Alternatives
Twenty dollars a week for forty years is $41,600 of contributions. Compounded weekly at an assumed 7% it is $229,004. Here is the formula, the full derivation, and every reason the second number might not arrive.
This article does exactly one thing: it applies the standard future-value formula to a recurring weekly amount, shows the working, and then spends the second half explaining which parts of the answer are arithmetic and which parts are assumption.
The arithmetic is certain. The rate of return is not. Keeping those two apart is the whole exercise.
Money paid in at the end of every period, compounding at a fixed rate, is an ordinary annuity. Its future value is:
FV = P × ((1 + r)^n − 1) ÷ r
where P is the amount paid each period, r is the rate per period, and n is the number of periods.
For a weekly contribution we set r = (annual rate) ÷ 52 and n = 52 × years. That is exactly what the invest-instead calculator does, so the numbers below and the numbers it produces are the same numbers.
Take P = $20, an assumed annual rate of 7%, and 30 years.
Contributions over those 30 years were 1,560 × $20 = $31,200. So $75,097.60 of the total is compounding and $31,200 is money you put in. Past roughly the eighteenth year the growth is adding more each year than you are.
Same formula, five rates, four horizons. Nothing here is a forecast; each row is "what happens if the rate is this".
| Assumed annual return | 10 years | 20 years | 30 years | 40 years |
|---|---|---|---|---|
| 0% (cash in a tin) | $10,400 | $20,800 | $31,200 | $41,600 |
| 4% | $12,781 | $31,846 | $60,283 | $102,700 |
| 5% | $13,485 | $35,713 | $72,352 | $132,745 |
| 7% | $15,047 | $45,335 | $106,298 | $229,004 |
| 10% | $17,843 | $66,299 | $197,889 | $555,244 |
Two things are worth noticing before anything else.
The 0% row is the honest floor. Even if every investment assumption below turns out worthless, $20 a week for 40 years is $41,600 that exists. That is the number to compare a lottery habit against if you refuse to assume any return at all, and it is the number the lifetime spend calculator reports.
The spread between rows is enormous at 40 years and trivial at 10. At ten years the gap between 4% and 10% is about $5,000. At forty years it is $452,544. Compounding does not reward the rate; it rewards the rate multiplied by time, and time enters as an exponent.
The longest clean series of US asset returns is Aswath Damodaran's annual returns dataset at NYU Stern, which runs 1928 to 2025. It reports that $100 invested in the S&P 500 with dividends reinvested at the start of 1928 was worth $1,157,598.95 at the end of 2025.
That is a 98-year geometric mean of:
(1,157,598.95 ÷ 100)^(1 ÷ 98) − 1 = 1.100183 − 1 = 10.02% a year, nominal
The same dataset gives $100 in 3-month Treasury bills growing to $2,578.30 (3.37% a year) and in 10-year Treasury bonds to $7,752.88 (4.54% a year).
So the 10% row is not invented. It is also not a promise. Four qualifications apply, and all four are large.
1. Inflation. That 10.02% is nominal. Prices rose over the same 98 years, so the purchasing power of the end figure is far below the headline. Future inflation is unknowable, so the honest treatment is to run the table twice. Assume 7% nominal and 3% inflation and the real rate is roughly 4%, which makes the 4% row your answer in today's money: $60,283 after 30 years, not $106,298. That is not a rounding adjustment. It is 43% of the number gone.
2. Fees. Fees come out of the rate, and they come out every year. Assume 7% with a 0.5% annual fee and you are compounding at 6.5%:
Half a percent sounds like nothing and removes a tenth of the outcome. That is the general shape of fee drag, and it is why the published expense ratio on any product is worth reading before you use it.
3. Tax. Depending on where you live and what account you use, dividends and gains may be taxed annually or on disposal. Tax paid along the way behaves exactly like a fee: it reduces r, and the reduction compounds. Tax-sheltered accounts exist in most jurisdictions precisely because this effect is so large.
4. Sequence risk. The formula assumes a constant r. Real returns are not constant, and the order matters when you are contributing. The 10.02% figure above is the outcome of 98 years that include 1929 to 1932 and 2007 to 2009. A 30-year window ending in a crash produces a materially different number from one ending in a boom, using identical average returns. Anyone quoting a single figure — this article included — is smoothing over that.
The formula is linear in P, so any weekly amount reads off by simple ratio:
| Weekly amount | At 7% for 30 years |
|---|---|
| $5 | $26,574 |
| $20 | $106,298 |
| $50 | $265,744 |
Which means the useful question is not "should I invest instead" but "what is my actual weekly number". Most people underestimate it substantially, and the lifetime spend calculator exists to produce the honest figure.
It is not claiming the investment path is risk-free: equities fall, sometimes by half, and the 40-year figure assumes you never sell during one of those falls. It is not claiming 7% or 10% will recur. And it is not claiming a lottery ticket and an index fund compete for the same slot in a budget — for most people a ticket is entertainment spending, and the comparison that matters is with other entertainment, which is the subject of setting a lottery budget you won't regret.
What it is claiming is narrower and harder to argue with: the future value of a recurring contribution is a closed-form calculation, and you should know what your number is. The distribution comparison between the two options is worked in index funds versus the lottery; if you want to know what capital any of this would have to reach to replace an income, that is how much capital generates a lottery-winner income.
Last verified: 2026-08-29