How the payment is calculated
A fixed-rate loan is repaid in equal payments. Each payment first covers the interest charged since the previous one, and the rest reduces what you owe. The payment that clears the loan exactly by the end of the term is:
A = P × r(1 + r)n ÷ ((1 + r)n − 1)
- A
- the regular payment
- P
- the loan amount
- r
- the interest rate per payment: the yearly rate divided by 12 for monthly payments, 26 for payments every two weeks, or 52 for weekly payments
- n
- the number of payments
With a balloon payment B, the regular payments only have to repay the part of the loan that isn’t left for the end, so the formula becomes A = (P(1 + r)n − B) × r ÷ ((1 + r)n − 1). At a 0% rate there is no interest, and the payment is simply (P − B) ÷ n.
Like a lender’s statement, the calculator rounds the payment to the cent and rounds each period’s interest to the cent. Because the rounded payment is slightly more or less than the exact figure, the last payment absorbs the difference. That’s usually a few cents; on a 30-year loan it’s about a dollar. Every total on this page is added up from the schedule itself, so the results, the table and the CSV always agree.
Worked example
Take the calculator’s starting values: $25,000 at 7.5% a year, repaid monthly over 5 years.
- Rate per month: r = 7.5% ÷ 12 = 0.625%, or 0.00625
- Number of payments: n = 5 × 12 = 60
- Growth factor: (1.00625)60 = 1.45329
- Payment: 25,000 × 0.00625 × 1.45329 ÷ 0.45329 = 500.9487, which rounds to $500.95
The first month’s interest is 25,000 × 0.00625 = $156.25, so $344.70 of the first payment goes to the balance. The next month’s interest is charged on the lower balance, so slightly more of each payment goes to principal:
| No. | Amount | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | 500.95 | 156.25 | 344.70 | 24,655.30 |
| 2 | 500.95 | 154.10 | 346.85 | 24,308.45 |
| 3 | 500.95 | 151.93 | 349.02 | 23,959.43 |
| … | ||||
| 60 | 500.91 | 3.11 | 497.80 | 0.00 |
Over the 60 payments the interest adds up to $5,056.96. The last payment is 4 cents lower than the others because of the rounding described above.
Interest rate vs. APR
Enter the loan’s interest rate here. The APR (annual percentage rate) is a different number: it rolls certain fees, such as an origination fee, into a single yearly rate so that loan offers can be compared. Because it includes those fees, the APR is usually higher than the interest rate (Consumer Financial Protection Bureau).
Suppose the $25,000 loan above comes with a $500 origination fee taken out of the money you receive. You get $24,500 but still repay $500.95 a month, which works out to an APR of about 8.36%. Entering 8.36% here would show a payment of $511.17, which isn’t what the lender will charge. Use the APR to compare offers and the interest rate to work out payments.
How amortization works
Interest is charged on the balance you still owe, so it is largest at the start and shrinks as the balance falls. The effect is easiest to see on a long loan. On $200,000 at 6% over 30 years, the monthly payment is $1,199.10. Of the first payment, $1,000.00 is interest and only $199.10 reduces the balance. Across the whole first year you pay $11,933.19 in interest and repay $2,456.01 of the loan.
On that loan, the principal part of the payment doesn’t overtake the interest part until payment 223, more than 18 years in. The balance doesn’t drop below half the original amount until payment 252, 21 years into the 30. The balance chart above shows the same curve for your numbers: slow at first, then faster toward the end. The schedule shows where every payment goes.
What extra payments do
Money paid on top of the regular payment goes straight to the balance, which lowers the interest charged on every payment after it. On the $200,000 loan, an extra $200 a month saves $79,800.86 in interest and ends the loan 9 years early.
Timing matters. A single extra $10,000 on the same loan saves $41,044.36 in interest if it goes in with payment 12, $21,085.57 with payment 120, and $7,580.09 with payment 240.
In this calculator, extra payments shorten the loan and the regular payment stays the same. Some lenders will instead recast a loan after a large extra payment, lowering the payment and keeping the original end date, often for a fee. That option isn’t modeled here. Before paying extra, ask your lender two things: whether the extra money is applied to the principal straight away (rather than held toward your next payment), and whether the loan has a prepayment penalty.
Assumptions and limitations
- The interest rate is fixed for the whole term. For a variable-rate loan, the results hold only until the rate changes.
- Interest is charged once per payment period at the yearly rate divided by the number of payments per year. Many auto and personal loans charge interest daily instead, which changes the total slightly (see the questions below).
- Every payment is made in full on its due date.
- Fees, insurance and taxes are not included.
- Amounts are rounded to the cent (or to whole units for currencies without cents, such as the yen), and the last payment absorbs the rounding.
- Canadian fixed-rate mortgages are usually quoted with interest compounded twice a year rather than monthly, so a Canadian lender’s payment will be a little lower than this calculator’s for the same rate.
- Your loan agreement and your lender’s figures have the final numbers.
Questions
Why is the last payment different from the others?
Usually because of rounding. Each payment is rounded to the cent, so the last one is adjusted by the few cents needed to leave a balance of exactly zero. It can also differ because it includes a balloon payment, or because extra payments leave only a small amount to pay at the end.
What’s the difference between paying every two weeks and “accelerated biweekly”?
Choosing “Every two weeks” here sets up the loan with 26 payments a year, each calculated for that schedule. On the $25,000 example that is $230.89 every two weeks: about the same per year as paying monthly ($6,003.14 versus $6,011.40), with slightly less interest ($5,015.32 versus $5,056.96).
An accelerated biweekly plan is different. You pay half the monthly payment every two weeks, and because a year has 26 of those half-payments, you end up paying the equivalent of 13 monthly payments a year. On the $200,000, 30-year loan, $599.55 every two weeks pays the loan off in about 24½ years and saves about $49,600 in interest. To get a close estimate here, keep monthly payments and put one monthly payment ($1,199.10) in the “Once a year” extra field. That shows a saving of $47,282.39 and a payoff of about 24¾ years.
My lender charges interest daily. Will my statement match?
Closely, but not to the cent. With daily interest, a 31-day month costs a little more than a 28-day one, and paying a few days early or late moves the interest too. Modeled with daily interest and payments on the same dates, the $25,000 example costs $4.82 more over five years, and a $30,000 six-year loan at 9% costs $9.79 more. The regular payment stays the same; the difference shows up in the last payment.
Does a balloon payment make a loan cheaper?
Usually not. A balloon lowers the regular payment because part of the loan isn’t repaid until the end, but you pay interest on that part the whole time. $30,000 at 8% over 5 years costs $608.29 a month and $6,497.52 in interest. With a $10,000 balloon, the payment drops to $472.19, but interest rises to $8,331.71 and the final payment is $10,472.50. If you plan to refinance the balloon when it comes due, you won’t know that future rate in advance.
Can I use this for a mortgage?
Yes, for the principal and interest. A mortgage payment usually also includes property tax and homeowners insurance, and sometimes mortgage insurance or HOA dues, which you would need to add to the payment shown here.