Dollar-cost averaging calculator

If you already hold a lump sum, dollar-cost averaging is a real decision: invest it all today, or feed it in over several months. This runs both paths on the same numbers and shows what averaging in costs you.

How the math works

Two paths, one set of inputs. Investing the whole sum today is the plain compound-growth formula. Averaging in splits the sum into equal monthly tranches, lets the money still waiting earn the cash rate, then compounds each tranche at the market rate for whatever horizon is left.

Where L is the lump sum, m is the monthly market rate, c is the monthly rate on cash, k is the number of monthly tranches, j counts the months a given tranche sat in cash before it went in, and N is the total horizon in months. The (1 + c)j term is the interest the waiting money earns before it is deployed. When the cash rate equals the market rate, the two formulas produce the same number and timing stops mattering.

The gap between the two is set entirely during the deployment window. After the last tranche goes in, both portfolios hold the same kind of money and grow at the same rate, so the percentage difference is frozen. A longer horizon does not change that percentage — it just compounds the dollar gap.

Worked example

Take a $50,000 windfall — an inheritance, a bonus, the proceeds of a sale. The choice is to invest it in a broad stock index today, or to spread it in over 12 months while the rest sits in a high-yield savings account. We use the S&P 500 long-run nominal return of 10.2% for the market and 4.00% APY for the waiting cash, held over a 10-year horizon.

Invest it all today and the $50,000 grows to $132,064. Average it in over 12 months and it reaches $128,623. The gap is $3,441 — about 2.68% — and the sidelined cash earned only $910 in interest along the way, nowhere near enough to close it.

That gap is not a horizon effect. Run the same inputs over one year instead of ten and the percentage is identical to the decimal; only the dollar figure shrinks. The decision is made in year one, when part of the money is earning 4% instead of the 10.2% the rest is earning. Everything after that just multiplies the head start.

When this calculator is wrong

The result assumes a market that rises at a steady rate. Real markets do not. The whole appeal of averaging in is the case this calculator's default inputs do not show: a market that falls during the deployment window, where feeding money in slowly buys more shares at lower prices and comes out ahead.

Here is what the number leaves out:

• It uses an average, not a sequence. Markets deliver their returns in a jagged order, not a smooth 10.2% a year. Averaging in wins in the periods where the early months are down. Investing today wins in the periods where they are up. Across U.S., U.K., and Australian history, investing the lump sum immediately came out ahead in about two-thirds of periods — roughly 68% — because markets rise more often than they fall.
• It prices the decision in dollars, not nerves. The two-thirds figure is a long-run average. The real reason people average in is to avoid putting $50,000 to work the week before a crash. That regret has a cost the arithmetic cannot see, and for some people it is the difference between staying invested and bailing out.
• It assumes the cash actually earns the rate you enter. If the money waiting to be deployed sits in a checking account at the 0.41% FDIC national average instead of a high-yield account, the drag is worse than the model shows and averaging in looks even weaker.
• It says nothing about taxes or fees on the way in. In a taxable account, spreading purchases across a rising market can mean buying at higher cost bases; the effect is small but it is not zero.

The honest reading of the Vanguard research is that lump-sum investing wins on average and averaging in is a way to buy peace of mind, priced at roughly 2.3% of expected return for a balanced 60/40 portfolio over the deployment window. Whether that price is worth paying is a question about you, not about the math.

What to do with the result

If the gap the calculator shows is small relative to the sleep you would lose deploying everything at once, average in and stop optimizing. Twelve months is the window the research uses; shorter windows capture most of the expected-return benefit while still smoothing the entry. The one thing to avoid is holding the cash indefinitely and calling it a strategy — that is where the real money is lost.

If you are not deploying a lump sum at all — if you are just investing part of each paycheck — then none of this applies to you. That is not dollar-cost averaging in the decision sense; it is simply investing as the money arrives, and the alternative (holding paychecks in cash to invest later) is the losing move the research already ruled out. Contribute on the schedule your income sets and let the compounding do the work.

Common questions

Is dollar-cost averaging better than investing a lump sum?

On average, no. Investing a lump sum immediately beat averaging it in over 12 months in about two-thirds of historical periods, because markets spend more time rising than falling. Averaging in wins in the minority of periods that start with a decline, and it reduces the odds of the worst-timed entry. It buys lower variance of outcomes, not higher expected returns.

How long should I spread a lump sum over?

The research typically models a 12-month window, which captures most of the emotional benefit while limiting how long the money sits in cash. Longer windows leave more money out of the market and widen the expected gap; shorter windows barely differ from investing all at once. There is no magic number — the trade-off is smoother entry against more time in cash.

Does dollar-cost averaging lower my average cost per share?

It lowers your average cost below the average of the prices you paid, because a fixed dollar amount buys more shares when the price is low and fewer when it is high. That is a real mathematical effect — the dollar-weighted average is always at or below the simple average price. It is not the same as beating a lump sum, which depends on the direction the market moves after you start.

Where should the un-invested cash sit while I average in?

In a high-yield savings account or a money-market fund, not a checking account. At today's rates the difference is roughly 4% versus the 0.41% FDIC national average — on the money waiting to be deployed, that spread is the only thing partly offsetting the cost of staying out of the market.

Should I average into my 401(k) the same way?

A 401(k) funded from your paycheck is already invested as the money arrives, so there is no lump sum to spread and nothing to decide. The averaging question only comes up when you are holding a pile of cash you could invest today — a rollover, a bonus, an inheritance — and are choosing whether to wait.