Accurate Amortization Calculator
Introduction to Amortization
Create a printable amortization schedule with dates to see how much principal and interest you'll pay over time.
- Export to Excel/.xlsx and Word/.docx files.
- Calculate loan payment amount or other unknowns
- Supports 9 types of amortization.
- User can set loan closing date and first payment date independently.
- Automatically calculates prepaid interest
Create a printable amortization schedule that includes payment dates and annual subtotals. The schedule shows how much principal and interest you will pay over the life of the loan. The calculator can calculate any one unknown value: the payment amount, loan amount, interest rate, or loan term.
- What is an amortization schedule?
- An amortization schedule is a table that shows a loan’s complete repayment plan. It lists each payment, detailing how much is applied to the loan’s principal and how much to interest, along with the remaining loan balance. Ideally, the schedule includes payment dates, and year-end subtotals.
- How do I create an amortization schedule?
- Leave all inputs and settings at their default values, then:
- Enter the Loan Amount.
- Enter the expected Number of Payments.
- Set the anticipated closing date and the first payment due date.
- Enter the expected Annual Interest Rate.
- Set the Payment Amount to 0.
(This tells the calculator to solve for the payment amount.) - Click either or .
- Leave all inputs and settings at their default values, then:
That’s it. These are the only steps needed to generate your schedule.
If your loan terms differ from the calculator’s default settings, additional options are available.
Keep reading. The following sections explain each option in more detail. More…
Create an amortization schedule with user-specified dates.
To set your preferred currency and date format, click the “$ : MM/DD/YYYY” link in the lower right corner of any calculator.
Information
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Useful Details —
They Will Help You Get What You Need
First — You must enter a zero (0) in any field where you want the calculator to solve for a value.
Why is this necessary?
The calculator generates a schedule based on the loan terms you specify. The payment amount can be any value, as long as both the lender and borrower agree. There is no single “correct” payment. If the calculator always solved for the previously unknown value, this feature would not be possible.
TIP — Use the amortization schedule to verify the periodic interest charges. These interest values are the most important amounts for borrowers to double-check.
Four values you must always set:
- Loan Amount — The total amount borrowed, also called the principal. This value does not include interest.
- Number of Payments (term) — The length of the loan, measured in payment periods. This value depends on the Payment Frequency setting. For example, for a 15-year loan with biweekly payments, enter 390 as the number of payments.
(390 biweekly payments = 15 years) - Annual Interest Rate — The nominal (quoted) interest rate for the loan.
- Payment Amount — The amount due on each payment date. For a standard amortizing loan, this value includes both principal and interest.
Set one of the values above to 0 if you want the calculator to solve for it.
What two dates are critical for an accurate amortization schedule?
If you only need an estimated schedule, you can skip this section.
For a schedule that is accurate down to the penny—including correct calculation of stub period interest—it is worth taking a few moments to understand the available date settings.
- Loan Closing Date
- This is the date the loan funds become available. It is also called the origination date, loan date, or start date.
- First Payment Due
- This is the date the first payment is scheduled. For most loans, payments typically begin after the loan funds are received. For leases, this date may be the same as the loan closing date.
Important — Entering actual dates may result in interest and payment calculations that differ from those of other calculators.
That is by design.
However, if you want your results to match those from other calculators, then set the "Loan Date" and "First Payment Due" so that the time between them equals one full period, based on the "Payment Frequency" setting.
Example: If the "Loan Closing Date" is April 10th and the "Payment Frequency" is "Monthly," then set the "First Payment Due" to May 10th—if you want to estimate interest based on one full month.
More details about stub period options, including odd-day and irregular-period interest.
Four loan options you likely do not need to change
- Payment Period or Frequency — How often should payments be made? The calculator supports 11 options, including biweekly, monthly, and semiannual (commonly used for bond coupon schedules). Payment dates are calculated starting from the first payment due date, not the closing date.
- Compounding Period or Frequency — In most cases, the compounding frequency should match the payment frequency. This results in simple periodic interest. Selecting Exact/Simple calculates interest based on exact day counts using a simple interest method.
- Points — One point equals 1% of the loan amount. Points are commonly applied to U.S. mortgages.Learn more about points, fees, and APR support.
- Amortization Method — Leave this set to normal unless you have a specific reason to change it.See all nine amortization methods.
Five loan settings you may want to adjust
These options are available by clicking Settings.
- 360 / 365 / 366 — Days-per-year setting. Also called the day count convention, this affects interest calculations when you select a day-based compounding method (such as daily, exact/simple, or continuous), or when the loan includes an irregular first period. The 366-day option applies in leap years. Otherwise, 365 is used.
- Payment & Initial Period Interest Options — Controls how interest is calculated and displayed when the first period (from closing date to first payment) is longer or shorter than the standard interval.More details and examples.
- Last Period Rounding Options — Because payments and interest are rounded to the nearest cent (e.g., $345.0457 is rounded to $345.05), most loans require a rounding adjustment in the final period. A note on the schedule will show the exact adjustment.
- Points, Charges, & APR Options —Learn more about loan schedules with points, fees, and APR options.
- Year-End Month — Sets the month after which year-end and running totals are calculated. This is helpful for businesses with a fiscal year that does not match the calendar year.
FAQs — Frequently Asked Questions
- How do I calculate how much I can borrow?
- Set the Loan Amount to 0.
- Enter the Number of Payments.
- Enter the Annual Interest Rate.
- Enter the expected or target Payment Amount.
- Click or .
- How do I calculate how long it will take to pay off a loan?
- Enter the Loan Amount.
- Set the Number of Payments to 0.
- Enter the Annual Interest Rate.
- Enter the expected or target Payment Amount.
- Click or .
- What interest rate allows me to pay $500 a month?
- Enter the Loan Amount.
- Enter the Number of Payments.
- Set the Annual Interest Rate to 0.
- Enter $500 as the Payment Amount.
- Click or .
Printing the Payment Schedule
Printing works from any type of device. For example, you can print a clean, well-formatted schedule directly from a smartphone to a wireless printer.(This functionality was tested on various iPhone models printing to an HP LaserJet Pro.)
Do not use your browser’s built-in Print menu option.
Always print from the “Print Preview…” window. This screen includes a print button, along with export buttons for .docx and .xlsx formats.
If you’re using a modern browser, you can also print to a PDF. For example, in Chrome, open the browser menu (three vertical dots), choose Print…, then click Change… and select Save as PDF. Other browsers offer similar functionality.
If you encounter printing issues, please let us know which browser and version you’re using. While we test across several browsers, we are unable to test with all printer models (unless you’d like to donate one!).
(Chrome, Edge, and Firefox all offer a “Save to PDF” option in their print menus.)
How do I create Excel (.xlsx) or Word (.docx) amortization schedules?
From the Print Preview screen (after the title page), you’ll see options to export the full amortization schedule as either an Excel (.xlsx) or Word (.docx) file. When exporting to Excel, the schedule is saved as unformatted data. Dates and numbers are preserved as true Excel date and number values—not text—so you can apply your own formatting.
When exporting to Word, the schedule is formatted for readability. You can edit the document freely, adding notes or customizing fonts, styles, and layout as needed. (In our opinion, the Word export is more visually refined than the version printed directly using the print button.)
Amortization Equations
Payment Amount Equation
Fig. 4 — Step-by-step solution of the monthly payment amount equation.
Variables: L = 50,000; c = (5% ÷ 12 months); n = 60.
Variable Definitions
- P
- Payment amount
- L
- Loan amount
- n
- Number of months. The term of the loan.
- c
- Monthly interest rate (nominal annual rate divided by 12).
Calculation Steps
- Substitute the given values into the annuity payment formula:
P = 50,000 × ( (r/n)(1 + r/n)60 ) ÷ ( (1 + r/n)60 – 1 ), withr = 0.05andn = 12. - Evaluate the periodic rate:
r/n = 0.05/12 ≈ 0.0041666666667…, and substitute it into the formula. - Simplify the base term:
(1 + 0.0041666666667…) ≈ 1.0041666666667…, keeping the exponent of 60 in both the numerator and denominator. - Compute the fraction:
(0.0041666666667… × (1.0041666666667…)60) ÷ ((1.0041666666667…)60 – 1) ≈ 0.018871233644…, then multiply by 50,000. - Round the payment to two decimal places for reporting:
P ≈ $943.56.
Step-by-step Solution – Fig. 4
P = 50,000 × ( (0.05/12)(1 + 0.05/12)60 ) ÷ ( (1 + 0.05/12)60 – 1 )≈ 50,000 × ( (0.0041666666667…)(1 + 0.0041666666667…)60 ) ÷ ( (1 + 0.0041666666667…)60 – 1 )≈ 50,000 × ( (0.0041666666667…)(1.0041666666667…)60 ) ÷ ( (1.0041666666667…)60 – 1 )≈ 50,000 × 0.018871233644…≈ 943.56
Final Answer
The final answer (P) is approximately 943.56.
Validate the calculator. Inputs for a six-year amortization.
| Loan Amount: | $50,000.00 | Number of Payments: | 60 |
|---|---|---|---|
| Annual Interest Rate: | 5.0000% | Payment Amount: | =943.56 |
| Loan Closing Date: | First Payment Due: | ||
| Payment Frequency: | Monthly | Compounding: | Monthly |
| Points: | 0.0 | Amortization Method: | Normal |
Notes:
- This example uses the same calculation shown in Fig. 4.
- Enter a zero for the payment amount. The calculated result matches the result above.
- The “Days In Year” setting has no effect in this example because the period spans exactly sixty months with no extra days.
Amortization Equation
Fig. 6 — Step-by-step solution of the normal (general) amortization equation.
Variables: L = 50,000; R = 5%; n = 60; A = 943.56 (See Fig. 4).
Normal amortization, for any period: ending balance = beginning balance + periodic interest − payment.
Variable Definitions
- R
- Nominal annual interest rate.
- i
- Periodic interest rate.
- I
- Periodic interest amount.
- r
- Growth factor per period (also called the per-period accumulation factor).
- t
- Period number.
- Pt-1
- Outstanding balance at the start of period t.
- Pt
- Outstanding balance at the end of period t.
- L
- Loan amount.
- n
- Number of months. The term of the loan.
- A
- Monthly payment amount.
Calculation Steps
- Compute the periodic rate:
i = 0.05/12 ≈ 0.00416666666…. - Compute the per-period growth factor:
r = 1 + i ≈ 1.00416666666…. - Set the period:
t = 1. - Start-of-period balance:
Pt−1 = 50,000. - Accumulate interest for the period:
50,000 × r ≈ 50,208.33333…. - Round the accumulated balance for display:
≈ 50,208.33. - Interest for the period:
I = 50,208.33 − 50,000 = 208.33. - Subtract the payment to get the end-of-period balance:
Pt = 50,208.33 − 943.56 = 49,264.77.
Step-by-step Solution – Fig. 6 (first period)
i = 0.05/12 ≈ 0.00416666666…r = 1 + i ≈ 1.00416666666…t = 1Pt−1 = 50,000= 50,000 × 1.00416666666… ≈ 50,208.33333…≈ 50,208.33I = 50,208.33 − 50,000 = 208.33Pt = 50,208.33 − 943.56 = 49,264.77
Validate the calculator. Five-year, sixty-month amortization schedule proof.
| #/Year | Date | Payment | Interest | Principal | Balance |
|---|---|---|---|---|---|
| Loan start | 0.00 | 0.00 | 0.00 | 50,000.00 | |
| 1:1 | 943.56 | 208.33 | 735.23 | 49,264.77 | |
| 2:1 | 943.56 | 205.27 | 738.29 | 48,526.48 | |
| Periods 3–59: Intermediate calculations. | |||||
| 59:5 | 939.75 | ||||
| 60:5 | 943.56 | 3.92 | 939.64 | 0.11 | |
| Without any final rounding, a $0.11 principal balance remains. | |||||
| 60:5 (final adjustment) | 943.67 | 3.92 | 939.75 | 0.00 | |
| Last payment increased by $0.11 due to interest rounding. | |||||
Notes:
- The results in the above table are taken from the calculator. They match the calculation shown in Fig. 6.
Beyond Basic Amortization Schedules
Need more options?
Explore seven additional loan amortization calculators
- Mortgage Calculator — estimate future home value and compare it to the total mortgage cost
- Extra Payment Calculator — apply lump-sum or recurring extra payments with a full amortization schedule
- Loan Calculator — includes support for date-based calculations in a mobile-friendly layout
- Auto Loan Calculator — evaluate the full cost of vehicle ownership
- Biweekly Calculator — compare a biweekly schedule to a standard monthly repayment in a single view
- Ultimate Financial Calculator — build schedules with skipped payments, rate changes, and more advanced conditions
- Loan Payoff Calculator — track regular or irregular payments on any date
We hope you find this to be a comprehensive amortization tool. If you need help with a specific scenario or are not sure how to achieve your result, feel free to leave a question in the comments section below.
Bill Phipps says:
By the way, I had never looked at the comments before, but this is a great tool and I happened upon it through pure luck and have used it ever since. Love the personalization that you can add to it and the features have really been extremely beneficial to me, a person who is not a whiz at computers. I genuinely appreciate the ability to use such a fine instrument and wanted to thank you for providing it.
Karl says:
You’re welcome. Now if only more folks would find it via either “pure luck” or users passing the word!
Aziz says:
karl,
This calculator works awesome! Small feedback.
When I change the data and click Calc button again it doesn’t calculate again based on changed data.
So I have to click clear and enter the data all over again to do the calculation again. So painful to keep reentering if i want to try different permutations and combinations for my loan.
Can you just not clear the amortization calcution table and retain the data in input fields?
Karl says:
Hi Aziz, what are you changing? For example, you can set up the first calculation to calculate the payment amount. If the calculator calculates 815.22 and creates a schedule, you should be able to change the payment to say 825.00 and click calc and a new schedule will be created using 825.00 as the payment.
Is this not happening for you?
Please give me a step-by-step example so I can try it and fix any issues.
Karl says:
But also, please realize this:
>>> When I change the data and click Calc button again it doesn’t calculate again based on changed data.
Taking my first example, if you change the interest rate and expect the calculator to recalculate the payment amount, that’s not how it’s supposed to work.
If you are changing any other loan attribute and you want to see the new payment, you must tell the calculator to calculate the payment by entering a 0 for payment.
This design feature is intentional so that users can use their payback details (like using a payment amount that is not the calculated payment result).
This is explained in a bit more detail on the page. Please see: “Always enter (and reenter) a 0 for the unknown value.” (or what you want calculated based on changed data.)
Chris Wheatley says:
When entering a short first period with Short Period setting of “Reduce all payments”, I’m seeing that the interest charged in the first period is reduced but the payments are not. The principal paid in the first period is increased in order to make the same payment, resulting in a lower payment and principal paid in the final installment.
Is there another setting I have to set to “Reduce all payments” for Short Periods?
I’m also seeing the same for Long Periods. Long Period setting is set to “Amortized” and I would expect all payments to be adjusted, I’m seeing that the interest is increased but the Principal is reduced to maintain the same payment as the standard period, resulting in a higher payment and principal paid in the final installment.
Am I misinterpreting what these settings are to accomplish?
Thank you for your time. Your calculator is great!
Karl says:
Please provide all the loan details so that I can take a look to see the actual results you are getting. Thanks.
Karl says:
Chris, I can’t duplicate what you are seeing.
If I use all the inputs from when the webpage is first loaded and only change the loan date to Dec 15, 2022 and the 1st payment date to Jan. 1, 2023, the first period’s payment is $687.89 and the interest is $66.76.
Then I change the short-period interest setting to reduce all and I recalculate. The payment changes to $737.76 (matching all other payments except for the last payment where the rounding takes place) and the interest charge remains the same, i.e. $66.76.
This does not happen for you?
Chris Wheatley says:
No, this is not happening for me.
When set to “Reduce First”, my first payment is $687.89 and the rest of my payments are $738.92 with the final being $738.93.
After changing the setting to “Reduce All” and recalculating, my first payment changes to $738.92, all of the other payments stay the same at $738.92, except the last which changes to $678.44.
Karl says:
Sorry, I should have told you to enter 0 for the payment amount after you changed the short period setting to reduce all.
The calculator uses the amounts entered, and you need to tell it to recalculate the payment. Please scroll to “Always enter (and reenter) a 0 for the unknown value” for details.
Using the example, the new, reduced payment will be $737.76.
Chris Wheatley says:
Zeroing out the Payment Amount before recalculating fixed it. Thank you so much for your help!
Karl says:
You’re welcome. I know it’s annoying to have to reset a value to 0 to have it recalculate after making a setting change. I wish I could think of a way to design the calculator not to need that step. The problem is, if I had the calculator automatically recalculate the last unknown, then the user would not be able to structure a customized loan. Continuing to use the same example, if the debtor said, “I will pay $750 a month,” the calculator would handle it making an adjustment to the final payment as needed.
COLIN says:
Great tool.
I AM TRYING TO CHECK A LOAN BALANCE GRANTED 10 YEARS AGO AT VARAIBLE INTEREST RATES (PRIME RELATED). REPAYMENTS ARE FIXED AMOUNTS MONTHLY.
IS THERE ANY WAY I CAN USE THIS CALCULATOR ?
Karl says:
Thank you. No, not using the amortization schedule.
However, you can with the loan payoff calculator. It is capable of calculating an exact date loan balance. The user can change interest rates and payment amounts on any date.
Scroll down the page below the calculator for instructions.
Jason says:
Hi Karl,
Firstly this is a very flexible and sophisticated calculator so thank you.
I am trying to understand how the repayments are being calculated for daily compounded interested, and included in that, how it factors in when the first payment date is more than a period from the loan date.
Any advice would be appreciated
Karl says:
You’re welcome, Jason. I can answer two types of questions. How a calculation is set up or what calculator should be used for a particular calculation. I never get involved with details about the calculations, however. Answering those questions tends to be time-consuming and takes me away from the task of creating this site.
Chris Wheatley says:
Hi Karl,
I have a question about this scenario using the Amortization Calculator.
Loan Amt $1,000,000
# Pmts 300
Annual Interest Rate 6%
Loan Date 1/31/2023
First Payment Date 2/27/2023
Compounding Monthly
Amortization Method Normal
Days Count 360
Long/Short Amortized/Reduce All
First period interest is being calculated as $4500 which appears to be based on 27 days of interest. When I change the first payment date to 2/28/2023 (one day later), the interest changes to $5000, which is based on 30 days (3 days more) of interest. I’m assuming this means when there are no odd days, the calculations are based on a 30/360 days count. When odd days are a factor, it seems like for the First period at least, this changes to ACTUAL/360. The rest of the periods seem to calculate on 30/360 days count. Is this accurate?
Thank you.
Karl says:
Hi Chris, odd-day interest is always calculated using actual days (not a fraction of a period). Whether it’s actual over 360 or 365 depends on the day count method selected. Full periods use the periodic interest rate, not a daily rate. The monthly periodic rate happens to produce the same results as a daily 30/360 rate when it’s applied for a “month.”
Chris Wheatley says:
Thanks Karl for the info.
So this is my understanding:
1) For a Short first period, it would calculate interest based on exact days
2) For a Long first period, it would calculate interest for the standard period based on monthly rate, and add additional days based on daily rate. Or would it calculate the interest based on the total days from the Loan Date the First Payment Date?
Thank you.
Karl says:
Whenever there is a whole period, the monthly rate (in your case, because you’ve selected monthly compounding) would be used.
Juan Diaz says:
Hi, my name is Juan Diaz. I am trying to print an amortization schedule, but is not letting me do it, because it saids that I need to be registered. How can I register?
Karl says:
Hi Juan, I’m not sure where you are seeing that message about registration, but at present, you do not need to be registered to print an amortization schedule. Are you clicking on the “Print” button that is located in the top left of the print preview window or at the bottom center of the same window? If you are, are you getting an error message? (When you see the window about the title page, you CANNOT click the “X” in the upper right corner, You MUST click either the “Skip” or “Continue” buttons at the bottom of the title page window.
Please let me know.
James Hann says:
i can’t print amortization schedule and I don’t know how to register.
Karl says:
No registration is required (yet).
Why can’t you print? Do you see any error messages?
Do you see the window asking you for details about the title page? If you do, if you click on either the "Skip" or "Continue" buttons (NOT the "X" in the upper right) do you then seen the schedule? If you do, there are 2 print buttons. One in the upper left corner and one at the end of the schedule in the center.
Please let me know where the problem is.
James Hann says:
I found my problem. There was a pop up ad that obstructed the buttons on the bottom of the page. Thanks for your help.
Karl says:
Thank you for letting me know. I’m working on a site update that will not allow that to happen (hopefully).
John Smythe says:
How do I create an amortization schedule – Canadian semi-annually with a monthly payment that only pays the interest and not any principle off? Thanks
Karl says:
You’ll notice that when you set the amortization method to "Canadian" what it is doing is setting the compounding to "semiannual". That’s all the "Canadian" option does.
Thus, for your case, set the "payment frequency" to "monthly" and the "compounding" to "semiannual" and for the "amortization method" set it to "interest-only".
Brett M. says:
Having issues calculating a new amortization schedule. I have a printed copy of one I did before that worked but as the clients purchase price and first payment date had changed I literally enter the same numbers, interest rate and payment frequency and the amount is like 200K + over and I can’t figure out why?
1st version (that made sense and checked out)
Loan Amount: $400,000
Annual Interest Rate: %7
Loan Date: Feb 15, 2023
Payment Frequency: Monthly
Number of Payments: 240 (20 years)
First Payment: April 6, 2023
Last Payment: March 6, 2043
Total All Payments: $529,444.07
2nd version (that does not add up)
Loan Amount: $407,295.04
Annual Interest Rate: %7
Loan Date: Feb 15, 2023
Payment Frequency: Monthly
Number of Payments: 240 (20 years)
First Payment: April 6, 2023
Last Payment: March 6, 2043
Total All Payments: $$746,800.61
The only thing that changed was the purchase price increased by 7,295.04. Any insight is appreciated.
Thank you.
Karl says:
The second one seems to be right. I can’t duplicate the first result. What payment amount is the first calculation using? ANd does your schedule for the first one mention a rounding adjustment? And is the balance after the 240th payment really 0?
Karl says:
The first one does not make sense when I think about it. At a 7% interest rate, the first year of interest should be nearly $28,000. For the total payments to equal $529,444, that means that in the next 19 years, there will only be a total of $100,000 in interest due. Of course, the amount of interest paid each year will decline as the balance declines. Still, even if the interest declined to $12,000 a year on average, that means in only 12 years, the loan will have required $144,000 in interest payments to amortize the amount fully. The first example calls for only $129,444.07 in interest in 20 years. Some setting was off. Perhaps you had it set to open balance rounding? Please send me the schedule if you can.
Karl says:
Thank you for sending a copy of the first schedule.
The first schedule shows the payment amount to be $3,812.22, which is a lot higher than what is required to pay the loan off in 20 years.
As mentioned in the documentation on this page (see: "Always enter (and reenter) a 0 for the unknown value"), this calculator will allow users to structure a loan. That means it will create a schedule using any numbers the user enters.
With the larger payment amount (in your case) the loan was paid off in less than 20 years and when it was paid off, the loan balance went negative (that is, the debtor has a positive balance [the account was overpaid]) and the balance started to EARN interest bring down the total paid in 20 years.
If the loan is being structured to call for a monthly payment of $3,812.22, probably what you want to do is leave the number of payments set to 0 so that the term is calculated and this will prevent the loan balance from going negative.