Page 264 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

(9.10)

Equation (9.10) represents the maximum effective annual interest rate for a given nominal rate.

The method for calculating continuously compounded interest is illustrated in Example 9.9.

Example 9.9

What is the effective annual interest rate for an investment made at a nominal rate of 8% p.a. compounded
continuously?
From Equation (9.10) for i nom = 0.08 we obtain

i = e 0.08 – 1 = 0.0833, or 8.33% p.a.
eff

Note: We can see, by comparison with Example 9.8, that by compounding continuously little was gained
over monthly compounding.

In comparing alternatives, the effective annual rate, and not the nominal annual rate of interest, must be
used.

9.4 Cash Flow Diagrams

To this point, we have considered only an investment made at a single point in time at a known interest
rate, and we learned to evaluate the future value of this investment. More complicated transactions
involve several investments and/or payments of differing amounts made at different times. For more
complicated investment schemes, we must keep careful track of the amount and time of each transaction.
An effective way to track these transactions is to utilize a cash flow diagram, or CFD. Such a diagram
offers a visual representation of each investment. Figure 9.2 is the cash flow diagram for Example 9.10,
which is used to introduce the basic elements of the discrete CFD.

Figure 9.2 An Example of a Representative Discrete Cash Flow Diagram (CFD)