rate of return

Suppose you invest P at time 0 and receive payments P1,,Pn at times t1,,tn corresponding to interest rates (evaluated from 0) r1,,rn. The net present value of this investment is


The rate of return r 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 r, as a real number, exists, it satisfies the following equation:



  • We typically assume that  t1t2tn,  and, in most situations, that they are integers, so that the equation is a polynomial equation.

  • However, there is no guarantee that r exists, and if it exists, that it is unique.

  • Nevertheless, one can usually, by trial-and-error, determine if such an r exists. If r exists, and if Pi are all non-negative, then by Descartes’ rule of signs (http://planetmath.org/DescartesRuleOfSigns), r is always unique and r>-1.

Title rate of return
Canonical name RateOfReturn
Date of creation 2013-03-22 16:41:05
Last modified on 2013-03-22 16:41:05
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 5
Author CWoo (3771)
Entry type Definition
Classification msc 91B28