bond valuation, capital budgeting, lease analysis, and many other important finan-
cial problems.
Problem Format
To help you understand the various types of time value problems, we generally use a
standard format. First, we state the problem in words. Next, we diagram the problem
on a time line. Then, beneath the time line, we show the equation that must be solved.
Finally, we present the three alternative procedures for solving the equation to obtain
the answer: (1) use a regular calculator to obtain a numerical solution, (2) use a finan-
cial calculator, and (3) use a spreadsheet program. For some very easy problems, we
will not show a spreadsheet solution, and for some difficult problems, we will not show
numerical solutions because they are too inefficient.
To illustrate the format, consider again our five-year, 5 percent example:
Time Line:
05%12345
100 FV ?
Equation:
- NUMERICAL SOLUTION
05%1 2 3 4 5
100 1.05 1.05 1.05 1.05 1.05 127.63
→→→→→
105.00 110.25 115.76 121.55
Using a regular calculator, raise 1.05 to the 5th power and multiply by $100 to get
FV 5 $127.63.
- FINANCIAL CALCULATOR SOLUTION
Inputs: 5 5 100 0
Output: 127.63
Note that the calculator diagram tells you to input N 5, I 5, PV 100, and
PMT 0, and then to press the FV key to get the answer, 127.63. Interest rates are
entered as percentages (5), not decimals (0.05). Also, note that in this particular prob-
lem, the PMT key does not come into play, as no constant series of payments is in-
volved. Finally, you should recognize that small rounding differences will often occur
among the various solution methods because rounding sometimes is done at interme-
diate steps in long problems.
FVnPV(1i)n$100(1.05)^5.
62 CHAPTER 2 Time Value of Money
60 Time Value of Money
