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Unformatted text preview: Math 16b Thomas Scanlon Autumn 2010 Thomas Scanlon Math 16b Income streams If at time t the rate of income generated by some enterprise is given by the value of the function f ( t ) , then the total income generated between time a and time b is R b a f ( t ) dt . However, this is only the nominal value of this income stream. To compare the value of this income stream with present payments, we should discount the future payments. Question What value should one assign to an expected future payment? Thomas Scanlon Math 16b Review of continuously compounded interest Recall that if one has a principal of P which earns continuously compounded interest at a rate of r , then after t years, the investment would be worth Pe rt . Thomas Scanlon Math 16b Present value The present value of a payment of $ A made t years in the future is the amount P for which with a principal of $ P dollars invested for t years with continuously compounded interest of rate r one would earn $ A . From the formula for continuously compounded interest, we conclude that Pe rt = A so that P = Ae rt Thomas Scanlon Math 16b Valuation of an income stream Suppose that some enterprise produces income at a steady rate of $ A per year. Of course, this income stream over the next T years will produce $ AT , but how much is it worth in present dollars? We may approximate the continuous income stream as one that is paid in discrete increments. Suppose that between now and T years from now N payments are made at uniform intervals. Then, the length of time between each payment is Δ = T N years....
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This note was uploaded on 02/08/2011 for the course MATH 16B taught by Professor Sarason during the Fall '06 term at Berkeley.
 Fall '06
 Sarason
 Math, Calculus

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