shown in Figure 2-3 to illustrate the various points. Refer to the figure constantly,
and try to find in it an example of the points covered as you go through this
summary.
Compoundingis the process of determining the future value (FV)of a cash flow
or a series of cash flows. The compounded amount, or future value, is equal to the
beginning amount plus the interest earned.
Future value: FVnPV(1 i)nPV(FVIFi,n).
(single payment)
Example:$1,000 compounded for 1 year at 4 percent:
FV 1 $1,000(1.04)^1 $1,040.
Discountingis the process of finding thepresent value (PV)of a future cash
flow or a series of cash flows; discounting is the reciprocal, or reverse, of com-
pounding.
Present value:
(single payment)
Example:$1,000 discounted back for 2 years at 4 percent:
.
An annuityis defined as a series of equal periodic payments (PMT) for a specified
number of periods.
Future value:
(annuity)
Example:FVA of 3 payments of $1,000 when i 4%:
FVA 3 $1,000(3.1216) $3,121.60.
PMT(FVIFAi,n).
PMTa
(1i)n 1
i
b
PMT a
n
t 1
(1i)nt
FVAnPMT(1i)n^1 PMT(1i)n^2 PMT(1i)n^3 PMT(1i)^0
PV
$1,000
(1.04)^2
$1,000 a
1
1.04
b
2
$1,000(0.9246)$924.60
PV
FVn
(1i)n
FVna
1
1 i
b
n
FVn(PVIFi,n).
Summary 91
04%1 2 3Years
1,000 1,000 1,000.00
1,040.00
961.50
1,081.60
924.60
889.00
Present value 2,775.10 Future value 3,121.60
↑
↑
↑
↑
↑
FIGURE 2-3 Illustration for Chapter Summary
(i 4%, Annual Compounding)
Time Value of Money 89
