chapter 3 note - CH3 THE TIME VALUE OF MONEY Using Present...

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1 CH3: THE TIME VALUE OF MONEY Using Present Value Tables and Formula By. Dr. M. Metghalchi Two types of calculations: I. Single Amount : A. Future Value of a single amount B. Present Value of a single amount II. Annuity: C. Future value of an annuity (Multiple cash flows) D. Present value of an annuity (Multiple cash flows) The mathematics of finance (time value of money) can be estimated by four methods: 1. Present Value Tables at the end of your book (Appendix A) 2. Calculator 3. Excel 4. Mathematics The easiest way would be to use Excel. This lecture uses present value tables, and sometimes calculator, however I have also included in my lecture notes an Excel file for time value of money. I strongly recommend students to use the Excel methods. I. Single Amount . A. future value of a single amount. The general formula for finding the future value of a single amount are as follow : FV = PV*FVIF(i/m, nm) (in table form) (1) FV = PV * (1 + i) n mathematical if annual compounding FV = PV * (1+ i/m) nm mathematical form, if m times compounding per year FVIF(i/m, nm) = (1+ i/m) nm The value of FVIF(i/m, nm) can be obtained from Present Value Tables or Mathematical Tables at the end of your book, Appendix A. The definitions of various variables in the above equations are: FV=future value, PV= present value, i= annual interest rate, m=number of times compounding per year and n= number of years.
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2 Example 1: What is the future value of $800 at 6% compounded annually after 5 years? (For Excel solution of all examples, please see Time Value of Money – Excel file). Here are what we have: PV=800, i=6%, n=5 years, FV? Using equation (1): FV 5 =800*FVIF(6/1,5*1)=800*1.3382=$1070.56 Note: m =1 since annual compounding. From Table Appendix A we look under number of period 6, and 5% interest rate and we find the value of 1.3382. Or: FV 5 = 800 * (1 + .06) 5 = $1,070.56 ( mathematical form) Example 2: What is the value of $100 compounded quarterly at 8% after two years? Here is what we have: PV=100, i=8%, m=4, n=2, FV? FV 2 = $100*FVIF(8/4,2*4)=100*FVIF(2,8)=100*1.1717==$117.17 Note : quarterly compounding, m=4. From Table Appendix A we look under number of period 2, and 8% interest rate and we find the value of 1.1717. Or: FV 2 = 100* (1+ .02) 8 = $117.17 ( mathematical form) Example 3: You can deposit $9,000 in Victoria bank that pays 12 % interest compounded monthly for 20 years or deposit the same $9,000 in Houston bank that pays 12 % compounded annually for 20 years. 1) where should you deposit? 2) Estimate the addition return of Victoria bank. ANSWER: 1) You should invest in Victoria bank since the more compounding the better for investors. 2) find the FV of a lump sum, we use: FV = PV * (1+ i/m) nm In Victoria Bank, you will have: FV = $9,000(1.01) 240 = $98,032.98 (i = 0.12, m=12, n=20) In Houston Bank, you will have:
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3 FV = $9,000(1.12) 20 = $86,816.64 (I = 0.12, m=1, n=20) Additional return = 98,032.98 – 86,816.64 = $11,216.34 Example 4: How long does it for an initial investment of $300 to grow to $774 if it is
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This note was uploaded on 09/21/2011 for the course FINANCE 4320 taught by Professor Omaral-nasser during the Spring '11 term at University of Houston-Victoria.

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chapter 3 note - CH3 THE TIME VALUE OF MONEY Using Present...

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