An annuity is a stream of equal payments at regular intervals — pensions, mortgages, bond coupons.
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20
Future value at 5%/yr: FV = 1000 × [(1.05ⁿ − 1) / 0.05] = —
Ordinary annuity vs annuity-due
An ordinary annuity pays at the *end* of each period (most bonds, loans). An annuity-due pays at the *start* (rent, some pensions) — worth one extra period of growth, so multiply the value by (1 + r).
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Future value of $1,000/year for 20 years at 5%
1000 × (1.05²⁰ − 1) / 0.05 ≈ $33,066.
Your turn
A pension pays $12,000 a year for 15 years. At a 4% discount rate, what's its present value? PV = PMT · [1 − (1+r)⁻ⁿ] / r.
Present value of annuity