How we calculate

Every formula this site uses, written out, along with the assumptions attached to it and the places where it will differ from your real account.

The rule that decides everything else

APY is an effective annual yield. Compounding is already inside it. That single fact determines how every projection on this site is built, and getting it wrong is the most common error in savings calculators.

To move a balance forward by one month using an APY, you invert the compounding:

monthlyRate = (1 + APY)1/12 - 1

You do not divide the APY by twelve. Dividing and then compounding applies compounding a second time and overstates the result. On a 4.00% APY, the correct monthly rate is 0.00327374 while APY divided by twelve gives 0.00333333. The gap looks trivial and it is not: on $10,000 over one year it is $7.42, and over thirty years it grows to $701.01.

A useful side effect of doing this correctly is that compounding frequency stops mattering. Convert the same APY to a daily rate with (1 + APY)1/365 - 1 and compound it 365 times and you land on the same annual figure. That is what APY means, and it is why this site does not offer a compounding frequency selector on the main calculator.

Projecting a balance

The main calculator runs an explicit loop, one iteration per month, rather than a closed-form annuity formula. Each month it credits interest, then adds your deposit:

interest = balance × monthlyRate
balance = balance + interest + monthlyDeposit

Two reasons for the loop. It produces the year-by-year table without a second calculation, and it has no division in it, so a 0% APY cannot produce a divide-by-zero the way the annuity formula can.

The assumptions, stated plainly

Your APY is held constant for the whole term. No variable-rate savings account has ever done this. A five-year projection is a reasonable planning figure; a thirty-year projection is an illustration of how compounding behaves, not a forecast.

Deposits post at the end of each month and earn nothing in the month they land. Some banks accrue from the day funds clear, which would produce a slightly larger balance. We chose the conservative version so the tool is more likely to understate than overstate.

Interest compounds monthly into the same account. Nothing is withdrawn, no fees are charged, and no minimum balance requirement is applied.

Tax and inflation are excluded unless you enter rates for them. Both are off by default because most people arrive wanting the gross number first.

Tax

When you enter a marginal rate, the calculator runs a second, parallel projection where tax on the interest is deducted from the account at the end of each year. This matters because tax paid is money that stops compounding, so deducting it once at the end would understate the cost.

It applies a single flat marginal rate. Real tax involves brackets, filing status, state rules, and thresholds that this model does not attempt. Treat the after-tax figure as an estimate for comparison, not a number to file with.

Inflation

The inflation-adjusted figure discounts the final balance back to today's money:

realValue = finalBalance ÷ (1 + inflationRate)years

It answers "what would this pile buy in today's terms", not "what will prices be". Your own inflation rate depends on what you actually spend money on and will not match the headline index.

Solving for time and for contributions

The savings goal calculator answers two questions with two different methods.

For "how long will this take", it steps the same monthly loop forward and returns the first month where the balance reaches the goal. That is exact rather than an approximation, and it returns nothing at all when a goal is genuinely unreachable, which happens when there is no deposit and no interest.

For "how much per month", it solves the end-of-month annuity for the payment:

payment = (goal - start × (1+r)n) ÷ ( ((1+r)n - 1) ÷ r )

When r is zero, that expression would divide by zero, so the code substitutes n for the annuity factor and the answer becomes the goal split evenly across the months.

APY conversions

The APY calculator uses the standard definition:

APY = (1 + r/n)n - 1

and reverses it with r = n × ((1 + APY)1/n - 1). This is the same calculation Regulation DD requires banks to use when they publish an APY.

Rounding

Every calculation runs at full floating-point precision and rounds only when a number is displayed. Rounding inside the loop would compound the rounding error along with the interest. Currency is formatted for a US audience with Intl.NumberFormat pinned to en-US, so the display does not change if your browser is set to another locale.

How we check the maths

The calculation library has an automated test suite that runs on every change. It asserts, among other things, that $10,000 at 4.00% APY for one year returns exactly $10,400.00, that converting an APY to any compounding frequency and back returns the original figure, that a 0% APY returns exactly the sum of deposits, that the contributions-only path matches the closed-form annuity to the cent, and that hostile inputs such as empty strings, negative numbers, and values beyond the input limits produce finite numbers rather than errors.

Inputs are clamped rather than rejected. A negative deposit becomes zero, an APY above 25% becomes 25%, and a term beyond 50 years becomes 50. This keeps the tool from producing nonsense from a typo.

What this site does not do

It does not model bank fees, minimum balance penalties, promotional rate expiry, tiered rates that change with balance, or withdrawal limits.

It does not track or publish rates from named banks. Rate tables go stale within weeks, and a stale rate table is worse than none. The only rate figures on the site are the FDIC national average and the general range online banks were advertising when we last checked, both dated wherever they appear.

It does not recommend accounts, take affiliate commissions, or run advertising.

Keeping this accurate

Rate figures are re-checked against the FDIC release and refreshed with a new "last checked" date. The current figures were checked on September 5, 2026 against the FDIC data dated August 17, 2026.

If you find a number on this site that is wrong, email contact@hysacalculator.us with the page and the inputs you used. Corrections get made and the change is noted in the updated date on the page.

Sources

1. Consumer Financial Protection Bureau, Regulation DD (Truth in Savings) . The standard APY calculation banks are required to use
2. FDIC, National Rates and Rate Caps . National average savings rate of 0.38%, updated August 17, 2026
3. IRS, Topic no. 403, Interest received
4. Investor.gov compound interest calculator . An SEC-run tool useful as an independent cross-check