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Unformatted text preview: APPLICATION OF THE INTEGRAL II: FUTURE AND PRESENT VALUE OF A CONTINUOUS INCOME STREAM Let us review some basic formulae from a few weeks ago involving the return on money deposited in a bank paying a given rate of interest. If an initial amount of M dollars is deposited in a bank paying an interest rate of r per year compounded continuously, the future value of this money is given by the formula (0.1) Future value = Me rt . Conversely, if one aims to obtain an amount of N dollars t years down the road from an account that accrues interest at the annual rate of r , then the present value for this amount, i.e., the amount of money that one needs to put in today is (0.2) Present value = Ne- rt . The calculation of future value above was made under the assumption that once the initial deposit is made, there is no future deposits or withdrawals. But a much more realistic frameworkis one where a sequence of future deposits is made into the account after the intial one and over a long period of time. If the deposits are made regularly enough and the time between deposits is relatively short compared to the overall lifetime of the account, we can think of the money as flowing continuously into the account rather than in a large number of discrete chunks. We will refer to this scenario as a continuous income stream. The goal of this note is to deduce a closed-form integral formula for future and present values of a continuous incone...
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This note was uploaded on 01/14/2012 for the course MATH 105 taught by Professor Malabikapramanik during the Fall '10 term at The University of British Columbia.
- Fall '10