Amortization Schedule Formula and Monthly Payment

An amortization schedule shows how each regular loan payment is divided between interest and principal, and how the balance changes over time. Enter the loan amount, annual APR, and term to calculate the monthly payment and total interest; the schedule’s rows can then be built from those figures.

Formula

For a fixed-rate loan repaid with equal monthly payments, the standard payment formula is:

M = P × r ÷ [1 − (1 + r)⁻ⁿ]

• M is the monthly payment, in dollars.
• P is the starting principal, or loan amount, in dollars.
• r is the monthly interest rate as a decimal: annual APR expressed as a percentage ÷ 1,200. For example, 8% APR gives r = 8 ÷ 1,200.
• n is the total number of monthly payments: loan term in years × 12.

The schedule formula applies that payment one month at a time. For payment number k, calculate interest as the previous balance multiplied by r; calculate principal paid as M minus that month’s interest; then subtract the principal paid from the previous balance. In symbols, if B_k−1 is the balance before payment k:

Interest_k = B_k−1 × r
Principal_k = M − Interest_k
B_k = B_k−1 − Principal_k

An equivalent direct balance formula is B_k = P(1 + r)^k − M[(1 + r)^k − 1] ÷ r, for a positive rate and payments made at the end of each period. A full schedule repeats the row calculation for each month, beginning with B₀ = P. Total interest in this calculator is the rounded monthly payment multiplied by the number of payments, minus the original principal.

Worked Example

Using the calculator’s defaults—P = $20,000, APR = 8%, and a five-year term—the monthly rate is 8 ÷ 1,200 = 0.0066667 and n = 5 × 12 = 60 payments.

1. Substitute into the payment formula: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
2. The unrounded payment is approximately $405.5276, which rounds to $405.53 per month.
3. Total of the rounded payments: $405.53 × 60 = $24,331.80.
4. Total interest: $24,331.80 − $20,000 = $4,331.80.

For the first schedule row, interest is $20,000 × 0.0066667, or about $133.33. Principal is $405.53 − $133.33 = $272.20, leaving a balance of about $19,727.80. Later interest amounts fall as the balance falls, while more of each unchanged payment goes toward principal.

Assumptions

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

How to Read an Amortization Schedule

A typical schedule includes the payment number or date, starting balance, payment amount, interest, principal, and ending balance. The ending balance in one row becomes the starting balance in the next. In the early months, interest is calculated on a larger balance, so it takes a larger share of the payment. As principal is repaid, the interest portion generally declines.

With the example above, the first payment applies about $133.33 to interest and $272.20 to principal. The exact cents shown by a lender can differ because of payment dates, daily-interest calculations, rounding rules, or other loan terms. The last payment may also be adjusted to clear a small remaining balance rather than equal the earlier payments.

When to Use the Formula

Use the formula to understand the mechanics of a level-payment, fixed-rate loan or to make an estimate when you know the principal, APR, and number of payments. It can help you inspect a quoted payment, estimate total interest under the stated assumptions, or see how principal and interest change through the term. Get the actual APR, fees, payment dates, and repayment terms from the lender’s disclosure; the calculator does not supply those inputs.

The formula is not a complete model for every borrowing arrangement. A variable-rate loan can change its payment or schedule when its rate resets. Interest-only periods, irregular payments, payment holidays, daily accrual, and fees added to the balance require additional rules or inputs. A schedule based on a single fixed APR cannot predict those changes.

Common Errors and Limits

• Using the APR as the monthly rate: for a monthly calculation, convert a percentage APR to a decimal monthly rate by dividing the percentage number by 1,200. Do not enter 8 as though it were a decimal rate.
• Mixing years and months: the formula needs a number of monthly periods. Convert a term in years to months by multiplying by 12.
• Rounding each intermediate step: repeated rounding of monthly interest and balances can create small discrepancies. Keep adequate precision during calculations and round displayed money amounts to cents; a lender may use its own method.
• Confusing total payments with interest: total payments include repayment of the amount borrowed. Estimated interest is total payments minus principal, not the entire total.

A zero-rate loan is a special case: its equal payment is P ÷ n, because no payment goes to interest. The calculator’s APR minimum is 0.01%, so it does not use the zero-rate case. The formula also assumes the payment fully amortizes the balance over the stated term; a payment that does not cover accruing interest would not do so.

Frequently Asked Questions

What is the formula for an amortization schedule?
First find the level payment with M = P × r ÷ [1 − (1 + r)⁻ⁿ]. For each period, multiply the current balance by the periodic rate to find interest, subtract that interest from the payment to find principal, and subtract principal from the balance.

How do I calculate the interest in each monthly payment?
Multiply the balance immediately before that payment by the monthly rate. For example, a $20,000 balance at an 8% APR under monthly-rate assumptions accrues about $133.33 for one month.

Why does the principal portion increase over time?
With a fixed rate and level payment, interest is calculated on the outstanding balance. As the balance shrinks, the interest amount tends to shrink too, leaving more of the same payment to reduce principal.

Does an amortization schedule include taxes and insurance?
Not in the standard loan amortization calculation. It tracks principal and interest; property-related costs, insurance, escrow, and fees are separate unless the schedule specifically models them.

Can extra payments change the schedule?
Yes. An extra amount applied to principal reduces the balance, which generally changes later interest and the payoff timing. The basic calculator does not model extra payments, and how they are applied depends on the loan’s terms and servicing.

This result is an estimate, and the lender’s disclosure gives the exact figures.

Related

• Interest Rate Right Now? What the Number Means
• RBA Interest Rate Calculator: See Monthly Interest
• Interest Rate Reduction Calculator and Loan Payment Effects

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