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Unformatted text preview: ) 1 ( 1 1 r r r C PV (6) ∞-= 1 1 r C PV Or, finally, (7) r C PV = IV. Equation (7) is very simple. It says that the present value of an annuity of C dollars per annum is C divided by r, where r is the average interest rate per annum. This makes considerable sense once you provide a numerical example. Suppose C =$10 per annum and the interest rate is .05, or 5 percent. How many dollars, designated by the letter P, would you have to put away today so that it produces $10 in each year forever? The answer is given by solving the following formula for P: . 200 $ 05 . 10 $ 10 $ 05 . = = = × P P Investing $200 at 5 percent generates $10 in interest per year and continues to do so forever. Thus, if an annuity promises to pay $10 forever and the annual interest rate is 5 percent, the value of that infinite stream of payments is $200. If the annuity were priced in a competitive market its price should be $200...
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This note was uploaded on 02/04/2010 for the course ECON 106v taught by Professor Miyakawa during the Spring '08 term at UCLA.
- Spring '08