An annuity is a mathematical stream, not automatically an insurance product. In this module it means equal payments, equal spacing, a finite number of payments, and explicit timing. Four annual payments of $6,000 may form an annuity. Payments of $5,000, $6,000, $7,000, and $8,000 do not.
Count payments separately from interval boundaries. A four-payment ordinary
annuity has payments at t = 1, 2, 3, 4; an annuity due has payments at
t = 0, 1, 2, 3. Both contain four payments, but the due stream receives one
more compounding interval when both streams are accumulated to the same later
date.
To test a proposed annuity, write one row for each payment with its amount and date. Equal amounts alone are insufficient. The gaps between dates must also be equal, the stream must end, and the first-payment date must be known. Only then can an ordinary-annuity or annuity-due factor replace the individual cash-flow calculation.
Irregular dates, changing payments, indefinite streams, skipped periods, or an unknown first-payment date require another model or cash-flow-by-cash-flow valuation. Do not force a convenient factor onto a nonannuity stream.
Put the concept to work
Understand this concept
- Explain the equal-amount, equal-interval, finite-horizon, and payment-timing conditions that define the module's annuity model.
Apply this concept
- Classify a bounded payment stream as an ordinary annuity, annuity due, or neither and map every payment to a timeline before valuation.
Learning resources
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Build on these ideas
- Annuity — Understand
To apply this concept: Required. The stream must satisfy the defining conditions.
- Cash-flow timeline — Apply
To apply this concept: Required. Classification depends on dates and boundary placement.
- Cash-flow timeline — Understand
To understand this concept: Required. An annuity is defined by the placement of payments on equal boundaries.
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Use this idea next
- Annuity — Apply
Required level here: understand. Required. The stream must satisfy the defining conditions.
- Ordinary annuity — Apply
Required level here: apply. Required. The payment stream must be classified and mapped before valuation.
- Ordinary annuity — Understand
Required level here: understand. Required. The stream must first satisfy the general annuity conditions.