An Amortization Schedule Calculator
An amortization schedule is the month-by-month ledger of a fixed-rate loan: every payment is the same size, but the split between interest and principal shifts a little each month. Early on almost everything goes to interest; near the end almost everything goes to principal. The monthly payment comes from one formula, and from it you can read off the first month's interest, the principal that payment retires, and the balance left afterwards.
Monthly payment
$386.66
- Number of payments
- 60
- First-month interest
- $100.00
- Principal in payment one
- $286.66
- Balance after payment one
- $19,713.34
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
M = P x r / (1 - (1 + r)^-n)
- P
- Amount borrowed after any down payment
- r
- Monthly interest rate, the annual nominal rate divided by 12
- n
- Total number of monthly payments, years times 12
- M
- Fixed monthly payment of principal and interest
How to check the result by hand
- 1
Convert the rate to monthly
A 6% annual nominal rate is 0.06 / 12 = 0.005 a month. Using 6% directly charges six percent every month and makes the payment look about twelve times too large.
- 2
Count the payments
Five years is 5 x 12 = 60 monthly payments. A 30-year mortgage is 360; the count, not the years, is what the formula wants.
- 3
Apply the payment formula
Compute (1+r)^-n first, subtract it from 1, then divide. For 20,000 at 0.005 over 60 months the payment is 386.66.
- 4
Split the first payment
Interest is 0.005 x 20000 = 100.00. Subtract it from the payment to get the principal portion, 286.66.
- 5
Roll the balance forward
Reduce the balance by the principal portion to get 19,713.34. Repeat for month two on the new balance; the interest shaves down every month.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate An Amortization Schedule page.