Page 262 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

9.2.3 Interest Rates Changing with Time

If we have an investment over a period of years and the interest rate changes each year, then the
appropriate calculation for compound interest is given by

(9.7)

9.3 Time Basis for Compound Interest Calculations

In industrial practice, the length of time assumed when expressing interest rates is one year. However, we
are sometimes confronted with terms such as 6% p.a. compounded monthly. In this case, the 6% is
referred to as a nominal annual interest rate, i , and the number of compounding periods per year is m
nom
(12 in this case). The nominal rate is not used directly in any calculations. The actual rate is the interest
rate per compounding period, r. The relationship needed to evaluate r is

(9.8)

This is illustrated in Example 9.7.

Example 9.7

For the case of 12% p.a. compounded monthly, what are m, r, and i nom ?

Given: m = 12 (months in a year), i = 12% = 0.12
nom

From Equation (9.8),
r = 0.12/12 = 0.01 (or 1% per month)

9.3.1 Effective Annual Interest Rate

We can use an effective annual interest rate, i , which will allow us to make interest calculations on
eff
an annual basis and obtain the same result as using the actual compounding periods. If we look at the