Introduction to Finance

Financial Calculator Solution:
Inputs: 10 
8 
1000
N 
%i 
PV
Press: CPT FV
Solution: 2158.93
Computer spreadsheet programs also are available for fi nding future values. Following is 
the same problem solved using 
Microsoft’s
Excel
spreadsheet program. For presentation pur-
poses, the solution for only the two-year version of the problem is shown. That is, how much 
would you accumulate after two years if you invested $1,000 at an 8 percent interest rate with 
annual compounding?
1
For problems involving PVs and FVs, HP calculators require one of the values to be entered as a negative. In contrast, 
both PVs and FVs are entered as positive values in TI calculators, and the internal program makes one of the values 
negative for calculation purposes. Other TI and HP diff erences when entering data also are noted later in this chapter.

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9.2 Compounding to Determine Future Values
223
Spreadsheet Solution:
We set up our spreadsheet with descriptive labels in cells A1 through A4. We then solve 
the compound interest problem by placing the interest rate in decimal form (0.08) in Cell B1. 
The time periods are placed on Row 2, beginning with period 0 (the current period) in Cell B2 
and so forth. The cash fl ow of 1000 (an investment) is listed in cell B3. In this simple problem, 
we fi rst replicate the basic “by hand” calculations in spreadsheet format and the future value 
calculations beginning in C4 and continuing to D4. 
In Cell C4, we place the formula = B3*(1 + B1), which refl ects compounding the $1,000 
investment at 8 percent interest for one year. Cell D4 shows compounding of the investment 
at 8 percent for a second year and can be calculated as C4*(1 + B1), so compounding at an 
8 percent interest rate results in a future value of $1,166.40 after two years. Of course, we 
could have made the FV calculation in one step as = B3*(1 + B1)^2, which also produces 
$1,166.40. 
Excel
 
and other spreadsheet programs have built-in “fi nancial functions” so that spread-
sheet solutions do not have to be calculated the “long way.” The bottom portion of the spread-
sheet solution example illustrates the use of the fi nancial function for future value. Here we 
enter the cash fl ow in time period zero as –1000 to refl ect an outfl ow and a present value. Click 
on the Excel fi nancial wizard (
fx
) icon, then Financial, then FV, and then press OK to bring up 
the dialogue box where the FV components for the problem at hand are requested. The equation 
is FV(Rate, Nper, Pmt, PV, Type). The Rate is 0.08; Nper is the number of time periods (2 in 
the preceding example); Pmt is 0, since there are no periodic payments; PV is –1000; and Type 
is 0, refl ecting that payments occur at the end of the period. Thus, we would have FV(0.08,2,0,
–1000,0). Pressing OK results in a FV of $1,166.40, or $1,166 rounded. Of course, rather than 
inserting numbers, one could insert specifi c cell references in the FV function. 
If the investment had been compounded for ten years, the FV function inputs would have 
been FV(0.08,10,0,–1000,0). Pressing OK would result in an answer of $2,158.92, or $2.159 
rounded. 
In addition, tables have been prepared to simplify the calculation eff ort if fi nancial calcu-
lators or spreadsheet programs are not available. Equation 9.1 can be rewritten as,
FV
n
= PV(FVIF
r
,
n
) (9.2)
where the (1 + 
r
)
n