An annuity due moves every ordinary-annuity payment one period earlier. At a positive rate, each payment therefore has one additional period of value at a common later date. For a matching stream with the same payment amount, count, spacing, rate, and valuation basis:
annuity-due value = ordinary-annuity value × (1 + i)
The four-payment stream occurs at t = 0, 1, 2, 3, not at t = 0, 1, 2, 3, 4.
Adding a payment at both endpoints is a five-payment stream, not an annuity-due
conversion:
correct four-payment due stream: t = 0, 1, 2, 3
incorrect five-payment stream: t = 0, 1, 2, 3, 4
At a positive rate, the due value exceeds the matching ordinary-annuity value because every payment moves earlier by one period. At a zero rate, timing does not change the numerical value, although the dates remain different. This direction check can catch a reversed timing factor before a result is used.
Rent, leases, insurance, subscriptions, and service contracts may use different timing conventions, partial periods, escalations, or legal terms. The label in a story is weaker evidence than the actual payment dates. Map the dates first.
Put the concept to work
Understand this concept
- Explain why shifting every ordinary-annuity payment one period earlier creates an annuity due and changes value at a positive rate.
Apply this concept
- Compute an annuity-due value and reconcile it to the otherwise identical ordinary-annuity value multiplied by one plus the periodic rate.
Learning resources
Choose a lesson, try an application, or inspect the sources behind this concept.
Build on these ideas
- Ordinary annuity — Apply
To apply this concept: Required. The due identity reuses the matching ordinary-annuity value.
- Ordinary annuity — Understand
To understand this concept: Required. The one-period shift is defined relative to ordinary-annuity timing.