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Loan-payment math

Amortization Formula and Worked Schedule Example

The standard fixed-payment formula calculates the regular principal-and-interest payment. The schedule then applies that payment one row at a time.

The standard amortization payment formula

M = P × [r(1 + r)n] ÷ [(1 + r)n − 1]
M
regular payment
P
principal or original loan balance
r
interest rate per payment period
n
total number of payments

For monthly payments, divide the nominal annual rate by 12 to obtain the monthly periodic rate. Multiply the term in years by 12 to obtain the number of payments.

Example: $200,000 at 6% for 30 years

  • Principal: $200,000
  • Annual rate: 6.00%
  • Monthly rate: 0.06 ÷ 12 = 0.005
  • Number of payments: 30 × 12 = 360
  • Calculated monthly payment: $1,199.10

The payment remains fixed, but the interest and principal portions change as the balance declines.

First three rows of the schedule

PaymentPayment amountInterestPrincipalBalance
1$1,199.10$1,000.00$199.10$199,800.90
2$1,199.10$999.00$200.10$199,600.80
3$1,199.10$998.00$201.10$199,399.70

Each row uses the prior row's ending balance. Interest equals the starting balance multiplied by 0.005. Principal equals the payment minus interest.

Why software and spreadsheets can differ by a few cents

Programs may round interest to cents on every row or retain additional precision until totals are displayed. Exact dates and day-count conventions can also produce a different result than a simple monthly periodic formula.

When comparing a lender statement, use the same dates, compounding assumptions, rounding rules, and payment-posting method.

Continue with more complex schedules

Once the basic formula is understood, review how extra payments, changing rates, and balloon maturities alter later rows.

Build and compare the schedule

Use the free amortization calculator for a standard schedule. Use the registered Windows amortization software when you need to edit individual dates, payments, rates, or notes and save the revised loan.

Questions

Frequently asked questions

What is the monthly rate for a 6% annual rate?

For a standard monthly periodic calculation, 6% divided by 12 equals 0.5% per month, or 0.005 as a decimal.

Why does the interest portion decline?

Interest is calculated from the remaining balance. As principal is repaid, the balance and later interest amounts decline.

Why might my lender schedule differ?

Dates, day-count conventions, compounding, payment posting, fees, and row-by-row rounding can cause differences.