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# The Time Value of Money

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1. The Time Value of Money Richard MacMinn

2. 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

3. 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

4. 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

5. Future Value • If a dollar is compounded m times per period then the future value may be expressed as Richard MacMinn

6. 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

7. Present Value • A dollar today is worth more than a dollar tomorrow! • Present value is the inverse of future value. Richard MacMinn

8. 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

9. Present Value • The present value of a stream of one dollar returns received at dates t = 1, 2, . . . , T is Richard MacMinn

10. 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

11. 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

12. Perpetuity • A perpetuity is an annuity payable indefinitely. • The present value of an indefinitely long one dollar stream is Richard MacMinn

13. 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

14. 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

15. 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

16. 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

17. Links • T. ROWE PRICE Good, simple ''what if'' program http://www.troweprice.com • VANGUARD Solid online retirement planning http://www.vanguard.com Richard MacMinn