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Annuity vs Perpetuity
Annuity vs Perpetuity
An annuity has a fixed number of equal payments. A perpetuity pays equal amounts forever.
Comparison Table
| Feature | Annuity | Perpetuity |
|---|---|---|
| Duration | Fixed number of periods | Infinite |
| PV formula | PMT × [(1-(1+r)^-n)/r] | PMT / r |
| Examples | Mortgages, car loans, leases | Preferred stock, some endowments |
| Growth variant | Growing annuity | Growing perpetuity (requires g < r) |
Key Differences
- →Annuity stops; perpetuity goes on forever
- →Perpetuity formula is simpler
- →Growing perpetuity is used in terminal value calculations
When to Use Annuity
- ✓Loan payments
- ✓Retirement savings accumulation
- ✓Any fixed-term payment stream
When to Use Perpetuity
- ✓Preferred stock valuation
- ✓Terminal value in DCF models
- ✓Endowment payouts
Common Confusions
- !Thinking perpetuity has infinite present value (it does not; PV is finite)
- !Confusing growing perpetuity with regular perpetuity
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FAQs
Common questions about this comparison
Technically yes, but the PV becomes extremely large and sensitive. In practice, g should be well below r.