Page 263 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

value of an investment after one year, we can write

which, upon rearrangement, gives

(9.9)

Effective annual interest rate is illustrated in Example 9.8.

Example 9.8

What is the effective annual interest rate for a nominal rate of 8% p.a. when compounded monthly?
From Equation (9.9), for i nom = 0.08 and m = 12, we obtain

12
i = (1 + 0.08/12) – 1 = 0.083 (or 8.3 % p.a.)
eff
The effective annual interest rate is greater than the nominal annual rate. This indicates that the effective
interest rate will continue to increase as the number of compounding periods per year increases. For the
limiting case, interest is compounded continuously.

9.3.2 Continuously Compounded Interest

For the case of continuously compounded interest, we must look at what happens to Equation (9.9) as m
→ ∞:

Rewriting the left-hand side as

and noting that

we find that for continuous compounding,