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.
Debbie says:
I need to enter specific payment daters and amounts. Can I do that?
Karl says:
Not with this calculator.
But you can with this loan payoff calculator.
Dennis Roberts says:
I am trying to resolve some discrepancies in my spreadsheet versus the “Calculation Method : Normal 360 Days per Year” amortization calculator.
When I input the data listed below, The Calculator shows interest for the first payment to be $26.49. But I believe after due diligence the result should be $25.64.
My formula used to calculate interest for the first payment is : “30751.88 * (1+ .01/360) power(30) -30751.88”. And using this formula (Start Amount * (1+Interest Rate/360)^30 – Start Amount) to term, the total interest is $1417.97 while The Calculator shows $1439.16.
Could you describe your formula used to calculate Interest in the “Calculation Method : Normal 360 Days per Year” amortization calculator? Could you be using the actual days per month instead of the normalized 30 days per month?
Loan Amount: 30,751.88
Annual Interest Rate: 1.0%
Loan Date: 01/01/2014
Payment Frequency: Monthly
Points: 0.0
Number of Payments: 108
Payment: 297.87
First Payment Date: 02/01/2014
Compounding: Daily (360)
Amortization Method: Normal
Karl says:
From only reading your comment and not doing any actual arithmetic, it looks to me as if you are only accounting for 30 days of interest. Jan 1 – Feb 1 should be for 31 days of interest.
Yes, I know the daily rate is based on a 30 day month, but the lender will still charge interest for the actual number of days the money is borrowed.
Dennis Roberts says:
OK, I get it now. Thanks.
Dennis Roberts says:
Do you have a 30/360 Calculator?
Karl says:
I don’t know what you mean by a 30/360 calculator.
Dennis Roberts says:
30/360 interest calculation assumes that all 12 months of a calendar year have 30 days and uses a 360-day year.
Karl says:
I got you, I guess you want an amortization schedule calculator that supports a 30/360 calculation. I didn’t know what you had meant by 30/360 calculator.
This calculator supports 30/360. Set compounding to "Monthly" and days-per-year "360". If you set up a calculation this way, then all full months will be the same length i.e. 30 days and odd day interest calculations will use a 360 day year.
Dennis Roberts says:
Ok, I see that….”Monthly Compounding” , 360 days .
But my situation is slightly different. I loaned some money with interest compounded “Daily” assuming that all 12 months of a calendar year have 30 days and every year has 360 days. I keep trying to force the Daily 360 option to do that, but as you described earlier, this option is really 360 days a year and exact days in each month. So what option(s) should I select to get my loan amortization schedule?
Also, since I accept irregular anytime payments, I need a corresponding loan payment schedule.
Thx
Karl says:
The 30/360 calculation, as you say, is the same as monthly compounding. I guess the issue that you are having is, when there are odd days, you want to have daily compounding. This calculator though uses exact/simple for the odd days. (Personally, I think it’s a bit unusual to have a loan based on monthly compounding and then switch to daily compounding for certain circumstances.)
You can have 30/360 for full months and change compounding to daily as needed if you want to use this loan payoff calculator.
paul says:
there is a bug… when i do the report using 365 days and then do it using 360 days, it usually comes out exactly the same… something isnt working right.
paul says:
usig the following loan amt$90,885.17 for 3.75% ans 120 months.. 0 for payment… i get the exact same results no matter if i set for 360 or 365 days.
Karl says:
Every setting for this calculator is important. How do you have compounding set? What are the dates you are using?
Also, are you looking for a payment amount change? Or are you looking at the calculated interest?
Believe me, there is no bug.
john says:
how do i get the amortization schedule to give me full terms and payments for 360 months?
I have them for the first year but then the chart stops. Please advise on how to get the full chart.
Karl says:
What unknown are you asking the calculator to solve for? What are your inputs? At the end of the first year, is there still a balance?
If there is a balance, then I assume you enter all values with no unknown value, and using the values you entered, the loan schedule is for the number of payments you entered.
Sorry, but without more details, I really can’t give you a specific answer.
But rest assured, this calculator will create a printable amortization schedule that runs for 360 months.
Trudy West says:
I used to print the amortization schedules I need, but now get the message that the full schedule will only be printed for registered users. So, how do I register as a user? I am assuming there is a fee, but I would like to know how I can proceed on this.
Karl says:
At this time, everyone should be able to print the full amortization schedule. In the future, printing may be limited to registered users, but that’s not the case now.
Use the "Print Preview" button and then "Print".
Trudy West says:
Thank you – I tried it again, and it worked. Not sure why I got that other message, but glad it’s gone!
Frank Price says:
The calculator has me making a payment the first month?
Karl says:
Please note, the user sets the first payment date. You can have the first payment paid on any day (on or after the loan date – when you get the money) that you want.
Also note, under "Settings", the user has control on how the interest is handled if the first payment period is shorter or longer than the other schedule payment periods.
Frank Price says:
But the calculator has me paying the first months interest it should be added into the interest of the first delayed months payment and paid there. And not at day one but at the delayed start date So where am I wrong here that is how my calculator works but I think mine has other problems because I don’t get there monthly payment. So I think that they’re adding the first months interest to my loan and charging me interest on the first month interest for the 72 months.
Karl says:
Alright, if I understand you correctly, it sounds as if the loan has a long first period (the time between the loan date and first payment date is longer than the selected payment frequency).
If that’s the case, click on "Settings" and pick "Long/Short Period Options".
Then in the first group of options for the long period, select "With first".
Does this help you? If not, please provide your loan date, first payment date, and payment frequency settings.
Frank Price says:
Loan Amount?:
$34,173.32
Number of Payments?:
72
Annual Interest Rate?:
0.9000%
Payment Amount?:
$487.74
Enter a “0” (zero) for one unknown value above.
Loan Date?:
04/02/2021
First Payment Due?:
05/17/2021
Payment Frequency?:
Monthly
Compounding?:
Monthly
Points?:
0.000
Amortization Method?:
Normal
No/YrDatePaymentInterestPrincipalBalance
1:104/02/202112.7512.750.0034,173.32
1:105/17/2021487.7425.63462.1133,711.
The 12.75 should not be paid or entered there, it should be added to the 25.83 and paid then.
WEBMASTER EDIT (I’m copying the multiple comments and making a single single comment below):
Thanks that did it. I should have done that first Thanks
That didn’t work either as it made my first payment increased by that interest amount
I clicked on amortized and now the last payment is more? 34173.32 at 0.9 for 72 months 45 day delay start. like you I get 487.74 but they get 487.91 and I’m trying to see whos calculator is right.
Another problem the number year doesn’t always match the year
Karl says:
Hi Frank, sorry not to have gotten to this earlier. I got sided track with getting ready for the holiday weekend.
There are several things going on here, and there are a few things a user has to remember.
a. There are no laws in any U.S. jurisdiction, that I’m aware of, that stipulate regulations for how a loan is paid back.
b. This calculator is very flexible, and it offers a lot of options that allow it to handle any (or almost any) REGULARLY amortization. (Unfortunately, all the options can lead to confusion.)
Given the above, there is no such thing as a “correct” loan payment amount. The payment amount can be any amount that both the lender and the borrower agree upon. That’s exactly why this calculator also lets the user set a payment amount for the regularly scheduled payments.
The above may sound silly, but it’s not. What IS IMPORTANT is the amount of interest that gets calculated. If a loan balance is $100,000 and the lender calculates $750 interest for the month and the borrower calculates $748.50 for the month, then there is a problem. But if both parties calculate a $750 interest amount and the lender says the payment is $1,000 and the borrower says it’s $998, that is not a real problem. All it means is, if the borrower pays the $1,000 payment, they will be paying an "extra" $2 toward principal which they owe anyway. They are not being cheated. Actually, the higher payment means they will be paying slightly less interest over the term of the loan – generally thought of as a good thing.
Now, about the extra $12.75 interest amount due because you have a longer initial period. You said the first payment was increased by that amount. Yes, that’s because that’s how you set the option.
How would you like the calculator to handle that $12.75? It is an accurate interest amount, and it is due to the lender. Notice you have 4 options:
"None"
"With origination"
"With first"
"Amortized"
"None" means the lender is willing to forget the interest for those extra days – not likely! 🙂
"Amortized" means that a small portion of the the $12.75 is added to each payment over the entire loan. Maybe this is why the lender’s payment is higher than this calculator’s calculated amount?
Does any of this help?
Please let me know.
I have another calculator on this site that is even more flexible if you need it.
Frank Price says:
Boy is all this confusing but I finally got the values I wanted and your calculator is good. The reason my calculator gets a lower payment than them is that the extra interest at the beginning is added to the last payment. So now I have got to look at the equations and see why they are wrong. Thanks for the help and I’m surprised that after looking for sometime I found you and the banks I have checked don’t have them that good and my own bank couldn’t even due it for me.
Karl says:
Glad it worked out for you. Yes, there are a lot of options to consider. For many cases, the options don’t make a lot of difference – for example if someone wants to see "about" how much a mortgage or car payment might be. But if you need to the penny accuracy, then all the settings are important.
Hillary says:
If an extra payment was made against principal in a specific month and year, how can I enter and calculate to have the balance adjusted but keep the same interest rate and set monthly payment.
Karl says:
You can’t do that with this calculator.
However, you can enter an extra payment on any date you want and create an amortization schedule with this loan calculator. See the "Options" tab.