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Name the date the answer belongs to
A time-zero value and a value three periods later answer different questions. In a fictional stream paying 100 at time 1 and 200 at time 3, a value at time 3 compounds the first payment forward two periods and leaves the second at its own date.
Calculate the value at time 3
At 5% per period, the time-3 value is 100×1.05² + 200 = 310.25. The time-zero value is 100/1.05 + 200/1.05³. Compounding that entire time-zero value three periods gives the same 310.25.
| Payment | Original date | Value at time 3 |
|---|---|---|
| 100 | 1 | 110.25 |
| 200 | 3 | 200 |
| Total | 310.25 |
Avoid adding unlike dates directly
Adding a payment’s time-zero PV to another payment’s undiscounted time-3 amount mixes dates. Keep the time label with each intermediate value until every term belongs to the chosen date.
State the rate assumptions
This example uses the same constant 5% rate for all relevant periods. A term structure or a different reinvestment assumption requires different factors. The common-date discipline remains useful, but the factors must match the model.