Appendix A 249Number of Interest Periods = 5 years × 12 mo/yr = 60 interest periods
A = P (A|P,i,n) = $12,500 (A|P,0.5,60) = $12,500 (0.0193) = $241.25
To solve this type of problem using an effective interest rate ap-
proach, we must define the effective interest rate. The effective annual
interest rate is the annualized interest rate that would yield results equiv-
alent to the period interest rate as previously calculated. However, the ef-
fective annual interest rate approach should not be used if the cash flows
are more frequent than annual (e.g., monthly). In general, the interest rate
for time value of money factors should match the frequency of the cash
flows. (For example, if the cash flows are monthly, use the period interest
rate approach with monthly periods.)
As an example of the calculation of an effective interest rate, assume
that the nominal interest rate is 12%/yr/qtr; therefore, the period interest
rate is 3%/qtr/qtr. One dollar invested for 1 year at 3%/qtr/qtr would
have a future worth as calculated:
F = P (F|P,i,n) = $1 (F|P,3,4) = $1 (1.03)^4
= $1 (1.1255) = $1.1255
To get this same value in 1 year with an annual rate, the annual rate
would have to be of 12.55%/yr/yr. This value is called the effective an-
nual interest rate. The effective annual interest rate is given by (1.03)^4 –1 =
0.1255 or 12.55%.
The general equation for the Effective Annual Interest Rate is:
Effective Annual Interest Rate = (1 + (r/m))m –1
where: r = nominal annual interest rate
m = number of interest periods per year
Example 26
What is the effective annual interest rate if the nominal rate is 12%/
yr compounded monthly?
nominal annual interest rate = 12%/yr/mo
period interest rate = 1%/mo/mo
effective annual interest rate = (1+0.12/12)^12 – 1 = 0.1268 or 12.68%