What a savings rate actually pays
Two accounts advertising the same percentage can pay different amounts, because a rate is meaningless until you know how often it is applied. A 12% nominal rate credited once a year turns $10,000 into $11,200. The same 12% credited monthly turns it into $11,268.25, because each month's interest starts earning interest of its own. That gap is compounding, and the whole point of the APY figure is to make it visible.
Under the Truth in Savings Act and its implementing rule, Regulation DD, US banks must disclose the annual percentage yield — the total percentage the account pays over a year once its own compounding is included. Two accounts quoting the same APY pay the same, whatever their compounding schedule. Two accounts quoting the same nominal rate do not. So compare on APY, and treat a nominal rate as an intermediate quantity that only becomes an answer after you know the frequency.
This calculator accepts either. Give it an APY and it converts straight to an equivalent monthly rate. Give it a nominal rate and a frequency and it computes the APY first, then the equivalent monthly rate, and shows you both in the steps so you can see what your account is really paying.
Why everything is converted to a monthly rate
Your deposits arrive monthly but your bank may compound daily, so the two schedules do not line up. The clean fix is to work in one unit. The calculator finds the monthly rate that produces the same annual growth as your account's stated schedule: r = (1 + i/m)m/12 − 1 for a nominal rate i compounded m times a year, or r = (1 + APY)1/12 − 1 when you enter an APY directly. Both are exact, not approximations — they are the same annual growth factor written with a different exponent.
With a monthly rate in hand, the balance follows the standard future-value identity: the opening deposit grows by (1 + r)n, and the stream of deposits grows by the ordinary annuity factor ((1 + r)n − 1) / r. The annuity factor assumes each deposit lands at the end of its month, so the first deposit earns interest for n − 1 months and the last earns none. If your transfer lands at the start of the month instead, every deposit earns one extra month and the annuity total is higher by a factor of (1 + r) — at 4.25% APY over five years that is about 0.35% more, roughly $58 on a $250 monthly deposit.
One trap is worth naming. Dividing an APY by twelve to get a monthly rate is wrong, because the APY already contains the compounding you would then be applying again. At 4.25% APY, the true monthly rate is 0.347450%, not 4.25 ÷ 12 = 0.354167%. Over five years on $10,000 that error is 10,000 × (1.0035416760 − 1.0034745060) = $49.55 — small, but it is an error in the direction that flatters the account.
Worked example: $10,000 at 5% compounded annually for ten years
Take the simplest case first, with no monthly deposits, so the arithmetic is checkable on paper.
- Rate per period. 5% compounded once a year is 0.05 per period, and the APY is (1 + 0.05)1 − 1 = 5.000%. Annual compounding is the one case where nominal rate and APY are equal.
- Growth factor. 1.0510 = 1.62889463.
- Ending balance. 10,000 × 1.62889463 = $16,288.95.
- Interest earned. 16,288.95 − 10,000 = $6,288.95. Simple interest would have paid 10,000 × 0.05 × 10 = $5,000, so compounding added $1,288.95, or 25.8% more than the simple-interest figure.
- Tax. At a 22% marginal rate you keep 6,288.95 × (1 − 0.22) = $4,905.38, and the after-tax balance is 10,000 + 4,905.38 = $14,905.38.
Now add $100 a month at 6% compounded monthly for ten years, with nothing to start. The monthly rate is exactly 0.5%, the annuity factor is (1.005120 − 1) ÷ 0.005 = 163.879347, and the balance is 100 × 163.879347 = $16,387.93 on $12,000 of deposits. The interest, $4,387.93, is smaller than in the first example despite the higher rate, because the average dollar has been in the account for about five years rather than ten.
Reading the result, and what erodes it
Three numbers deserve attention. Interest earned against total paid in tells you how much of the ending balance the bank provided rather than you: on the default settings most of the balance is your own money, which is normal for a savings account and is exactly why the deposit amount matters more than the rate over short horizons. Effective APY is the number to carry when comparing offers. And the after-tax interest is what you actually keep.
Two forces work against the headline. Tax takes your marginal rate off every dollar of interest, in the year it is credited, reported on Form 1099-INT — interest is ordinary income, not capital gain, so a 22% federal bracket plus a 5% state tax leaves you 73% of the yield. Inflation takes the rest: a 4.25% APY against 3% inflation is a real return of (1.0425 ÷ 1.03) − 1 = 1.21%, not 1.25%. Put the after-tax yield and your inflation assumption into the real interest rate calculator to see what the balance is worth in today's money, or the inflation purchasing power calculator to age the ending balance directly.
Finally, check the rate is one you will keep. Savings APYs are variable and can change without notice, promotional rates expire, and some accounts pay the headline rate only up to a balance cap. The projection here assumes the rate you enter holds for the whole term, which is a modelling convenience rather than a promise from the bank.
What a nominal rate becomes once compounded
| Nominal rate | Annually | Quarterly | Monthly | Daily (365) |
|---|---|---|---|---|
| 1.00% | 1.0000% | 1.0038% | 1.0046% | 1.0050% |
| 2.00% | 2.0000% | 2.0151% | 2.0184% | 2.0201% |
| 4.00% | 4.0000% | 4.0604% | 4.0742% | 4.0808% |
| 5.00% | 5.0000% | 5.0945% | 5.1162% | 5.1267% |
| 8.00% | 8.0000% | 8.2432% | 8.2999% | 8.3278% |
| 12.00% | 12.0000% | 12.5509% | 12.6825% | 12.7475% |
Read the 12% row: moving from annual to monthly compounding adds 0.68 points of yield, while moving from monthly to daily adds a further 0.065. Frequency matters, but far less than the rate itself.
Assumptions and limits of this projection
- The rate is held constant. Savings APYs are variable by nature. A five-year projection at today's APY is a scenario, not a forecast, and the honest way to use it is to run the high and low rates you think plausible.
- Deposits land at the end of each month. Beginning-of-month deposits earn one extra month of interest each, which raises the annuity portion by a factor of (1 + r).
- Tax is treated as paid from other money. The after-tax figures apply your marginal rate to the total interest without removing it from the balance. If you withdraw the tax each year instead, the compounding slows, and the closer model is to enter an after-tax APY of APY × (1 − tax rate) with the tax field set to zero.
- No fees, minimums or balance tiers. Monthly maintenance fees, balances that drop below a minimum, and tiered rates that only pay the headline APY up to a cap will all reduce the result.
- Insurance limits apply. FDIC and NCUA coverage is $250,000 per depositor, per insured institution, per ownership category. A projection that crosses that line needs a second institution, not just a bigger balance.
- Interest is credited monthly here even when the account compounds daily. The monthly rate used is exactly equivalent over a year, so the ending balance matches; only the intermediate month-end figures differ by a few cents.
When a savings account is the wrong tool
A high-yield savings account is the right home for money you may need without notice: an emergency fund, a house deposit within a year or two, a tax bill you are accruing for. Size the first of those with the emergency fund calculator, and work backwards from a dated target with the savings goal calculator.
It is the wrong tool for money with a long horizon. Over twenty years, the difference between a deposit yield and a diversified portfolio return dominates every decision on this page, and the liquidity you are paying for has no value if you were never going to touch the money. It is also the wrong tool while you carry high-rate debt: interest earned at 4.25% and taxed at 22% nets around 3.3%, against 20% or more charged on a card balance, so the payoff calculator shows a better return than any savings rate on offer. And if the horizon is fixed and known, a certificate of deposit or a Treasury bill usually pays more than an on-demand account — you are simply selling back the liquidity you do not need.