The mechanical difference
An ordinary annuity deposits at the end of each period. An annuity due deposits at the start. In an annuity due every single payment sits in the account one period longer, so the entire balance is larger by exactly the factor (1 + r).
That is the complete story. There is no second effect, no interaction with the horizon, and no dependence on the payment size. The relative advantage is the periodic rate itself.
FV(due) = FV(ordinary) × (1 + r)- r — the rate for one period, not the annual rate
- At 6% nominal compounded monthly, r = 0.005, so the advantage is 0.5%
- The percentage advantage does not change with the number of periods
What it is worth in dollars
The percentage is fixed but the dollar amount is not, because it applies to a balance that grows over time. On a 30-year plan the same 0.5% is worth several thousand dollars simply because the balance it multiplies is large.
| Years | End of month | Start of month | Difference |
|---|---|---|---|
| 5 | $34,885 | $35,059 | $174 |
| 10 | $81,940 | $82,349 | $410 |
| 20 | $231,020 | $232,176 | $1,155 |
| 30 | $502,258 | $504,769 | $2,511 |
The difference is 0.5% of the ending balance in every row — one month at the periodic rate.
Frequency changes the size of the effect
Because the advantage is one period of growth, it is larger when periods are longer. Annual deposits at 6% gain a full 6% from moving to the start of the year; monthly deposits gain 0.5%; weekly deposits gain about 0.115%.
So the timing question matters most for people making one large annual contribution — funding an account in January rather than December is worth a full year of growth on that deposit, every year.
| Deposit frequency | Periodic rate | Advantage from paying in advance |
|---|---|---|
| Annual | 6.000% | 6.00% |
| Quarterly | 1.500% | 1.50% |
| Monthly | 0.500% | 0.50% |
| Weekly | 0.115% | 0.12% |
What this means in practice
For monthly savers the honest conclusion is that timing is a minor optimisation. Half a percent is real and it is free, so take it by scheduling transfers for the start of the month — but do not let it displace decisions that move the result by tens of percent, such as the contribution amount or the horizon.
For annual contributors the conclusion is stronger. Funding early in the year rather than late is worth a full year of growth on each contribution, and over a long horizon that compounds into a genuinely material difference.
Why the convention still matters when modelling
Even where the dollar effect is small, mismatched conventions cause confusion. Two calculators given identical inputs will disagree by exactly one period of growth if one assumes advance payments and the other does not, and the discrepancy looks like a bug.
Every Quantus calculator that accepts a contribution states its timing convention and lets you change it, so a difference against another tool can be attributed rather than guessed at.
The same convention on the paying side
Loans have the same distinction, and there it has a name: payments in advance against payments in arrears. A lease or rent is usually paid in advance; a mortgage is usually paid in arrears, at the end of the period the interest accrued over.
The consequence mirrors the savings case. Paying in advance reduces the balance a period earlier, so less interest accrues and the total cost is slightly lower. The size of the effect is again one period of interest, which makes it small on a monthly loan and material on anything billed annually.
It also explains a small discrepancy people notice when checking a lender's figures against a generic calculator: if one assumes arrears and the other advance, the payment will differ by roughly the periodic rate. That is a convention mismatch, not an error.
Where this sits on the list of things that matter
It is worth being explicit about proportion. Contribution timing changes a result by the periodic rate — half a percent for a monthly saver at 6%. Raising the contribution by 10% changes the result by 10%. Extending the horizon by five years on a thirty-year plan changes it by far more than either.
So the order of attention should be: how much, for how long, at what rate, and then when in the period. Timing is a genuine free improvement and worth taking once, by setting the transfer date and forgetting about it. It is not worth agonising over, and it should never be presented as a technique that transforms an outcome.
The exception, again, is the annual contributor. For someone funding an account once a year, the choice between January and December is a full year of growth on every contribution — which moves from the rounding-error category into the material one.
Making the choice once
The practical implementation is trivial and permanent: schedule the transfer for the first working day after income arrives rather than the last day of the month. It takes one change and never needs revisiting.
There is a behavioural argument that outweighs the arithmetic one. Money moved at the start of the period is money that cannot be spent during it, and the gap between intended and actual saving is usually larger than half a percent. The timing advantage is real, but the reliability advantage is bigger.
For lump-sum contributors the same logic points to funding early in the year rather than at the deadline, which is both the mathematically better choice and the one least likely to be forgotten.
Educational tool. This article explains arithmetic, not personal circumstances. It is general educational content, not investment, tax or insurance advice, and every figure in it is a projection from stated assumptions rather than a prediction. Check any result against your own situation, and see the editorial policy for how this content is produced and corrected.