Time Value of Money

Selected Financial Formulae Purpose Basic Time Value Formulae Future Value of a Single Sum Present Value of a Single Sum FV = PV  1 + i  N FV PV = ----------------- 1 + iN FV ln  ------   PV N = -------------------ln  1 + i  i =

N

Formula

Solve for N for a Single Sum

Solve for i for a Single Sum Present Value of an Ordinary Annuity

FV – 1 -----PV

1 – 1   1 + i N PV A = Pmt ---------------------------------i  1 + i N – 1 FV A = Pmt --------------------------i

 1 – 1   1 + i   N – 1PV Ad = Pmt -------------------------------------------- + Pmt i

Future Value of an Ordinary Annuity

Present Value of an Annuity Due

Future Value of an Annuity Due Present Value of an Annuity Growing at a Constant Rate (g) Future Value of an Annuity Growing at a Constant Rate (g) Holding Period Return (single period)

 1 + i N – 1 FV Ad = Pmt ---------------------------  1 + i  i Pmt 1 1+g N PV GA = ------------  1 –  -----------    1 + i  i–g Pmt 1 1+g N N FV GA = ------------  1 –  -----------    1 + i   1 + i   i–g P 1 +  Cash Flows HPR = ---------------------------------------------- – 1 P0

Basic Financial Formulae © 1995-2011 by Timothy R. Mayes, Ph.D.

1

Selected Financial Formulae Purpose Formula

Holding Period Return with Reinvestment (for multiple sub-period returns)

HPR Reinvest =

t=1

  1 + HPRt  – 1

N

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