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SECTION 9:
DISCOUNTING TO PRESENT VALUE
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View Full Document 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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View Full Document 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.
 Spring '08
 Kenkel
 Macroeconomics

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