What this calculator does
An annuity due pays at the start of each period rather than the end. Rent, insurance premiums and lease payments usually work this way, while loan repayments and most investment contributions do not.
The difference is exactly one period of interest, applied to the whole annuity. At 5 per cent over ten periods, paying at the start is worth $628.89 more in future value, because every payment has an extra period to compound.
The formula
The ordinary annuity values are calculated first, then multiplied by one plus the periodic rate. That single adjustment accounts for every payment arriving one period earlier.
| Term | Meaning |
|---|---|
| Annuity due | Payments at the start of each period. |
| Ordinary annuity | Payments at the end of each period, the more common convention in finance. |
| The (1+i) factor | The single multiplier that converts between the two. |
The inputs explained
| Field | What to enter |
|---|---|
| Payment per period ($) | The payment made each period. |
| Interest rate per period (%) | The interest rate per period, not per year unless the periods are years. |
| Number of periods | The number of payments. |
When to use it
Valuing a lease
Lease payments are typically made in advance, which makes them an annuity due.
Comparing a savings plan
Contributing at the start of each period rather than the end gains an extra period of compounding on everything.
Checking a textbook problem
Getting the timing convention wrong is one of the most common errors in annuity calculations.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much is paying early worth?
The two conventions compared over four durations.
| Number of periods | Future value, annuity due | Future value, ordinary annuity |
|---|---|---|
| 5 periods | $5,801.91 | $5,525.63 |
| 10 periods | $13,206.79 | $12,577.89 |
| 20 periods | $34,719.25 | $33,065.95 |
| 30 periods | $69,760.79 | $66,438.85 |
Questions
When is an annuity due the right convention?
Whenever payment is made in advance: rent, insurance premiums, lease instalments and many subscription arrangements. Loan repayments and most investment contributions are ordinary annuities, paid in arrears.
Why is the adjustment just one multiplication?
Because every payment shifts forward by exactly one period, so the whole series gains one period of interest uniformly. Multiplying by one plus the rate captures that for all of them at once.
Does the difference matter in practice?
It is about 5 per cent at a 5 per cent rate, which is small on one payment and meaningful across a long series. At higher rates it grows proportionally, so it matters more the more expensive money is.
Which convention do financial calculators default to?
Ordinary annuity, almost always. Most have a separate mode or setting for annuity due, and forgetting to switch it is a very common source of error.
For a stream that grows each period, see the growing annuity calculator. For a stream with no end, see the perpetuity calculator.