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ECON 0110 (84)

Section 9 Notes.doc

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Course Code
ECON 0110

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SECTION 9: DISCOUNTING TO PRESENT VALUE Assume I owe you $X one year from today. Assume you can invest moneyat an interest rate = i How much should I payyou todayto clear the debt? EXAMPLE: I owe you $11,000 oneyear from today Assume i = .10 (or 10%) PV = Present Value of the debt = Amount I should giveyou today ANSWER: $10,000 PROOF: Suppose I gaveyou $10,000 today. You could invest it for 1 year at 10% interest. You would get $1,000 in interest. You would havea total of $11,000. MATHEMATICAL SOLUTION: You could invest PV for one year at i = 10% After one year, you would get 10% interest and would have PV + .10 PV = PV x (1.10) Thus, the amount PV should be the solution of PV x (1.10) = $11,000 PV = $11,000 / (1.10) = $10,000 WHAT IF THE INTEREST RATE IS i = .05 (5%)? I should giveyou an amount PV todayso that in one year you would have PV x (1.05) = $11,000 Therefore, the amount I should giveyou todayis PV = $11,000 / (1.05) = $10,476.19 DISCOUNTING TO PRESENT VALUE: GENERAL CASE FOR MONEY DUE IN ONE YEAR F1= Amount owedin oneyear i = Interest rate PV = Present value PV x (1 + i) = F1 PV = F 1 (1 + i) What if moneyis owedin two years? Suppose I oweyou $12,100 in two years Let i = .10 (or 10%) PV x (1.10) = Result after investing the amount PV for oneyear PV x (1.10) x (1.10) = Result after investing for two years Therefore, PV x (1.10) x (1.10) = PV x (1.10) = $12,100 PV = $12,100 / (1.10) = $10,000
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