Amortization Schedule With Known Payment Calculator

This calculator estimates the monthly payment and total interest for a fixed-rate loan when you enter the loan amount, APR, and term; those figures determine the payment used in a level-payment amortization schedule. It does not build a row-by-row schedule, but the explanation below shows how to calculate each period’s interest, principal, and remaining balance from a known payment.

Formula

For a fixed-rate loan with equal monthly payments, first calculate the periodic interest rate and number of payments:

• Monthly rate: r = APR / 1,200, where APR is entered as a percentage per year and r is the decimal rate per month.
• Number of payments: n = 12 × years.
• Monthly payment: M = P × r / [1 − (1 + r)⁻ⁿ]. The calculator rounds M to the nearest cent.
• Total interest: I = M × n − P, using the rounded monthly payment.

Here, P is the original principal in dollars, APR is the annual percentage rate in percent, r is the monthly rate as a decimal, n is the number of monthly payments, M is the monthly payment in dollars, and I is total interest in dollars. A full schedule then uses the payment to split each installment between interest and principal.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and a five-year term:

1. Convert the APR to a monthly decimal rate: r = 8 / 1,200 = 0.0066667.
2. Find the number of payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: M = 20,000 × 0.0066667 / [1 − (1.0066667)⁻⁶⁰] ≈ $405.53 per month.
4. Calculate total interest using the rounded payment: I = $405.53 × 60 − $20,000 = $4,331.80.

The result is an estimated level payment of $405.53 and total interest of $4,331.80 over 60 payments. The last installment may differ slightly in a lender’s actual schedule because of rounding or payment-date conventions.

Assumptions

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

How to Build a Schedule With a Known Payment

Once the monthly payment is known, calculate the schedule one period at a time. At the start of a month, take the outstanding balance and multiply it by the monthly rate. That is the period’s interest. Subtract the interest from the payment to find the principal paid. Then subtract that principal from the prior balance.

• Interest for month t: I_t = B_t−1 × r.
• Principal for month t: C_t = M − I_t.
• New balance: B_t = B_t−1 − C_t.

B_t−1 is the balance before the payment, B_t is the balance after it, and M is the known payment. For example, on the default loan, month one’s interest is $20,000 × 0.0066667, or about $133.33. Of the $405.53 payment, about $272.20 reduces principal, leaving roughly $19,727.80. Repeating the calculation creates the schedule. Keep full precision in intermediate calculations when possible and round displayed amounts to cents; repeatedly rounding intermediate rates or balances can create small discrepancies.

What the Schedule Shows

An amortization schedule is a time-ordered record of how payments repay a loan. Typical columns include payment number or date, starting balance, payment, interest, principal, and ending balance. Early in a standard amortizing loan, the balance is larger, so the interest portion is generally larger. As principal falls, interest for later periods generally falls too, leaving more of the same payment to reduce principal.

The schedule helps distinguish the stated monthly payment from total borrowing cost. A payment is not all principal: the interest portion is the charge for that period under the calculation assumptions. The total-interest figure is the sum of scheduled interest, not an additional amount to add to the monthly payment. It also does not necessarily equal the total finance cost if charges outside this calculator apply.

When a Payment Is Already Known

If a lender has supplied a payment amount, use that amount as M in the period-by-period formulas rather than relying on the calculator’s calculated payment. You still need the current balance, the rate for each period, and the payment timing to produce a meaningful schedule. If the loan has a variable rate, different fees, irregular payment dates, or a payment that changes, one fixed monthly-rate formula cannot represent every period; calculate each period using the terms that apply then.

A payment may also be too small to cover the period’s interest. If M is less than B × r, then principal paid, M − B × r, is negative and the balance grows rather than amortizes. A schedule that assumes payoff by a set end date must also account for a final payment adjusted to clear any small balance caused by cent rounding. Do not assume the last regular payment is exactly the same as every earlier one.

Common Errors and Limits

• Mixing rate units: Enter APR as a percentage, such as 8, not 0.08. The formula divides by 1,200 to convert percent per year into a decimal monthly rate.
• Using the wrong payment frequency: This calculator assumes monthly installments. A weekly or biweekly payment schedule needs a matching periodic rate and payment count.
• Confusing payment with principal: Only payment minus period interest reduces the balance.
• Ignoring timing and extra charges: Late payments, fees, and payments made on dates other than the assumed monthly schedule can change actual balances.
• Overinterpreting totals: Total interest is based on the entered principal, APR, term, and rounded payment. It does not model taxes, insurance, or other charges.

The standard formula is designed for a fixed rate, regular equal payments, and a fully amortizing balance. It is an estimate, not a replacement for the loan’s actual payment and balance records.

Frequently Asked Questions

How do I calculate an amortization schedule with a known payment?
For each period, multiply the beginning balance by the periodic rate to get interest. Subtract that interest from the payment to get principal, then subtract principal from the balance.

Can I make a schedule if I know the payment but not the loan term?
You can calculate each period’s balance if you know the starting balance and rate, but you cannot determine the full schedule or payoff date without enough information to establish how long payments continue.

Why does the interest portion decrease over time?
With a fixed rate and a declining principal balance, each period’s interest is calculated on a smaller amount. When the payment stays level, a larger share can then go toward principal.

Does the monthly payment include taxes and insurance?
Not in this calculator. It estimates principal and interest only; any taxes, insurance, escrow, or fees must be considered separately using the figures that apply to the loan.

Why might my lender’s schedule differ by a few cents?
Rounding conventions, exact payment dates, daily-interest methods, fees, or a final payment adjustment can produce small differences. Check the lender’s disclosure for the contractual figures.

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

Related

• Amortization Schedule in Excel: Formula and Example
• Amortization Schedule Maker: Payments and Balance
• Amortization Schedule: Interest-Only Loan Calculator

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