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Investing

How To Dollar-Cost Average

Dollar-cost averaging is the discipline of investing a fixed amount on a fixed schedule, whatever the market is doing. It replaces a timing decision with a calendar.

Quick Answer

value = initial x (1+r)^n + payment x ((1+r)^n - 1) / r

P
Initial lump sum invested at the start
A
Amount invested each period
r
Return per period, monthly rather than annual
n
Number of periods, in months

£1,000 up front plus £250 a month for ten years at 7% is £31,000 invested and £44,730.08 in the account. £13,730.08 of that, about 31%, is growth.

What Is How To Dollar-Cost Average?

Dollar-cost averaging means investing the same amount of money at regular intervals, regardless of price. The schedule is fixed, the amount is fixed, and no judgement about the market enters the decision at all.

The mechanism that makes it work is mechanical. A fixed dollar amount buys fewer shares when prices are high and more when they are low, so the average cost per share ends up below the average price per share over the same period.

That effect is not a free lunch. It is the same arithmetic that makes a fixed dollar amount buy less when prices rise, and it produces no gain at all if the price rises steadily from the very first purchase.

The real benefit is behavioural rather than mathematical. Averaging removes the decision of when to start, which is the decision most investors get worst, and it stops a painful drop from feeling like a reason to stop investing.

Averaging into a falling market lowers the average cost with every contribution, which is why a long decline is less alarming for someone investing monthly than for someone holding a lump sum.

Timing within the month matters less than most people expect, but it is not nothing. Contributing at the start of the month gives the money one more month of compounding than contributing at the end, worth about half a percentage point a year at a 6% return.

The maths is an ordinary annuity. A stream of equal payments at a constant return has a closed-form future value, which is why a ten-year projection can be computed exactly rather than simulated.

The closed form assumes a constant return. Real markets deliver a sequence of returns that is lumpy and unpredictable, so the formula gives an expected value rather than a forecast.

Sequence risk is the other side of the same coin. A £250 monthly investor sees far less variation in the outcome than a lump-sum investor, because later contributions are not exposed to the early-year losses.

Lump-sum investing beats averaging most of the time on average. If markets rise over long periods, investing everything immediately captures more of that rise, but it does so with far more volatility and a much worse experience in a bad start.

Costs matter more than the timing. A high ongoing charge compounds against the portfolio exactly as the return compounds for it, and the drag from fees is far larger and far more certain than the benefit from moving a payment to the start of the month.

Averaging works best when it is automatic. A standing order on the day after payday turns the intention into an event that happens without a decision, which is the whole point of the approach.

The contribution needs to grow, or inflation quietly erodes it. £250 a month for twenty years is a fixed commitment in a world where prices double, so increasing the amount annually is closer to the spirit of the strategy.

The calculator projects a monthly contribution over a chosen horizon at a chosen annual return, adds any initial lump sum, and reports how much of the final total is money invested and how much is growth.

Formula

FV = A x ((1+r)^n - 1) / r

This is the ordinary annuity future-value formula. Each payment compounds for the months remaining after it is made, and the sum of all those factors collapses into a single closed form.

SymbolMeaning
AContribution
rPeriodic return
nPeriods
FVFuture value

FV(due) = FV(ordinary) x (1+r)

Moving every payment to the start of the period gives each one an extra period of growth, which multiplies the whole result by one plus the periodic return.

SymbolMeaning
FV(ordinary)End-of-period value
rPeriodic return
FV(due)Start-of-period value

monthly rate = (1 + annual rate)^(1/12) - 1

An annual return is converted by taking its twelfth root rather than by dividing by twelve, because the compounding has to compound rather than merely accumulate.

SymbolMeaning
r_aAnnual return
r_mMonthly return

How To Calculate How To Dollar-Cost Average

  1. 1

    Convert the annual return to a monthly one

    Take the twelfth root of one plus the annual rate and subtract one. Dividing by twelve understates the monthly rate and understates the final value.

  2. 2

    Count the periods

    Multiply the number of years by twelve. A ten-year horizon is 120 contributions, and the count drives the compounding far more than the return does.

  3. 3

    Project the initial lump sum

    Multiply the starting amount by one plus the monthly rate raised to the number of months. Every month of the horizon compounds it.

  4. 4

    Project the stream of contributions

    Use the annuity formula, then multiply by one plus the monthly rate if the contributions are made at the start of the month rather than the end.

  5. 5

    Separate growth from investment

    Subtract the total contributed, which is the lump sum plus every payment, from the final value. The remainder is growth, and it is the part that grows with time.

Examples

Example 1: £1,000 up front plus £250 a month for ten years

Initial lump sum
£1,000
Monthly contribution
£250
Years
10
Annual return
7%
Timing
End of month
StepCalculationResult
Monthly rate1.07^(1/12) - 10.565%
Months10 x 12120
Total invested£1,000 + £250 x 12031000
Value of the contributions£250 x 171.0542762.93
Value of the initial £1,000£1,000 x 1.07^101967.15
Portfolio value£42,762.93 + £1,967.1544730.08
Growth£44,730.08 - £31,00013730.08

Result: Over 120 months the £250 contributions grow to £42,762.93 and the £1,000 start to £1,967.15, giving £44,730.08 on £31,000 invested. Growth is £13,730.08, so about 31% of the total is return rather than money you put in.

Example 2: £500 a month for five years, contributed at the start

Initial lump sum
£0
Monthly contribution
£500
Years
5
Annual return
4%
Timing
Start of month
StepCalculationResult
Monthly rate1.04^(1/12) - 10.327%
Months5 x 1260
Total invested£500 x 6030000
Contributions at the start of each month£500 x 66.1833197.84
Portfolio value£33,197.8433197.84
Growth£33,197.84 - £30,0003197.84

Result: Sixty payments of £500 made at the start of each month are £30,000 invested and grow to £33,197.84 at 4% a year. Growth is £3,197.84, and moving the payments to the start of each month is what adds the £108 of difference.

Calculator

Portfolio value

$44,730.08

Total invested
$31,000.00
Growth
$13,730.08
Value per £1 invested
1.4429
Contributions made
120
Monthly return
0.005654145387

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

Prefer a full-width tool? Open the How To Dollar-Cost Average calculator page.

Common Mistakes

  • Dividing the annual rate by twelve

    Twelfth-rooting converts a compounding rate correctly while dividing by twelve does not. On a ten-year projection the difference between the two is several hundred pounds.

  • Expecting the projection to be a forecast

    The formula assumes a constant return, and real markets deliver a lumpy sequence instead. Treat the result as an expected value under one assumption, not as a prediction.

  • Assuming averaging beats a lump sum

    Invested money has more time to compound than scheduled money, so a lump sum wins more often than not. Averaging trades a slightly lower average return for a much calmer experience.

  • Using the average price as the cost basis

    The point of averaging is that the average cost per share is below the average price per share. Reporting the price instead of the cost misrepresents the strategy's benefit.

  • Forgetting that fees compound

    An ongoing charge reduces the return every single year, so its effect compounds in exactly the way the return does. It is a far larger and far more certain drag than the timing of a contribution.

  • Leaving the contribution frozen for decades

    A fixed amount in nominal terms is a shrinking amount in real terms. Increasing the contribution at least with inflation is what keeps the strategy meaningful.

  • Starting with a round number instead of the schedule

    The value comes from consistency rather than from the size of any single contribution. Skipping the month after a bad headline is what breaks the strategy.

FAQ

Does dollar-cost averaging actually work?

It works mechanically and behaviourally. A fixed amount buys fewer units at high prices and more at low ones, and the removal of the timing decision stops most investors from freezing at the wrong moment.

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

Not in expected return. A lump sum has more time invested and therefore a higher expected value, but it carries far more volatility and a worse experience if the market falls straight after investing.

Is it better to invest at the start or the end of the month?

The start is slightly better because each contribution gets an extra month of growth, worth about half a percentage point a year at a 6% return. The effect is small next to the effect of simply contributing.

How many months of contributions make a difference?

The count compounds, so the count matters more than the size of each contribution. Doubling the horizon adds far more value than doubling the monthly amount.

Does averaging protect me from losses?

It reduces the effect of a bad entry point but it does not prevent losses. A prolonged decline lowers the average cost with each contribution, yet the portfolio can still be worth less than was invested.

Should I increase my contributions over time?

Yes, at least with inflation. A fixed nominal amount buys less of the fund every year, so raising the contribution periodically is what keeps pace with the rising cost of the goal.

References

  1. [1]U.S. Securities and Exchange Commission, Dollar cost averaging — https://www.investor.gov/introduction-investing/investing-basics/investment-products/dollar-cost-averaging
  2. [2]Charles Schwab Corporation, Systematic investing and market timing — https://www.schwab.com/learn/story/does-market-timing-work
  3. [3]Corporate Finance Institute, Annuity future value and present value — https://corporatefinanceinstitute.com/resources/valuation/annuity/