Loan Constant Amortization Table: Formula and Example

A loan constant amortization table shows how each scheduled payment is divided between interest and principal, and how the balance declines over time. Enter the loan amount, APR, and term below to calculate the fixed monthly payment and total interest; the table’s rows can then be built from those figures.

Formula

This calculator uses the standard level-payment amortization formula. It finds the monthly payment first; a complete amortization table applies that payment period by period to calculate interest, principal repaid, and the remaining balance.

• Monthly payment: M = P × r ÷ [1 − (1 + r)⁻ⁿ]
• Monthly interest rate: r = APR ÷ 1,200, when APR is entered as a percentage per year.
• Number of monthly payments: n = term in years × 12.
• Total interest: I = M × n − P, using the unrounded formula payment in this calculator’s expression.

P is the starting loan principal in dollars, M is the monthly payment in dollars, r is the monthly rate as a decimal, and n is the number of monthly payments. The calculator displays the payment and interest to two decimal places. For an actual lender schedule, payment rounding and the lender’s stated accrual method can change the final cents.

Worked Example

Using the defaults—$20,000 principal, 8% APR, and a five-year term:

1. Convert APR to a monthly rate: 8 ÷ 1,200 = 0.0066667, or about 0.66667% per month.
2. Find the number of payments: 5 × 12 = 60.
3. Substitute into the payment formula: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
4. The monthly payment is approximately $405.53.
5. Total interest from the calculator’s formula is approximately 405.53 × 60 − 20,000 = $4,331.80, using the displayed, rounded payment.

Small differences in the final total can arise if a schedule rounds each monthly payment to cents before multiplying. The calculator’s total-interest output follows its displayed expression, so it is an estimate rather than a lender-issued payoff schedule.

Assumptions

• The interest rate remains fixed for the full term.
• Payments are equal, made monthly, and paid at the end of each period.
• Interest is calculated monthly using APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, late charges, and extra payments are not included.

How to Read a Loan Amortization Table

A conventional amortization table has one row for each payment period. Common columns show the payment number or date, beginning balance, payment amount, interest, principal, and ending balance. For a standard fully amortizing fixed-rate loan, the payment remains level, while the shares going to interest and principal change.

To calculate a row, multiply the beginning balance by the monthly interest rate to get that period’s interest. Subtract the interest from the scheduled payment to find principal repaid. Subtract that principal from the beginning balance to get the ending balance, which becomes the next row’s beginning balance.

• Period 1 interest: $20,000 × 0.0066667 is about $133.33.
• Period 1 principal: about $405.53 − $133.33 = $272.20.
• Period 1 ending balance: about $20,000 − $272.20 = $19,727.80.

As the balance falls, the interest portion generally falls too, leaving more of a level payment to reduce principal. The final scheduled payment may need a small adjustment because amounts are rounded to cents.

Building or Checking the Table

To create a table in a spreadsheet or by hand, use the loan’s actual principal, periodic rate, payment, and payment dates. Begin with the lender’s disclosed figures when available. Then repeat the row calculation above until the balance reaches zero. Keep more than two decimal places in intermediate calculations if you are doing a mathematical illustration, but use the lender’s rounding and timing conventions when checking its statement.

Before relying on a table, confirm these details:

• Whether the stated APR is fixed or can change, and whether the rate entered represents the rate used to accrue interest.
• Whether payments are monthly and when they are due.
• Whether the amount entered is the amount financed or only the amount borrowed before financed charges.
• Whether extra principal payments, fees, skipped payments, or irregular first periods affect the schedule.

Common Misunderstandings and Limits

A loan constant is often used to mean the annual debt service divided by the original loan principal. That is different from a full amortization table: the constant is one ratio, while the table traces each payment and the changing balance. A loan constant may be expressed as a percentage, but it is not the same thing as the APR. APR describes a rate under stated assumptions; a constant summarizes scheduled payment amounts relative to principal.

Another frequent mistake is treating the whole monthly payment as principal repayment. Interest is charged on the outstanding balance, so early payments on a typical amortizing loan include a larger interest share than later payments. Also, total interest is not simply the APR multiplied by the original balance and term: the balance declines as principal is repaid.

This calculator assumes a fixed rate and regular monthly payments. It does not model adjustable rates, daily interest accrual, payment holidays, balloon payments, irregular schedules, lender-specific rounding, or extra payments. A variable-rate loan or a loan with unusual payment timing needs its actual contract terms and a schedule built for those terms. For a balance after a particular date, use the lender’s payment history and posted transactions rather than assuming every payment occurred exactly as scheduled.

Frequently Asked Questions

What is a loan constant amortization table?
A loan amortization table lists each scheduled payment and shows how much goes to interest and principal, along with the remaining balance. “Loan constant” can also refer to annual debt service divided by original principal, which is a separate summary ratio.

How do I calculate the interest in each table row?
Multiply the period’s beginning balance by the periodic interest rate. For monthly calculations using an APR stated per year, the usual simplified rate is APR divided by 12, with APR first expressed as a decimal.

Why does the principal portion increase over time?
With a fixed payment and rate, a lower balance produces less interest in a later period. The remaining part of the payment therefore goes toward more principal.

Does APR equal the loan constant?
No. APR is an annualized rate measure, while the loan constant is typically scheduled annual payments divided by original principal. They answer different questions and generally have different values.

Why might my lender’s table differ from this estimate?
The lender may use different rounding, accrual timing, payment dates, fees, or loan terms. Variable rates and extra or late payments also change the balance path. Check the loan disclosure or servicing statement for the contract-specific schedule.

This result is an estimate for educational arithmetic; the lender’s disclosure gives the exact figures.

Related

• Amortization Table With Quarterly Payments
• Amortization Table With Start Date: How It Works
• Amortization Table With Fixed Monthly Payments

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2