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## The Time Value of Money

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**The Time Value of Money**Richard MacMinn**Objectives**• To stress that the time value of money is an integral part of financial decision making. • To discuss compounding techniques • To discuss discounting techniques Richard MacMinn**Future Value**• Suppose you place $100 in a savings account that pays 7.2% interest, compounded annually. How does the account grow? • fv1 = 100 (1.072) • fv2 = 100 (1.072)2 • fvT = 100 (1.072)T Richard MacMinn**Future Value**• The future value of a one dollar stream of savings for n years, i.e., one dollar saved at dates t = 1, 2, . . . , T, is Richard MacMinn**Future Value**• If a dollar is compounded m times per period then the future value may be expressed as Richard MacMinn**Future Value**• As m approaches infinity, the factor where e = 2.71828 • Given continuous compounding, the future value of a dollar n periods hence is Richard MacMinn**Present Value**• A dollar today is worth more than a dollar tomorrow! • Present value is the inverse of future value. Richard MacMinn**Present Value**• The present value of a dollar received in one year is • The present value of a dollar received in T years is Richard MacMinn**Present Value**• The present value of a stream of one dollar returns received at dates t = 1, 2, . . . , T is Richard MacMinn**Annuity**• An annuity is a stream of equal dollar returns for a specified number of periods, e.g., pension funds, insurance contracts, sinking funds. • The value of a T year annuity that pays one dollar per year is Richard MacMinn**Annuity**• Loans paid off in equal installments over a fixed period are annuities, or equivalently, amortized loans. • The value L of the of the amortized loan is Richard MacMinn**Perpetuity**• A perpetuity is an annuity payable indefinitely. • The present value of an indefinitely long one dollar stream is Richard MacMinn**Growing Perpetuity**• A growing perpetuity is a perpetuity with a payment that grows at a constant rate g. • The payment stream may be specified as 1, (1 + g), (1 + g)2, (1 + g)3, . . . , and its value as Richard MacMinn**Annuity Again**• The present value of an annuity is • This is the difference between a perpetuity that begins paying at t = 1 and one that begins paying at t = T + 1. Richard MacMinn**Bond Value**• A bond that pays a level interest stream and then the principal at maturity is a combination of an annuity and a single payment. • Bonds also typically pay interest semiannually and the bond value B is Richard MacMinn**Links**• QUICKEN FINANCIAL PLANNER Extensive planning software http://www.quicken.com/ • RETIRE SECUREPrice Waterhouse Cooper's retirement aidhttp://www.pwcglobal.com/ • S&P PERSONAL WEALTH Standard & Poor's asset allocation modelhttp://www.personalwealth.com/ Richard MacMinn**Links**• T. ROWE PRICE Good, simple ''what if'' program http://www.troweprice.com • VANGUARD Solid online retirement planning http://www.vanguard.com Richard MacMinn