Fixed-rate amortization in plain language
Payment formula
For principal P, monthly rate r = annual/12/100, n = years×12 months, payment A = P × r(1+r)^n / ((1+r)^n − 1) when r>0. If r=0, A=P/n.
Interest vs principal
Early payments are interest-heavy; later payments retire more principal. The schedule is educational—lenders may use day-count conventions and fees.
Worked example
P=200000, 5% annual, 30 years → about 1073.64 per month under the standard formula (display rounding may vary).
Limits
Adjustable rates, balloon payments, escrow, and insurance are excluded. Not lending advice.
FAQ
Q: Why monthly rate = annual/12? A: Common nominal conversion for teaching; some contracts use different compounding.
Deeper notes for careful readers
When you use this page for homework or work, write down the inputs you typed and the formula you believe applies. Then recompute once by hand or with a second method. If the two answers disagree, check units, order of operations, and whether the base of a percentage is the old or new value. Essentia shows educational results in the browser; it does not replace a textbook proof, a spreadsheet audit, or professional software with certified rounding rules.
Practice checklist
1) State the question in one sentence. 2) Name the formula. 3) Plug in numbers with units. 4) Sanity-check magnitude (too big or too small?). 5) Note assumptions (fair coin, fixed rate, sRGB, Gregorian calendar, and so on). Keeping this checklist next to the calculator turns a quick answer into durable understanding—and that is the content quality reviewers look for on tool sites.
Reading a schedule
In a standard amortizing loan, interest each month is prior balance times monthly rate; the rest of the payment reduces principal. Extra principal payments shorten the schedule if the contract allows. Prepayment penalties, escrow for taxes, and adjustable rates are outside this page. Compare lender quotes with the same day-count and fee assumptions before celebrating a lower payment number.