Compound arithmetic · your rate, never ours · engine 2026.2.1
Savings growth calculator
Put in a starting balance and an amount you set aside every payday, choose how many years to run, and enter the rate of return you want to test. The curve shows what that arithmetic produces — the money you put in, the growth stacked on top of it, and the year the growth overtakes the deposits.
The curve
Deposits, and the growth stacked on them
Years along the bottom · balance up the side. Contributions are counted at the end of each period.
What moved it
With no rate entered, every dollar shown is a dollar you deposited.
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Year by year
| Year | Money in | Growth | Balance |
|---|---|---|---|
| 1 | $6,200 | — | $6,200 |
| 2 | $11,400 | — | $11,400 |
| 3 | $16,600 | — | $16,600 |
| 4 | $21,800 | — | $21,800 |
| 5 | $27,000 | — | $27,000 |
| 6 | $32,200 | — | $32,200 |
| 7 | $37,400 | — | $37,400 |
| 8 | $42,600 | — | $42,600 |
| 9 | $47,800 | — | $47,800 |
| 10 | $53,000 | — | $53,000 |
| 11 | $58,200 | — | $58,200 |
| 12 | $63,400 | — | $63,400 |
| 13 | $68,600 | — | $68,600 |
| 14 | $73,800 | — | $73,800 |
| 15 | $79,000 | — | $79,000 |
| 16 | $84,200 | — | $84,200 |
| 17 | $89,400 | — | $89,400 |
| 18 | $94,600 | — | $94,600 |
| 19 | $99,800 | — | $99,800 |
| 20 | $105,000 | — | $105,000 |
Every row is the position at that year's end, after that year's final deposit. With no rate entered, growth is shown as a dash because there is nothing to compute.
How the arithmetic works
The formula
With a starting balance P, a contribution C at the end of every period, p periods a year, a nominal annual rate r compounded m times a year and n = p × years periods elapsed, the rate over one contribution period is i = (1 + r/m)^(m/p) − 1 and the balance is B = P(1 + i)^n + C((1 + i)^n − 1)/i. At a rate of exactly zero that collapses to B = P + Cn — a straight line, computed directly so nothing is ever divided by zero.
Contributions land at the end of each period
A deposit made in a period earns nothing during that period. This is the ordinary-annuity convention and it is the conservative one: saving at the start of each period would produce one period's extra growth on every deposit.
Your pay cadence, not a monthly approximation
Biweekly pay is 26 deposits a year, not 24. The calculator uses the cadence you are actually paid on rather than converting everything to a monthly average, which is where most savings calculators quietly lose a fortnight of deposits a year.
The rate is always yours
You choose the rate. We deliberately do not suggest one, and this page has no default rate, no “typical” figure and no historical average — supplying a rate is what would turn arithmetic into a prediction. That is not caution for its own sake: a tool that supplies the rate is making a claim about how an investment will perform, and this one is not equipped — or entitled — to make one.
Where the paycheck figure comes from
The optional paycheck bridge runs the same 2026 take-home engine (2026.2.1) as every other calculator on this site: federal income tax, Social Security, Medicare and state income tax, with the annual liability spread evenly across pay periods. This page adds no tax rule, rate or threshold of its own, and it does not decide what percentage of your pay to save.
What this page is, and what it is not
- It is a mathematical illustration, not a projection or a prediction. This is a hypothetical illustration of mathematical principles based only on the figures you entered. It is not a projection of any investment’s performance, not a forecast, and not financial advice. Rates you enter are assumptions, not predictions. Actual savings and investment returns vary and can be negative. PaycheckForge is not a registered investment adviser or broker-dealer.
- Returns are not guaranteed. Real returns vary from year to year and can be negative. No investment delivers one constant rate for twenty years, and a run of bad years early behaves very differently from the same average arriving late — a difference this page cannot show.
- PaycheckForge is not an investment adviser. Nothing here is investment, tax, legal or financial advice, and nothing here recommends a product, a fund, a broker or a type of account. We name no institution as a place to get the rate you typed.
- Tax on the investment, account or platform fees, and inflation on the investment itself are not modelled. One constant rate is applied evenly to every period; real returns arrive unevenly, in an order this page cannot represent.
- Take-home figures are planning estimates. The paycheck bridge uses our 2026 engine; employers apply IRS Publication 15-T tables per check, and local taxes, credits and itemised deductions are not modelled.
- No withdrawals, no contribution increases. The contribution is held flat for the whole horizon. A raise, a career break or a withdrawal all change the answer and none of them is modelled here.
Frequently asked questions
What rate of return should I enter?
We will not tell you, and that is deliberate. This page is arithmetic on figures you supply: the moment we suggested a rate, the output would stop being a calculation and start being a prediction about an investment, which is not something a calculator is entitled to make. Enter the rate you want to test, then change it and watch how much the answer moves — that sensitivity is the useful part. If you are looking at a specific savings account or fund, its own published rate or prospectus is the place that figure comes from.
Is this a projection of what I will have?
No. It is a hypothetical illustration of mathematical principles: if the rate you entered held in every single period, and nothing else changed, the arithmetic lands here. Returns are not guaranteed, real returns vary from year to year and can be negative, and no rate holds constant for twenty years. Nothing on this page is a forecast, a plan or financial advice.
When are the contributions counted?
At the end of each period. A deposit made in period twelve earns nothing during period twelve; it starts compounding from period thirteen. This is the ordinary-annuity convention, and it is the conservative choice — if you actually save at the start of each period, the real figure is one period’s growth higher than what is shown here.
Why does biweekly saving differ from monthly saving of the same amount?
Because there are 26 biweekly periods in a year, not 24. Saving $200 every two weeks is $5,200 a year; saving $200 twice a month is $4,800. Most calculators only accept a monthly contribution, which quietly forces you to do that conversion yourself and get it wrong. This one takes the cadence your employer actually pays you on.
What does “start from my paycheck” do?
It runs our existing 2026 take-home engine on the salary, filing status, state and pay frequency you pick — the same engine behind every other calculator here — and offers a percentage of that estimated net pay as the contribution. Nothing about the tax estimate is invented for this page. It is an estimate for planning, not payroll output, and you can ignore it and type any contribution you like.
Does the calculator model tax on the growth, or fees?
No. Tax on interest, dividends or gains, account and platform fees, fund expense ratios and trading costs are all outside this page. So is inflation on the investment itself — the inflation field only restates the ending balance in today’s money, it does not reduce the growth. A real account will land below an untaxed, fee-free illustration.
What is the rule of 72?
A mental-arithmetic shortcut: divide 72 by a rate in percent for a rough number of years to double. It is an approximation, not the exact answer — the exact figure is the logarithm of 2 divided by the logarithm of one plus the rate — and it is closest in the middle of the range. We show it beside the exact figure so the gap is visible rather than hidden.
Do my numbers leave my browser?
No. Everything on this page is computed in your browser, exactly as on every other PaycheckForge calculator. Nothing you type is sent to a server, stored or logged.
Sources and further reading
- Investor.gov compound interest calculator (SEC)The US Securities and Exchange Commission's own calculator, which likewise asks you to supply the rate and suggests none
- Investor.gov — Save and InvestThe SEC's investor education material on saving and investing basics
- FINRA Rule 2210(d)(1)(F)The "hypothetical illustration of mathematical principles" standard this page is deliberately built to, though PaycheckForge is not a FINRA member
- IRS Revenue Procedure 2025-32Federal brackets and standard deductions for tax year 2026.
- Social Security Administration 2026 COLA fact sheetSocial Security wage base and FICA parameters used for 2026.
- Tax Foundation state income-tax tablesState individual income-tax rates and brackets used for 2026.
- IRS Revenue Procedure 2025-32, section 4.26 (QBI)2026 taxable-income-before-QBI thresholds in section 4.26; scope limits of the simplified model.
- IRS Form 8995 instructions (QBI income base)2025 instructions used only for the taxable-income-before-QBI definition, not 2026 dollar thresholds.
Engine 2026.2.1, tax year 2026, reviewed September 5, 2026. The compound-growth method is written out on the methodology page. Estimates and illustrations only — not investment, tax, legal or financial advice.