The formula, and what the rate is not
With a nominal annual rate, monthly compounding, and no contributions, the balance after t years is the starting amount times one plus the rate divided by 12, raised to 12 times t. With a contribution C at the end of each month, add C times the quantity of that same growth factor minus one, divided by the monthly rate. At a zero rate the balance is the starting amount plus C times the number of months. The ending figure on this page is that result, rounded half-up to the cent. The year table uses the same formula at each year-end.
Investor.gov, the Securities and Exchange Commission's investor site, publishes a compound interest calculator with those inputs: an initial investment, an amount you plan to add every month, an interest rate, and how many times a year the interest is compounded. This page always compounds monthly. It does not submit numbers to Investor.gov, and that calculator's page does not print the worked totals below. The totals are the formula, checked in the tests. Five percent is the example in the form so the arithmetic can be repeated. It is not a forecast of a savings account, a bond, or a fund, and it is not financial advice.
Giuseppe Ilarda, the site owner, writes and checks this page. The disclaimer says the same limit in more words: the site does not know what you should do with the money, and a result here is not a recommendation. The editorial policy is where the loan pages' rounding lives. This formula is separate. It does not amortize a debt. It grows a balance.
Two checked examples
Start with $10,000.00, add nothing, and compound 5% monthly for 10 years. The unrounded balance is 10,000 times (1 + 0.05/12) to the 120th power, which is 16,470.09497… before the cent rounding. Half-up, the page shows $16,470.09. The growth above the $10,000.00 you started with is$6,470.09. No contribution was added, so the contributions line is$0.00.
Start at zero and add $100.00 at the end of each month, still at 5% monthly for 10 years. You put in$12,000.00, which is 100 times 120. The formula result rounds to$15,528.23. The difference, $3,528.23, is growth under that assumption, not a yield someone promised. Change the rate and both totals move. The page will not pick a rate for you, and it will not label 5% as typical, average, or safe. Those words would be a claim this site has not sourced.
Why the deposit waits until the end of the month
A contribution can be modeled at the start of the period or at the end. The start-of-month version multiplies each new deposit by one plus the monthly rate before the month is over. The end-of-month version, which this page uses, adds the deposit after the growth step. Over many years the gap is real, and it favors the start-of-month story. Publishing both without saying which one is on the screen would let a reader compare two silent conventions. End-of-month is the one in the tests. If you are paid at the beginning of the month and you move the money the same day, a start-of-month model would be a little higher. This page will not quietly use that higher model.
Monthly compounding is the only frequency on the form for the same reason. Investor.gov lets a reader pick annual through daily. A monthly deposit inside an annual compound period needs a rule: all twelve deposits at the end of the year, or spread through the year, or credited on a chosen day. Each rule changes the balance. This page refuses the choice by compounding once a month, in step with the contribution. Daily compounding is not estimated from a 365-day year here, because that would be another convention this page has not pinned to a published worked example.
What the balance leaves out
Taxes are not subtracted. Interest in a taxable account can be taxed in the year it is credited. A retirement account can defer that tax or, in a Roth account, treat qualified withdrawals differently. This page does not know the account type, and it does not apply a tax rate. Fees are not subtracted. An expense ratio of a fraction of a percent, year after year, changes the ending balance. The rate you type is used as if it were the rate after whatever you meant it to be after. If you want a net rate, type the net rate. The page will not invent a fee.
Inflation is not removed. The balance is in the same dollars you typed, not in purchasing power. A$16,470.09 result ten years out does not say what that sum buys. Contribution limits are not applied. You can type a monthly amount no workplace plan would accept. Theretirement savings calculator is the page that caps an elective deferral at the 2026 IRS limit and then uses this same monthly growth formula. The loan pages go the other direction: they charge interest on a balance you owe. Thepayoff calculator is that direction. Do not read a compound-interest balance as the payoff of a debt.
How to read the year table
Each row is the balance after that many years, the contributions added during that year, and the change in the rounded balance minus those contributions. Because each year-end balance is rounded to the cent, a single year's growth line can be a cent away from the unrounded formula for that year alone. The ending balance at the top of the calculator is the rounded value of the full formula, and the tests check that figure, not a story about markets. If the rate is zero, every growth cell is zero and the balance is the money you put in.
The form accepts a starting amount of zero, a contribution of zero, or both. Both at zero stays at zero. A rate above 100% is rejected, as is a term longer than 80 years. Those bounds are there so a mistyped number does not produce a balance this page cannot show. They are not investment rules. Nothing in the table is a suggestion to save a particular monthly amount, and nothing here is a substitute for the disclosures on an account you actually open.