09 PRESENT VALUE

# 09 PRESENT VALUE - SECTION 9 DISCOUNTING TO PRESENT VALUE DISCOUNTING TO PRESENT VALUE Assume I owe you \$X one year from today Assume you can

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SECTION 9: DISCOUNTING TO PRESENT VALUE

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DISCOUNTING TO PRESENT VALUE Assume I owe you \$X one year from today. Assume you can invest money at an interest rate = i How much should I pay you today to clear the debt?
EXAMPLE: I owe you \$11,000 one year from today Assume i = .10 (10%) PV = Present Value of the debt = Amount I should give you today ANSWER: \$10,000 Suppose I gave you \$10,000 today. You could invest it for 1 year at 10% interest. You would get \$1,000 in interest. You would have a total of \$11,000.

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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 give you an amount PV today so that in one year you would have PV x (1.05) = \$11,000 Therefore, the amount I should give you today is PV = \$11,000 / (1.05) = \$10,476.19

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## This note was uploaded on 04/07/2008 for the course ECON 0110 taught by Professor Kenkel during the Spring '08 term at Pittsburgh.

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09 PRESENT VALUE - SECTION 9 DISCOUNTING TO PRESENT VALUE DISCOUNTING TO PRESENT VALUE Assume I owe you \$X one year from today Assume you can

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