gen-briefly-explain-annuities-and-perpetuities-and-one-common-mi-23e3

Briefly explain annuities and perpetuities and one common misconception about it.

# Annuities and Perpetuities ## **Annuities** An annuity is a series of **equal payments** made at **regular intervals** for a **fixed period of time**. Examples include mortgage payments, car loans, or retirement payouts over 20 years. **Present Value Formula:** PV = PMT × [(1 - (1 + r)^-n) / r] Where PMT = payment, r = interest rate, n = number of periods ## **Perpetuities** A perpetuity is an annuity that continues **forever** — equal payments at regular intervals with no end date. Examples include certain preferred stocks or endowment funds designed to pay out indefinitely. **Present Value Formula:** PV = PMT / r (Much simpler since payments never stop) ## **Common Misconception** **"The total value of a perpetuity is infinite because payments continue forever."** This is **false**. While a perpetuity makes infinite payments, its present value is actually **finite**. This is because: - Future payments are discounted back to today's dollars - Money received far in the future is worth very little today - The discount factor makes distant payments approach zero value For example, a perpetuity paying $100/year at 5% interest is worth only $2,000 today ($100 / 0.05), not an infinite amount.