$1,000
7.0%
20 years
2.0%
Standard Annuity (Fixed Payments)
Annuity (Ordinary) PV:
$11,563.50
Annuity (Due) PV:
$12,373.34
PV = C/r × [1 - 1/(1+r)^n]
(Due = Ordinary × (1+r))
(Due = Ordinary × (1+r))
Growing Annuity
Growing Annuity PV:
$14,028.85
PV = C/(r-g) × [1 - ((1+g)/(1+r))^n]
Perpetuity (Infinite Payments)
Perpetuity PV:
$14,285.71
Growing Perpetuity PV:
$20,000.00
Perpetuity: PV = C/r
Growing: PV = C/(r-g)
Growing: PV = C/(r-g)
Key Insight: Annuity Due payments start immediately, making them worth more (multiplied by 1+r). When discount rate equals growth rate, perpetuities are undefined.
Cash Flow Timeline (First 10 Periods)
Understanding the Timeline: Each bar represents a cash payment. The height shows its relative value. Annuity Due payments start at year 0; Ordinary Annuity payments start at year 1.