account that pays a nominal rate of 12 percent, compounded quarterly. How
much would you have after two years?
For compounding more frequently than annually, we use the following modifi-
cation of Equation 2-1:
(2-12)
Time Line and Equation:
03%12345678
Quarters
100
FV?
FVn = PV(l iPER)Number of periods.
- NUMERICAL SOLUTION
Using Equation 2–12,
FV = $l00 (1 0.03)^8
= $126.68.
- FINANCIAL CALCULATOR SOLUTION
Inputs: 8 3 –100 0
Output: 126.68
Input N 2 4 8, I 12/4 3, PV –100, and PMT 0, and then press the FV
key to get FV $126.68.
- SPREADSHEET SOLUTION
A spreadsheet could be developed as we did earlier in the chapter in our discussion of
the future value of a lump sum. Rows would be set up to show the interest rate, time,
cash flow, and future value of the lump sum. The interest rate used in the spreadsheet
would be the periodic interest rate (iNom/m) and the number of time periods shown
would be (m)(n).
3.Effective (or equivalent) annual rate (EAR).This is the annual rate that pro-
duces the same result as if we had compounded at a given periodic rate m
times per year. The EAR, also called EFF% (for effective percentage), is found
as follows:
EAR (or EFF%)a 1 (2-13)
iNom
m
b
m
1.0.
FVnPV(1iPER)Number of periodsPV a 1
iNom
m
b
mn
.
Semiannual and Other Compounding Periods 85
Time Value of Money 83
