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rate of return
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(Definition)
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Suppose you invest  at time 0 and receive payments
 at times
 corresponding to interest rates (evaluated from 0)
 . The net present value of this investment is
The rate of return  of this investment is a compound interest rate, compounded at every unit time period, such that the net present value of the investment is 0. In other words, if  , as a real number, exists, it satisfies the following equation:
Remarks.
- We typically assume that
 , and, in most situations, that they are integers, so that the equation is a polynomial equation.
- However, there is no guarantee that
 exists, and if it exists, that it is unique.
- Nevertheless, one can usually, by trial-and-error, determine if such an
 exists. If  exists, and if  are all non-negative, then by Descartes' rule of signs,  is always unique and  .
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"rate of return" is owned by CWoo. [ full author list (2) ]
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Cross-references: polynomial, integers, equation, real number, period, unit, compound interest, net present value, interest rates
There is 1 reference to this entry.
This is version 2 of rate of return, born on 2007-02-11, modified 2007-02-11.
Object id is 8896, canonical name is RateOfReturn.
Accessed 572 times total.
Classification:
| AMS MSC: | 91B28 (Game theory, economics, social and behavioral sciences :: Mathematical economics :: Finance, portfolios, investment) |
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Pending Errata and Addenda
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