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Time Value of Money: Present Value, Future Value, Annuities, and Perpetuities

Formulas for single-sum compounding and discounting, ordinary annuities, perpetuities, and applications with numerical examples for finance and CFA exam study.

10 cards· by GuruOwl

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  1. 01
    The fundamental principle that a dollar today is worth more than a dollar in the future is known as the time value of money.
    This is due to earning potential and the impact of inflation.
    Flashify::Finance::TimeValueMoney
  2. 02
    The formula for the future value (FV) of a single sum is FV = PV × (1 + r)^n.
    Where PV is present value, r is the periodic interest rate, and n is the number of periods.
    Flashify::Finance::Formulas
  3. 03
    The effective annual rate (EAR) formula for m compounding periods per year is (1 + r/m)^m − 1.
    More frequent compounding increases the effective yield.
    Flashify::Finance::Compounding
  4. 04
    For continuous compounding, the future value formula is FV = PV × e^(rn).
    e is the mathematical constant approximately equal to 2.718.
    Flashify::Finance::Compounding
  5. 05
    An ordinary annuity consists of equal payments made at the end of each period.
    This is the default assumption for most financial formulas unless specified otherwise.
    Flashify::Finance::Annuities
  6. 06
    To convert an ordinary annuity value to an annuity due value, multiply the result by (1 + r).
    Annuity due payments occur at the beginning of the period, allowing for one extra period of interest.
    Flashify::Finance::Annuities
  7. 07
    The present value of a perpetuity is calculated as PV = PMT / r.
    A perpetuity is an infinite series of equal payments.
    Flashify::Finance::Perpetuities
  8. 08
    The Gordon growth model for a growing perpetuity is PV = PMT / (r − g).
    g represents the constant growth rate of the payments.
    Flashify::Finance::Perpetuities
  9. 09
    The Rule of 72 estimates that money doubles in approximately 72 / r years.
    For example, at an 8% interest rate, money doubles in roughly 9 years.
    Flashify::Finance::RulesOfThumb
  10. 10
    The Fisher equation relating nominal and real rates is (1 + nominal) = (1 + real) × (1 + inflation).
    This accounts for the erosion of purchasing power over time.
    Flashify::Finance::Inflation