Introduction to Finance

TA B L E 9 . 4
Present Value Interest Factor (PVIFA) for a $1 Ordinary Annuity
Year
5%
6%
7%
8%
9%
10%
1
0.952
0.943
0.935
0.926
0.917
0.909
2
1.859
1.833
1.808
1.783
1.759
1.736
3
2.273
2.673
2.624
2.577
2.531
2.487
4
3.546
3.465
3.387
3.312
3.240
3.170
5
4.329
4.212
4.100
3.993
3.890
3.791
6
5.076
4.917
4.767
4.623
4.486
4.355
7
5.786
5.582
5.389
5.206
5.033
4.868
8
6.463
6.210
5.971
5.747
5.535
5.335
9
7.108
6.802
6.515
6.247
5.995
5.759
10
7.722
7.360
7.024
6.710
6.418
6.145

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238
C H A PT E R 9 Time Value of Money
Table-based Solution:
The answer can be found by setting up the problem using equation 9.6 and Table 9.3 as follows:
FVA
5
= PMT(FVIFA
r
,5
)
$5,751 = $1,000(FVIFA
r
,5
)
FVIFA
r
,5
= 5.751
Since we know that the number of time periods is fi ve, we can turn to Table 9.3 and read 
across the year-fi ve row until we fi nd the FVIFA of 5.751. Notice that this occurs under the 
7 percent column, indicating that the interest rate, 
r
, is 7 percent.
Let’s now assume that we know that the present value of the preceding ordinary annuity 
is $4,100. We could then fi nd the interest rate for the problem using present value annuity 
tables as follows:
PVA
5
= PMT(PVIFA
r
,5
)
$4,100 = $1,000(PVIFA
r
,5
)
PVIFA
r
,5
= 4.100
Turning to Table 9.4, we read across the year-fi ve row until we fi nd the PVIFA of 4.100. 
This occurs under the 7 percent column, indicating that the interest rate, 
r
, is 7 percent.
Solving for Time Periods
Let’s assume that the future value of an ordinary annuity is $5,751, the annual payment is 
$1,000, and the interest rate is 7 percent. How long would it take for your $1,000 annual 
investments to grow to $5,751? 
We can solve this problem using a fi nancial calculator. We know that the future value 
of the ordinary annuity is $5,751, so enter FV = 5751, PMT = –1000, %i = 7, and press 
the CPT key followed by the N key to fi nd an n of fi ve years. If we knew the present value 
of the annuity instead of the future value, we could work the problem by substituting the 
PV for the FV.