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(n is the upper-case Greek letter pi, here signifying present.) This differs from the single-value formula only in the replacement of V by R, and in the insertion of the E sign.

The idea of the sum readily carries over to the case of a continuous cash flow, but in the latter context the £ symbol must give way, of course, to the definite integral sign. Consider a continuous revenue stream at the rate of R(t) dollars per year. This means that at ? = the rate of flow is P(^) dollars per year, but at another point of time t = t2 the rate will be R(t2) dollars per year—with t taken as a continuous variable. If at any point of time t we allow an infinitesimal time interval dt to pass, the amount of revenue during the interval [t,t + dt] can be written as R(t) dt [cf. the previous discussion of dK = I(t) dt]. When continuously discounted at the rate of r per year, its present value should be R(t)e~r' dt. If we let our problem be that of finding the total present value of a three-year stream, our answer is to be found in the following definite integral:

This expression, the continuous version of the sum in (13.11), differs from the single-value formula only in the replacement of V by R(t) and in the appending of the definite integral sign.*

Example 6 What is the present value of a continuous revenue flow lasting for y years at the constant rate of D dollars per year and discounted at the rate of r per year? According to (13.11'). we have

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