Adjustable-rate loans, interest-only periods and balloon payments are not modeled.
• Monthly payment dates keep the day of the first payment and move to the last day of shorter months; they are not moved for weekends or holidays.
• The results are an educational estimate, not a loan offer or financial advice.

Common mistakes

• Entering the APR as the interest rate. The APR includes fees, so the payment comes out slightly too high.
• Typing months with Years selected. 60 years is not a loan term; choose Months for 60 months. The calculator flags terms over 50 years and suggests months for 36 or 48 years.
• Entering a monthly rate as the annual rate. 0.6875% a month is 8.25% a year; the field wants 8.25.
• Treating a half-payment plan as a bi-weekly loan. Half of the monthly payment every two weeks adds an extra payment each year; a bi-weekly loan does not.
• Rebuilding the schedule without rounding. A spreadsheet that keeps every fraction of a cent won’t match a lender’s schedule, and its final payment won’t be adjusted. Round each period’s interest to the cent.
• Choosing a loan by the payment alone. In the table above, the 7-year loan has the lowest payment and the highest total interest.