What Compounding Looks Like Over Decades

Over decades, compounding looks like a curve that stays nearly flat for years and then bends sharply upward, because each year's growth is calculated on a base that already includes earlier growth. At a steady 7% a year, $200 a month grows to about $34,600 after 10 years and about $525,000 after 40, of which only $96,000 is money paid in. The shape depends on three inputs, the rate, the number of years and the deposits, and the same arithmetic runs in reverse on debt.

Key takeaways

At 7% compounded monthly, $200 a month reaches about $34,600 after 10 years, $104,200 after 20, $244,000 after 30 and $525,000 after 40; growth makes up 31%, 54%, 70% and 82% of those balances.
In a deposit plan started from zero, monthly growth catches up with the monthly deposit after exactly one doubling period of the rate, which is about 10 years at 7%.
At 7%, starting $200 a month at 25 instead of 35 leaves about $525,000 rather than $244,000 at 65; the later starter would need about $430 a month to catch up.
With annual compounding, the Rule of 72 is within about 1% of the exact doubling time between 6% and 10% but understates it by about 6% at 22.36%, the Federal Reserve's latest average card rate; with interest added monthly, an unpaid balance at that rate doubles in about 3.1 years.
In S&P 500 data for 1928–2025, a saver putting in a fixed $2,400 a year in real terms ended 30-year windows with anywhere from about $111,500 to $536,900 in starting-year dollars, so the record shows a wide range, not a single number.

The two formulas behind the curve

Investor.gov, the SEC's investor education site, defines compound interest as interest paid on principal and on accumulated interest. Two formulas cover most long-horizon questions: one for a single lump sum and one for a series of equal deposits (an annuity, in finance terms).

Lump sum:          FV = PV × (1 + r)^n
Regular deposits:  FV = P × [(1 + i)^m − 1] / i

PV = amount invested today      r = return per year (0.07 for 7%)
n  = number of years            P = deposit per period
i  = return per period          m = number of periods
     (r / 12 for monthly)            (years × 12 for monthly)
FV = value at the end

The deposit formula assumes each deposit lands at the end of its period. Deposits at the start of each period earn one extra period of growth, so the result is multiplied by (1 + i). Both formulas assume a constant rate with no fees, taxes or withdrawals, which is why they describe the shape of compounding rather than any real account.

Compounding frequency also matters. A 7% rate credited monthly works out to about 7.23% a year, so a monthly calculation ends a little higher than an annual one. The site's Investment Growth calculator compounds monthly and adds deposits at the end of each month, so its results run slightly above annual-compounding tables.

Illustrative example: $10,000 at 7%	Compounded annually	Compounded monthly
After 10 years	$19,672	$20,097
After 20 years	$38,697	$40,387
After 30 years	$76,123	$81,165
After 40 years	$149,745	$163,114

Checking a figure that gets repeated

A widely repeated claim says $200 a month for 40 years at 7% grows to close to $1 million. With P = $200, i = 0.07 / 12 and m = 480, the deposit formula gives about $524,963, or about $528,025 if each deposit is made at the start of the month. Reaching $1 million would take a steady return of about 9.2% a year, about $381 a month at 7%, or about 49 years at $200 and 7%.

Costs compound too: a 1-percentage-point annual cost on a 7% return cuts a 30-year lump sum's ending value by about 25% ($57,435 instead of $76,123 on $10,000), a large drag but not the "half" sometimes quoted.

Doubling time and the Rule of 72

Doubling time is the number of years it takes money to grow to twice its starting value at a fixed rate. The exact answer comes from solving the lump-sum formula for FV = 2 × PV. The Rule of 72 is a shortcut that divides 72 by the rate in percent.

Exact doubling time:  n = ln(2) / ln(1 + r)
Rule of 72:           n ≈ 72 / (rate in percent)

Annual rate	Exact years to double (annual compounding)	Rule of 72	Rule's error
4%	17.7	18.0	+1.9%
6%	11.9	12.0	+0.9%
7%	10.2	10.3	+0.4%
8%	9.0	9.0	−0.1%
10%	7.3	7.2	−1.0%
15%	5.0	4.8	−3.2%
22.36%	3.4	3.2	−6.3%
30%	2.6	2.4	−9.2%

The rule is most accurate near 8%. Below that it slightly overstates the waiting time, and above it the rule understates it by a growing margin. More frequent compounding shortens every exact figure, slightly at ordinary rates and more at high ones: at 22.36% compounded monthly, doubling takes about 3.1 years instead of 3.4. A checklist line such as "money doubles every 10 years" is true only for a return of about 7.2% a year; at 4% doubling takes about 17.7 years, and at 10% about 7.3.

The same math on a card balance

The Federal Reserve's G.19 consumer credit release of October 7, 2026 puts the average commercial bank credit card rate for August 2026 (preliminary, subject to revision) at 22.36% for accounts assessed interest and 21.19% across all accounts. According to the Consumer Financial Protection Bureau, many issuers calculate interest daily on the average daily balance. Paying the full balance by the due date each month can avoid interest on purchases, but a grace period usually covers only new purchases and only when no balance was carried over.

Illustrative example: a $5,000 balance at 22.36% with no payments, no new charges and interest added monthly grows to about $6,240 after one year, $9,719 after three and $15,137 after five, doubling in about 3.1 years against about 9.9 years for savings at 7% compounded monthly. Daily accrual barely changes that (about $15,288 after five years). Real accounts require minimum payments, so this shows the direction of the arithmetic rather than a typical account.

Contributions vs growth by decade

The table follows one illustrative plan: $200 deposited at the end of every month for 40 years, earning a steady 7% a year compounded monthly.

End of year	Total deposited	Balance	Growth to date	Growth share of balance	Growth earned in that decade
10	$24,000	$34,617	$10,617	30.7%	$10,617
20	$48,000	$104,185	$56,185	53.9%	$45,568
30	$72,000	$243,994	$171,994	70.5%	$115,809
40	$96,000	$524,963	$428,963	81.7%	$256,968

Deposits arrive at the same pace every decade, $24,000 each time, but growth does not. The fourth decade alone produced about $257,000 of growth, nearly half the final balance. Measured year by year, growth was about $79 in year 1, $2,245 in year 10, $6,935 in year 20, $16,361 in year 30 and $35,303 in year 40. That last figure exceeds 14 years of deposits.

Why the curve looks flat at first

Early on, the balance is mostly the saver's own deposits, and 7% of a small number is a small number. Monthly growth equals the monthly deposit once the balance reaches P / i; substituting that into the deposit formula gives (1 + i)^m = 2, so for a plan started from zero with end-of-month deposits, growth catches up after exactly one doubling period of the rate.

At 7% compounded monthly, that period is about 9.9 years, so the crossover arrives in month 120; year 11 is the first full year in which growth ($2,581) exceeds the $2,400 deposited. The crossover takes about 17.4 years at 4% and about 7 years at 10%.

This is also why a chart of any long compounding plan looks unimpressive for its first decade and steep near the end. Nothing changes in the mechanism; the base simply becomes large enough for the same percentage to produce large dollar amounts.

Starting earlier vs paying more

Time and deposits trade off against each other, and the exchange rate depends on the assumed return. The table compares four illustrative savers who all stop at 65, at two steady rates compounded monthly.

Illustrative saver	Total deposited	Balance at 65, 4% a year	Balance at 65, 7% a year
$200 a month from 25 to 65	$96,000	$236,392	$524,963
$200 a month from 35 to 65	$72,000	$138,810	$243,994
Monthly deposit from 35 needed to match the first saver	$122,616 (4%) $154,911 (7%)	$341 a month	$430 a month
$200 a month from 25 to 35, then nothing	$24,000	$97,582	$280,968

Ten extra years at the start more than double the 7% outcome, and the cost of catching up rises with the rate: the late starter needs 70% more per month at 4% but 115% more at 7%. The last row carries a frequently quoted lesson, that ten years of early saving can beat thirty years of later saving. At 7% it does, by about $37,000. At 4% it does not: the early-only saver ends about $41,000 behind. The claim is a consequence of an assumed high rate, not a general rule.

Nominal dollars vs real dollars

Every figure above is nominal, meaning it counts dollars without adjusting for what they buy. Over long horizons, inflation changes the picture a great deal. The Bureau of Labor Statistics Consumer Price Index for All Urban Consumers, as published on FRED, rose from 109.3 in December 1985 to 324.054 in December 2025, so prices roughly tripled (×2.96) over those 40 years, an average of about 2.75% a year.

Illustrative example: deflating the $524,963 from the 40-year plan by that same factor leaves about $177,000 in starting-year purchasing power; at a steady 3% inflation it would be about $160,900. A 7% return with 3% inflation is a real return of about 3.9% a year, found as 1.07 / 1.03 − 1.

Deposits that rise with inflation offset part of that. If the $200 monthly deposit is raised by 3% at the start of each year, the 40-year balance at 7% is about $764,800 nominal, or about $234,500 in starting-year dollars, on total nominal deposits of about $181,000. At 3% inflation, prices double in about 23 years. The site's Purchasing Power calculator restates a future amount in today's dollars for a chosen inflation rate.

A saver's record, 1928 to 2025

Steady rates are a teaching device; markets do not deliver them. To see how the same plan would have played out historically, the calculation below uses calendar-year S&P 500 total returns with dividends reinvested from Aswath Damodaran's historical returns data set at NYU Stern (data through 2025), deflated by the December-to-December change in the CPI series above. Over 1928–2025 the index returned about 10.0% a year nominal and about 6.8% a year after inflation.

The illustrative saver deposits $2,400 at the start of every year, held constant in purchasing power, into the index, with no fees, taxes or withdrawals. Every possible 30-year window (69 of them) and 40-year window (59) was tested, and the ending value is in starting-year dollars.

Window length	Real deposits	Worst window	Median window	Best window
30 years	$72,000	$111,512 (1952–1981) 2.7% a year	$253,157 (1990–2019) 7.2% a year	$536,907 (1970–1999) 11.1% a year
40 years	$96,000	$324,453 (1942–1981) 5.3% a year	$514,093 (1964–2003) 7.0% a year	$886,699 (1929–1968) 9.0% a year

The percentages are the real money-weighted return each saver earned. Two things stand out. The best 30-year saver ended with about 4.8 times as much as the worst, despite identical deposits. And the windows' ending decades did much of the sorting: the index lost about 1.9% a year after inflation over 1972–1981 but gained about 14.7% a year over 1990–1999. Because a deposit plan's balance is largest near the end, late returns move far more dollars than early ones.

This is a record of one country's large-company stocks over one stretch of history, without costs or taxes. It is not a forecast, and a different market or period could produce results outside this range.

Frequently asked questions

What is the difference between APY and an interest rate?

Under the federal Truth in Savings rules (Regulation DD, 12 CFR 1030.2), a deposit account's interest rate is the annual rate that does not reflect compounding, while the annual percentage yield (APY) reflects both the rate and how often interest compounds over a 365-day period. Two accounts with the same rate can show different APYs if one compounds more often, so comparing APYs puts deposit accounts on the same footing. Regulation DD covers banks and other depository institutions except credit unions; federally insured credit unions follow a parallel NCUA Truth in Savings rule (12 CFR Part 707).

Does compounding daily instead of monthly make a big difference?

Not much at ordinary rates. At 7%, $10,000 grows over 30 years to about $81,645 with daily compounding, about 0.6% more than the $81,165 from monthly compounding. Even continuous compounding, the mathematical limit, only lifts the effective yearly rate to about 7.25%, against 7.23% for monthly.

Do stock investments compound like a savings account?

The mechanism is similar, because each year's return applies to a base that includes earlier gains, but there is no stated rate. In the NYU Stern data, the S&P 500 returned about −18.0% in 2022 and +26.1% in 2023, including dividends. A steady-rate formula shows the shape of compounding, while actual results depend on the order and size of returns that nobody knows in advance.

How do taxes affect compounding?

The IRS says interest generally is taxable in the year it becomes available to the account holder, so tax paid each year leaves less to compound. Illustrative example: $10,000 earning 7% with a flat 22% tax on each year's interest grows to about $49,300 in 30 years, versus about $61,600 if the same tax is applied once to all the growth at the end. In a traditional IRA, earnings and gains generally are not taxed until withdrawn, but under IRS Topic 451 distributions are fully taxable if all contributions were deductible, and under IRS Topic 557 withdrawals before age 59½ generally owe an extra 10% tax unless an exception applies.

Is there a quick rule for tripling or tenfold growth?

Rough equivalents exist. Dividing about 110 to 115 by the rate in percent estimates tripling time, and dividing about 240 by it estimates tenfold growth for rates around 7% to 10%. At 7%, the exact figures are 16.2 years to triple and 34.0 years to grow tenfold, against shortcut estimates of about 16.4 and 34.3 years.

Running your own numbers

Use a range of rates rather than one. The Investor.gov compound interest calculator lets users set a variance range around the rate and choose the compounding frequency; check how any tool compounds before comparing its output with another.
Restate any 30- or 40-year result in today's dollars before treating it as spending power.
Compare starting 10 years earlier with paying more later at both a modest and a higher rate, to see how much the conclusion depends on the rate.
Sanity-check any quoted figure with the deposit formula above: deposit, rate per period and number of periods are enough.