- SPREADSHEET SOLUTION
For the annuity due, use the FV function just as for the ordinary annuity except enter
1 for Type to indicate that we now have an annuity due. Then, when you click OK, the
answer $331.01 will appear.
What is the difference between an ordinary annuity and an annuity due?
How do you modify the equation for determining the value of an ordinary annu-
ity to find the value of an annuity due?
Other things held constant, which annuity has the greater futurevalue: an ordi-
nary annuity or an annuity due? Why?
Present Value of an Annuity
Suppose you were offered the following alternatives: (1) a three-year annuity with
payments of $100 or (2) a lump sum payment today. You have no need for the money
during the next three years, so if you accept the annuity, you would deposit the pay-
ments in a bank account that pays 5 percent interest per year. Similarly, the lump sum
payment would be deposited into a bank account. How large must the lump sum pay-
ment today be to make it equivalent to the annuity?
Ordinary Annuities
If the payments come at the end of each year, then the annuity is an ordinary annuity,
and it would be set up as follows:
Time Line:
05%1 2 3
100 100 100
95.24
90.70
86.38
PVA 3 272.32
The regular time line is shown at the top of the diagram, and the numerical solution
values are shown in the left column. The PV of the annuity, PVAn,is $272.32.
Equation:
The general equation used to find the PV of an ordinary annuity is shown below:
(2-5)
PMT(PVIFAi,n).
PMT°
1
1
(1i)n
i
¢
PMT a
n
t 1
a
1
1 i
b
t
PVAnPMTa
1
1 i
b
1
PMTa
1
1 i
b
2
PMTa
1
1 i
b
n
74 CHAPTER 2 Time Value of Money
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72 Time Value of Money
