# pv - The Time Value of Money Economics 71a Spring 2007 Mayo...

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The Time Value of Money Economics 71a Spring 2007 Mayo, Chapter 7 Lecture notes 3.1

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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

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First example PV = 1000 R = 10% n = 1 FV = ? FV = 1000*(1.10) = 1,100
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

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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 )

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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
Retirement Savings at 5% interest

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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

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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
Goals Compounding and Future Values Present Value Valuing an income stream > Annuities > Perpetuities Mixed streams Term structure again Compounding More applications

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pv - The Time Value of Money Economics 71a Spring 2007 Mayo...

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