Accurate Amortization Calculator

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?

1. Set the Loan Amount to 0.
2. Enter the Number of Payments.
3. Enter the Annual Interest Rate.
4. Enter the expected or target Payment Amount.
5. Click Calc or Print Preview.

How do I calculate how long it will take to pay off a loan?

1. Enter the Loan Amount.
2. Set the Number of Payments to 0.
3. Enter the Annual Interest Rate.
4. Enter the expected or target Payment Amount.
5. Click Calc or Print Preview.

What interest rate allows me to pay $500 a month?

1. Enter the Loan Amount.
2. Enter the Number of Payments.
3. Set the Annual Interest Rate to 0.
4. Enter $500 as the Payment Amount.
5. Click Calc or Print Preview.

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.)

Payment Amount Equation

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

1. Substitute the given values into the annuity payment formula: P = 50,000 × ( (r/n)(1 + r/n)60 ) ÷ ( (1 + r/n)60 – 1 ), with r = 0.05 and n = 12.
2. Evaluate the periodic rate: r/n = 0.05/12 ≈ 0.0041666666667…, and substitute it into the formula.
3. Simplify the base term: (1 + 0.0041666666667…) ≈ 1.0041666666667…, keeping the exponent of 60 in both the numerator and denominator.
4. Compute the fraction: (0.0041666666667… × (1.0041666666667…)60) ÷ ((1.0041666666667…)60 – 1) ≈ 0.018871233644…, then multiply by 50,000.
5. Round the payment to two decimal places for reporting: P ≈ $943.56.

Step-by-step Solution – Fig. 4

1. P = 50,000 × ( (0.05/12)(1 + 0.05/12)60 ) ÷ ( (1 + 0.05/12)60 – 1 )
2. ≈ 50,000 × ( (0.0041666666667…)(1 + 0.0041666666667…)60 ) ÷ ( (1 + 0.0041666666667…)60 – 1 )
3. ≈ 50,000 × ( (0.0041666666667…)(1.0041666666667…)60 ) ÷ ( (1.0041666666667…)60 – 1 )
4. ≈ 50,000 × 0.018871233644…
5. ≈ 943.56

Final Answer

The final answer (P) is approximately 943.56.

Validate the calculator. Inputs for a six-year amortization.

Amortization Equation

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.

P_t-1

Outstanding balance at the start of period t.

P_t

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

1. Compute the periodic rate: i = 0.05/12 ≈ 0.00416666666….
2. Compute the per-period growth factor: r = 1 + i ≈ 1.00416666666….
3. Set the period: t = 1.
4. Start-of-period balance: Pt−1 = 50,000.
5. Accumulate interest for the period: 50,000 × r ≈ 50,208.33333….
6. Round the accumulated balance for display: ≈ 50,208.33.
7. Interest for the period: I = 50,208.33 − 50,000 = 208.33.
8. 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)

1. i = 0.05/12 ≈ 0.00416666666…
2. r = 1 + i ≈ 1.00416666666…
3. t = 1
4. Pt−1 = 50,000
5. = 50,000 × 1.00416666666… ≈ 50,208.33333…
6. ≈ 50,208.33
7. I = 50,208.33 − 50,000 = 208.33
8. Pt = 50,208.33 − 943.56 = 49,264.77

Validate the calculator. Five-year, sixty-month amortization schedule proof.