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**Unformatted text preview: **1 The Time Value of Money Economics 71a Spring 2007 Mayo, Chapter 7 Lecture notes 3.1 Goals • Compounding and Future Values • Present Value • Valuing an income stream > Annuities > Perpetuities • Mixed streams • Term structure again • Compounding • More applications Compounding • PV = present or starting value • FV = future value • R = interest rate • n = number of periods First example • PV = 1000 • R = 10% • n = 1 • FV = ? FV = 1000*(1.10) = 1,100 2 Example 2 Compound Interest • PV = 1000 • R = 10% • n = 3 • FV = ? FV = 1000*(1.1)*(1.1)*(1.1) = 1,331 FV = PV*(1+R)^n Example 3: The magic of compounding • PV = 1 • R = 6% • n = 50 • FV = ? > FV = PV*(1+R)^n = 18 > n = 100, FV = 339 > n = 200, FV = 115,000 Example 4: Doubling times • Doubling time = time for funds to double FV PV = 2 = (1 + R ) n log(2) = n log(1 + R ) n = log(2) log(1 + R ) Example 5 Retirement Saving • PV = 1000, age = 20, n =45 • R = 0.05 > FV = PV*(1+0.05)^45 = 8985 > Doubling 14 • R = 0.07 > FV=PV*(1+0.07)^45 = 21,002 > Doubling = 10 • Small change in R, big impact 3 Retirement Savings at 5% interest Goals • Compounding and Future Values • Present Value • Valuing an income stream > Annuities > Perpetuities • Mixed streams • Term structure again • Compounding • More applications Present Value • Go in the other direction • Know FV • Get PV • Answer basic questions like what is $100 tomorrow worth today PV = FV (1 + R ) n Example Given a zero coupon bond paying $1000 in 5 years • How much is it worth today? • R = 0.05 • PV = 1000/(1.05)^5 = $784 • This is the amount that could be stashed away to give 1000 in 5 years time 4 Goals • Compounding and Future Values • Present Value • Valuing an income stream > Annuities > Perpetuities • Mixed streams • Term structure again • Compounding...

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