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ANotes on Compound Interest and Interest Tables
A p p e n d i x
Interest is the cost of using money. It is the rental charge for funds, just as renting abuilding and equipment entails a rental charge. When the funds are used for a periodof time, it is necessary to recognize interest as a cost of using the borrowed(“rented”) funds. This requirement applies even if the funds represent ownershipcapital and if interest does not entail an outlay of cash. Why must interest be consid-ered? Because the selection of one alternative automatically commits a given amountof funds that could otherwise be invested in some other alternative.
Interest is generally important, even when short-term projects are under con-sideration. Interest looms correspondingly larger when long-run plans are studied.The rate of interest has significant enough impact to influence decisions regardingborrowing and investing funds. For example, $100,000 invested now and com-pounded annually for 10 years at 8% will accumulate to $215,900; at 20%, the$100,000 will accumulate to $619,200.
Many computer programs and pocket calculators are available that handle computa-tions involving the time value of money. You may also turn to the following fourbasic tables to compute interest.
Table 1—Future Amount of $1Table 1 shows how much $1 invested now will accumulate in a given number of peri-ods at a given compounded interest rate per period. Consider investing $1,000 nowfor three years at 8% compound interest. A tabular presentation of how this $1,000would accumulate to $1,259.70 follows:
Cumulative InterestCalled Compound Total at End of
Year Interest per Year Interest Year
0 $ — $ — $1,000.001 80.00 80.00 1,080.002 86.40 166.40 1,166.403 93.30 259.70 1,259.70
interest tables
Horngren APP A.QXD 07/06/06 17:57 Page A-1
This tabular presentation is a series of computations that could appear as follows:
S1 = $1,000(1.08)1
S2 = $1,000(1.08)2
S3 = $1,000(1.08)3
The formula for the “amount of 1,” often called the “future value of $1” or“future amount of $1,” can be written
S = P(1 + r)n
S = $1,000(1 + 0.08)3 = $1,259.70
S is the future value amount; P is the present value, $1,000 in this case; r is the rate ofinterest; and n is the number of time periods.
Fortunately, tables make key computations readily available. A facility in select-ing the proper table will minimize computations. Check the accuracy of the preced-ing answer using Table 1.
Table 2—Present Value of $1In the previous example, if $1,000 compounded at 8% per year will accumulate to$1,259.70 in 3 years, then $1,000 must be the present value of $1,259.70 due at theend of 3 years. The formula for the present value can be derived by reversing theprocess of accumulation (finding the future amount) that we just finished.
If S = P(1 + r)n
then P =
P = = $1,000
Use Table 2 to check this calculation.When accumulating, we advance or roll forward in time. The difference
between our original amount and our accumulated amount is called compound inter-est. When discounting, we retreat or roll back in time. The difference between thefuture amount and the present value is called compound discount. Note the followingformulas (where P = $1,000):
Compound interest = P[(1 + r)n − 1] = $259.70
Compound discount = S[1 − ] = $259.70
Table 3—Amount of Annuity of $1An (ordinary) annuity is a series of equal payments (receipts) to be paid (or received)at the end of successive periods of equal length. Assume that $1,000 is invested at theend of each of 3 years at 8%:
1(1 + r)n
$1,259.70(1.08)3
S(1 + r)n
A-2 APPENDIX A
End of Year Amount
1st payment $1,000.00 $1,080.00 $1,166.40, which is $1,000(1.08)2
2nd payment $1,000.00 1,080.00, which is $1,000(1.08)1
3rd payment 1,000.00Accumulation (future amount) $3,246.40
0 1 2 3
Horngren APP A.QXD 07/06/06 17:57 Page A-2
The preceding arithmetic may be expressed algebraically as the amount of anordinary annuity of $1,000 for 3 years = $1,000(1 + r)2 + $1,000(1 + r)1 + $1,000.
We can develop the general formula for Sn, the amount of an ordinary annuityof $1, by using the example above as a basis:
1. Sn = 1 + (1 + r)1 + (1 + r)2
2. Substitute: Sn = 1 + (1.08)1 + (1.08)2
3. Multiply (2) by (1 + r): (1.08)Sn = (1.08)1 + (1.08)2 + (1.08)3
4. Subtract (2) from (3): 1.08Sn − Sn = (1.08)3 − 1Note that all terms onthe right-hand side areremoved except (1.08)3in equation (3) and 1in equation (2).
5. Factor (4): Sn(1.08 −1) = (1.08)3 − 1
6. Divide (5) by (1.08 − 1): Sn = =
7. The general formula forthe amount of an ordinaryannuity of $1 becomes: Sn = or
This formula is the basis for Table 3. Look at Table 3 or use the formula itselfto check the calculations.
Table 4—Present Value of an Ordinary Annuity of $1Using the same example as for Table 3, we can show how the formula of Pn, the pres-ent value of an ordinary annuity, is developed.
End of Year
1st payment = $ 925.93 $1,000
2nd payment = $ 857.34 $1,000
3rd payment = $ 793.83 $1,000
Total present value $2,577.10
For the general case, the present value of an ordinary annuity of $1 may beexpressed:
1. Pn � � �
2. Substitute Pn � � �
3. Multiply by : Pn � � �
4. Subtract (3) from (2): Pn − Pn = −
5. Factor: Pn (1 − ) = [1 − ]6. or Pn( ) = [1 − ]1
(1.08)31
1.08.08
1.08
1(1.08)3
11.08
1(1.08)
1(1.08)4
11.08
11.08
1(1.08)4
1(1.08)3
1(1.08)2
11.08
11.08
1(1.08)3
1(1.08)2
11.08
1(1 � r)3
1(1 � r)2
11 � r
1,000(1.08)3
1,000(1.08)2
1,000(1.08)1
Compound interestRate
(1 + r)n − 1r
(1.08)3 − 1.08
(1.08)3 − 1)1.08 − 1
A-3APPENDIX A
0 1 2 3
Horngren APP A.QXD 07/06/06 17:57 Page A-3
7. Multiply by : Pn = [1 − ]The general formula for the present value of an annuity of $1.00 is:
Pn = [1 − ] =
Solving,
Pn = = 2.577
The formula is the basis for Table 4. Check the answer in the table. The pres-ent value tables, Tables 2 and 4, are used most frequently in capital budgeting.
The tables for annuities are not essential. With Tables 1 and 2, compoundinterest and compound discount can readily be computed. It is simply a matter ofdividing either of these by the rate to get values equivalent to those shown in Tables3 and 4.
0.20620.08
Compound discountRate
1(1 + r)n
1r
1(1.08)3
10.08
1.080.08
A-4 APPENDIX A
Horngren APP A.QXD 07/06/06 17:57 Page A-4
TABL
E1
Com
poun
d Am
ount
of $
1.00
(The
Fut
ure
Valu
e of
$1.
00).
S=
P(1
+r)n . I
n th
is ta
ble
P=
$1.0
0.
Per
iods
2%4%
6%8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
30%
32%
40%
Per
iods
11.
020
1.04
01.
060
1.08
01.
100
1.12
01.
140
1.16
01.
180
1.20
01.
220
1.24
01.
260
1.28
01.
300
1.32
01.
400
1
21.
040
1.08
21.
124
1.16
61.
210
1.25
41.
300
1.34
61.
392
1.44
01.
488
1.53
81.
588
1.63
81.
690
1.74
21.
960
2
31.
061
1,12
51.
191
1.26
01.
331
1.40
51.
482
1.56
11.
643
1.72
81.
816
1.90
72.
000
2.09
72.
197
2.30
02.
744
3
41.
082
1.17
01.
262
1.36
01.
464
1,57
41.
689
1.81
11.
939
2.07
42.
215
2.36
42.
520
2.68
42.
856
3.03
63.
842
4
51.
104
1.21
71.
338
1.46
91.
611
1.76
21.
925
2.10
02.
288
2.48
82.
703
2.93
23.
176
3.43
63.
713
4,00
75.
378
5
61.
126
1.26
51.
419
1.58
71.
772
1.97
4 2.
195
2.43
62.
700
2.98
63.
297
3.63
54.
002
4.39
84.
827
5.29
07.
530
6
71.
149
1.31
61.
504
1.71
41.
949
2.21
12.
502
2.82
63.
185
3.58
34.
023
4.50
85.
042
5.62
96.
275
6.98
310
.541
7
81.
172
1.36
91.
594
1.85
12.
144
2.47
62.
853
3.27
83.
759
4.30
04.
908
5.59
06.
353
7.20
68.
157
9.21
714
.758
8
91.
195
1.42
31.
689
1.99
92.
358
2.77
33.
252
3.80
34.
435
5.16
05.
987
6.93
18.
005
9.22
310
.604
12.1
6620
.661
9
101.
219
1.48
01.
791
2.15
92.
594
3.10
63.
707
4.41
15.
234
6.19
27.
305
8.59
410
.086
11.8
0613
.786
16.0
6028
.925
10
111.
243
1.53
91.
898
2.33
22.
853
3.47
94.
226
5.11
76.
176
7.43
08.
912
10.6
5712
.708
15.1
1217
.922
21.1
9940
.496
11
121.
268
1,60
12.
012
2.51
83.
138
3.89
64.
818
5.93
6 7.
288
8.91
610
.872
13.2
1516
.012
19.3
4323
.298
27.9
8356
.694
12
131.
294
1.66
52.
133
2.72
03.
452
4.36
35.
492
6.88
68.
599
10.6
9913
.264
16.3
8620
.175
24.7
5930
.288
36.9
3779
.371
13
141.
319
1,73
22.
261
2.93
73.
797
4.88
76.
261
7.98
810
.147
12.8
3916
.182
20.3
1925
.421
31.6
9139
.374
48.7
5711
1.12
014
151.
346
1.80
12.
397
3.17
24.
177
5.47
47.
138
9.26
611
.974
15.4
0719
.742
25.1
9632
.030
40.5
6551
.186
64.3
5915
5.56
815
161.
373
1.87
32.
540
3.42
64.
595
6.13
08.
137
10.7
4814
.129
18.4
8824
.086
31.2
4340
.358
51.9
2366
.542
84.9
5421
7.79
516
171.
400
1.94
82.
693
3.70
05.
054
6.86
69.
276
12.4
6816
.672
22.1
8629
.384
38.7
4150
.851
66.4
6186
.504
112.
139
304.
913
17
181.
428
2.02
62.
854
3.99
65.
560
7.69
010
.575
14.4
6319
.673
26.6
2335
.849
48.0
3964
.072
85.0
7111
2.45
514
8.02
442
6.87
918
191.
457
2.10
73.
026
4.31
66.
116
8.61
312
.056
16.7
7723
.214
31.9
4843
.736
59.5
6880
.731
108.
890
146.
192
195.
391
597.
630
19
201.
486
2.19
13.
207
4.66
16.
727
9.64
613
.743
19.4
6127
.393
38.3
3853
.358
73.8
6410
1.72
113
9.38
019
0.05
025
7.91
683
6.68
320
211.
516
2.27
93.
400
5.03
47.
400
10.8
0415
.668
22.5
7432
.324
46.0
0565
.096
91.5
9212
8.16
917
8.40
624
7.06
534
0.44
911
71.3
5621
221.
546
2.37
03.
604
5.43
78.
140
12.1
0017
.861
26.1
8638
.142
55.2
0679
.418
113.
574
161.
492
228.
360
321.
184
449.
393
1639
.898
22
231.
577
2.46
53.
820
5.87
18.
954
13.5
5220
.362
30.3
7645
.008
66.2
4796
.889
140.
831
203.
480
292.
300
417.
539
593.
199
2295
.857
23
241.
608
2.56
34.
049
6.34
19.
850
15.1
7923
.212
35.2
3653
.109
79.4
9711
8.20
517
4.63
125
6.38
537
4.14
454
2.80
178
3.02
332
14.2
0024
251.
641
2.66
64.
292
6.84
810
.835
17.0
0026
.462
40.8
7462
.669
95.3
9614
4.21
021
6.54
232
3.04
547
8.90
570
5.64
110
33.5
9044
99.8
8025
261.
673
2.77
24.
549
7.39
611
.918
19.0
4030
.167
47.4
14
73.9
4911
4.47
517
5.93
626
8.51
240
7.03
761
2.99
891
7.33
313
64.3
3962
99.8
3126
271.
707
2.88
34.
822
7.98
813
.110
21.3
2534
.390
55.0
0087
.260
137.
371
214.
642
332.
955
512.
867
784.
638
1192
.533
1800
.927
8819
.764
27
281.
741
2.99
95.
112
8.62
714
.421
23.8
8439
.204
63.8
0010
2.96
716
4.84
526
1.86
441
2.86
464
6.21
210
04.3
3615
50.2
9323
77.2
2412
347.
670
28
291.
776
3.11
95.
418
9.31
715
.863
26.7
5044
.693
74.0
0912
1.50
119
7.81
431
9.47
451
1.95
281
4.22
812
85.5
5020
15.3
8131
37.9
3517
286.
737
29
301.
811
3.24
35.
743
10.0
6317
.449
29.9
6050
.950
85.8
5014
3.37
123
7.37
638
9.75
863
4.82
010
25.9
2716
45.5
0526
19.9
9641
42.0
7524
201.
432
30
352.
000
3.94
67.
686
14.7
8528
.102
52.8
0098
.100
180.
314
327.
997
590.
668
1053
.402
1861
.054
3258
.135
5653
.911
9727
.860
1659
9.21
713
0161
.112
35
402.
208
4.80
110
.286
21.7
2545
.259
93.0
5118
8.88
437
8.72
175
0.37
814
69.7
7228
47.0
3854
55.9
1310
347.
175
1942
6.68
936
118.
865
6652
0.76
770
0037
.697
40
Horngren APP A.QXD 07/06/06 17:57 Page A-5
TABL
E2
(Pla
ce a
clip
on
this
pag
e fo
r eas
y re
fere
nce.
)Pr
esen
t Val
ue o
f $1.
00.
P=
.In
this
tabl
e S
= $1
.00.
S(1
+r)
n
Per
iods
2%4%
6%8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
30%
32%
40%
Per
iods
10.
980
0.96
20.
943
0.92
60.
909
0.89
30.
877
0.86
20.
847
0.83
30.
820
0.80
60.
794
0.78
10.
769
0.75
80.
714
12
0.96
10.
925
0.89
00.
857
0.82
60.
797
0.76
90.
743
0.71
80.
694
0.67
20.
650
0.63
00.
610
0.59
20.
574
0.51
02
30.
942
0.88
90.
840
0.79
40.
751
0.71
20.
675
0.64
10.
609
0.57
90.
551
0.52
40.
500
0.47
70.
455
0.43
50.
364
34
0.92
40.
855
0.79
20.
735
0.68
30.
636
0.59
20.
552
0.51
60.
482
0.45
10.
423
0.39
70.
373
0.35
00.
329
0.26
04
50.
906
0.82
20.
747
0.68
10.
621
0.56
70.
519
0.47
60.
437
0.40
20.
370
0.34
10.
315
0.29
10.
269
0.25
00.
186
56
0.88
80.
790
0.70
50.
630
0.56
40.
507
0.45
60.
410
0.37
00.
335
0.30
30.
275
0.25
00.
227
0.20
70.
189
0.13
36
70.
871
0.76
00.
665
0.58
30.
513
0.45
20.
400
0.35
40.
314
0.27
90.
249
0.22
20.
198
0.17
80.
159
0.14
30.
095
78
0.85
30.
731
0.62
70.
540
0.46
70.
404
0.35
10.
305
0.26
60.
233
0.20
40.
179
0.15
70.
139
0.12
30.
108
0.06
88
90.
837
0.70
30.
592
0.50
00.
424
0.36
10.
308
0.26
30.
225
0.19
40.
167
0.14
40.
125
0.10
80.
094
0.08
20.
048
910
0.82
00.
676
0.55
80.
463
0.38
60.
322
0.27
00.
227
0.19
10.
162
0.13
70.
116
0.09
90.
085
0.07
30.
062
0.03
510
110.
804
0.65
00.
527
0.42
90.
350
0.28
70.
237
0.19
50.
162
0.13
50.
112
0.09
40.
079
0.06
60.
056
0.04
70.
025
1112
0.78
80.
625
0.49
70.
397
0.31
90.
257
0.20
80.
168
0.13
70.
112
0.09
20.
076
0.06
20.
052
0.04
30.
036
0.01
812
130.
773
0.60
10.
469
0.36
80.
290
0.22
90.
182
0.14
50.
116
0.09
30.
075
0.06
10.
050
0.04
00.
033
0.02
70.
013
1314
0.75
80.
577
0.44
20.
340
0.26
30.
205
0.16
00.
125
0.09
90.
078
0.06
20.
049
0.03
90.
032
0.02
50.
021
0.00
914
150.
743
0.55
50.
417
0.31
50.
239
0.18
30.
140
0.10
80.
084
0.06
50.
051
0.04
00.
031
0.02
50.
020
0.01
60.
006
1516
0.72
80.
534
0.39
40.
292
0.21
80.
163
0.12
30.
093
0.07
10.
054
0.04
20.
032
0.02
50.
019
0.01
50.
012
0.00
516
170
714
0.51
30.
371
0.27
00.
198
0.14
60.
108
0.08
00.
060
0.04
50.
034
0.02
60.
020
0.01
50.
012
0.00
90.
003
1718
0.70
00.
494
0.35
00.
250
0.18
00.
130
0.09
50.
069
0.05
10.
038
0.02
80.
021
0.01
60.
012
0.00
90.
007
0.00
218
190.
686
0.47
50.
331
0.23
20.
164
0.11
60.
083
0.06
00.
043
0.03
10.
023
0.01
70.
012
0.00
90.
007
0.00
50.
002
1920
0.67
30.
456
0.31
20.
215
0.14
90.
104
0.07
30.
051
0.03
70.
026
0.01
90.
014
0.01
00.
007
0.00
50.
004
0.00
120
210.
660
0.43
90.
294
0.19
90.
135
0.09
30.
064
0.04
40.
031
0.02
20.
015
0.01
10.
008
0.00
60.
004
0.00
30.
001
2122
0.64
70.
422
0.27
80.
184
0.12
30.
083
0.05
60.
038
0.02
60.
018
0.01
30.
009
0.00
60.
004
0.00
30.
002
0.00
122
230.
634
0.40
60.
262
0.17
00.
112
0.07
40.
049
0.03
30.
022
0.01
50.
010
0.00
70.
005
0.00
30.
002
0.00
20.
000
2324
0.62
20.
390
0.24
70.
158
0.10
20.
066
0.04
30.
028
0.01
90.
013
0.00
80.
006
0.00
40.
003
0.00
20.
001
0.00
024
250.
610
0.37
50.
233
0.14
60.
092
0.05
90.
038
0.02
40.
016
0.01
00.
007
0.00
50.
003
0.00
20.
001
0.00
10.
000
2526
0.59
80.
361
0.22
00.
135
0.08
40.
053
0.03
30.
021
0.01
40.
009
0.00
60.
004
0.00
20.
002
0.00
10.
001
0.00
026
270.
586
0.34
70.
207
0.12
50.
076
0.04
70.
029
0.01
80.
011
0.00
70.
005
0.00
30.
002
0.00
10.
001
0.00
10.
000
2728
0.57
40.
333
0.19
60.
116
0.06
90.
042
0.02
60.
016
0.01
00.
006
0.00
40.
002
0.00
20.
001
0.00
10.
000
0.00
0 28
290.
563
0.32
10.
185
0.10
70.
063
0.03
70.
022
0.01
40.
008
0.00
50.
003
0.00
20.
001
0.00
10.
000
0.00
00.
000
2930
0.55
20.
308
0.17
40.
099
0.05
70.
033
0.02
00.
012
0.00
70.
004
0.00
30.
002
0.00
10.
001
0.00
00.
000
0.00
030
350.
500
0.25
30.
130
0.06
80.
036
0.01
90.
010
0.00
60.
003
0.00
20.
001
0.00
10.
000
0.00
00.
000
0.00
00.
000
3540
0.45
30.
208
0.09
70.
046
0.02
20.
011
0.00
50.
003
0.00
10.
001
0.00
00.
000
0.00
00.
000
0.00
00.
000
0.00
040
Horngren APP A.QXD 07/06/06 17:57 Page A-6
TABL
E3
Com
poun
d Am
ount
of A
nnui
ty o
f $1.
00 in
Arr
ears
* (F
utur
e Va
lue
of A
nnui
ty).
S n=
(1 +
r)n
− 1
r
Per
iods
2%4%
6%8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
30%
32%
40%
Per
iods
11.
000
1.00
01.
000
1.00
01.
000
1.00
01.
000
1.00
01.
000
1.00
01.
000
1.00
01.
000
1.00
01.
000
1.00
01.
000
1
22.
020
2.04
02.
060
2.08
02.
100
2.12
02.
140
2.16
02.
180
2.20
02.
220
2.24
02.
260
2.28
02.
300
2.32
02.
400
2
33.
060
3.12
23.
184
3.24
63.
310
3.37
43.
440
3.50
63.
572
3.64
03.
708
3.77
83.
848
3.91
83.
990
4.06
24.
360
3
44.
122
4.24
64.
375
4.50
64.
641
4.77
94.
921
5.06
65.
215
5.36
85.
524
5.68
45.
848
6.01
66.
187
6.36
27.
104
4
55.
204
5.41
65.
637
5.86
76.
105
6.35
36.
610
6.87
77.
154
7.44
27.
740
8.04
88.
368
8.70
09.
043
9.39
810
.946
5
66.
308
6.63
36.
975
7.33
67.
716
8.11
58.
536
8.97
79.
442
9.93
010
.442
10.9
8011
.544
12.1
3612
.756
13.4
0616
.324
6
77.
434
7.89
88.
394
8.92
39.
487
10.0
8910
.730
11.4
1412
.142
12.9
1613
.740
14.6
1515
.546
16.5
3417
.583
18.6
9623
.853
7
88.
583
9.21
49.
897
10.6
3711
.436
12.3
0013
.233
14.2
4015
.327
16.4
9917
.762
19.1
2320
.588
22.1
6323
.858
25.6
7834
.395
8
99.
755
10.5
8311
.491
12.4
8813
.579
14.7
7616
.085
17.5
1919
.086
20.7
9922
.670
24.7
1226
.940
29.3
6932
.015
34.8
9549
.153
9
1010
.950
12.0
0613
.181
14.4
8715
.937
17.5
4919
.337
21.3
2123
.521
25.9
5928
.657
31.6
4334
.945
33.5
9342
.619
47.0
6269
.814
10
ll12
.169
13.4
8614
.972
16.6
4518
.531
20.6
5523
.045
25.7
3328
.755
32.1
5035
.962
40.2
3845
.031
50.3
9856
.405
63.1
2298
.739
11
1213
.412
15.0
2616
.870
18.9
7721
.384
24.1
3327
.271
30.8
5034
.931
39.5
8144
.874
50.8
9557
.739
65.5
1074
.327
84.3
2013
9.23
512
1314
.680
16.6
2718
.882
21.4
9524
.523
28.0
2932
.089
36.7
8642
.219
48.4
9755
.746
64.1
1073
.751
84.8
5397
.625
112.
303
195.
929
13
1415
.974
18.2
9221
.015
24 2
1527
.975
32.3
9337
.581
43.6
7250
.818
59.1
9669
.010
80.4
9693
.926
109.
612
127.
913
149.
240
275.
300
14
1517
.293
20.0
2423
.276
27.1
5231
.772
37.2
8043
.842
51.6
6060
.965
72.0
3585
.192
100.
815
119.
347
141.
303
167.
286
197.
997
386.
420
15
1618
.639
21.8
2525
.673
30.3
2435
.950
42.7
5350
.980
60.9
2572
.939
87.4
4210
4.93
512
6.01
115
1.37
718
1.86
821
8.47
226
2.35
654
1.98
816
1720
.012
23.6
9828
.213
33.7
5040
.545
48.8
8459
.118
71.6
7387
.068
105.
931
129.
020
157.
253
191.
735
233.
791
285.
014
347.
309
759.
784
17
1821
.412
25.6
4530
.906
37.4
5045
.599
55.7
5068
.394
84.1
4110
3.74
012
8.11
715
8.40
519
5.99
424
2.58
530
0.25
237
1.51
845
9.44
910
64.6
9718
1922
.841
27.6
7133
.760
41.4
4651
.159
63.4
4078
.969
98.6
0312
3.41
415
4.74
019
4.25
424
4.03
330
6.65
838
5.32
348
3.97
360
7.47
214
91.5
7619
2024
.297
29.7
7836
.786
45.7
6257
.275
72.0
5291
.025
115.
380
146.
628
186.
688
237.
989
303.
601
387.
389
494.
213
630.
165
802.
863
2089
.206
20
2125
.783
31.9
6939
.993
50.4
2364
.002
81.6
9910
4.76
813
4.84
117
4.02
122
5.02
629
1.34
737
7.46
548
9.11
063
3.59
382
0.21
510
60.7
7929
25.8
8921
2227
.299
34.2
4843
.392
55.4
5771
.403
92.5
0312
0.43
615
7.41
520
6.34
527
1.03
135
6.44
346
9.05
661
7.27
881
1.99
910
67.2
8014
01.2
2940
97.2
4522
2328
.845
36.6
1846
.996
60.8
9379
.543
104.
603
138.
297
183.
601
244.
487
326.
237
435.
861
582.
630
778.
771
1040
.358
1388
.464
1850
.622
5737
.142
23
2430
.422
39.0
8350
.816
66.7
6588
.497
118.
155
158.
659
213.
978
289.
494
392.
484
532.
750
723.
461
982.
251
1332
.659
1806
.003
2443
.821
8032
.999
24
2532
.030
41.6
4654
.865
73.1
0698
.347
133.
334
181.
871
249.
214
342.
603
471.
981
650.
955
898.
092
1238
.636
1706
.803
2348
.803
3226
.844
1124
7.19
925
2633
.671
44.3
1259
.156
79.9
5410
9.18
215
0.33
420
8.33
329
0.08
840
5.27
256
7.37
779
5.16
511
14.6
3415
61.6
8221
85.7
0830
54.4
4442
60.4
3415
747.
079
26
2735
.344
47.0
8463
.706
87.3
5112
1.10
016
9.37
423
8.49
933
7.50
247
9.22
168
1.85
397
1.10
213
83.1
4619
68.7
1927
98.7
0639
71.7
7856
24.7
7222
046.
910
27
2837
.051
49.9
6868
.528
95.3
3913
4.21
019
0.69
927
2.88
939
2.50
358
6.48
181
9.22
311
85.7
4417
16.1
0124
81.5
8635
83.3
4451
64.3
1174
25.6
9930
366.
674
28
2938
.792
52.9
6673
.640
103.
966
148.
631
214.
583
312.
094
456.
303
669.
447
984.
068
1447
.608
2128
.965
3127
.798
4587
.680
6714
.604
9802
.923
4321
4.34
329
3040
.568
56.0
8579
.058
113.
263
164.
494
241.
333
356.
787
530.
312
790.
948
1181
.882
1767
.081
2640
.916
3942
.026
5873
.231
8729
.985
1294
0.85
960
501.
081
30
3549
.994
73.6
5211
1.43
517
2.31
727
1.02
443
1.66
369
3.57
311
20.7
1318
16.6
5229
48.3
4147
83.6
4577
50.2
2512
527.
442
2018
8.96
632
422.
868
5186
9.42
732
5400
.279
35
4060
.402
95.0
2615
4.76
225
9.05
744
2.59
376
7.09
113
42.0
2523
60.7
5741
63.2
1373
43.8
5812
936.
535
2272
8.80
339
792.
982
6937
7.46
012
0392
.883
2078
74.2
7217
5009
1.74
140
*Pay
men
ts (o
r re
ceip
ts) a
t the
end
of e
ach
peri
od.
Horngren APP A.QXD 07/06/06 17:57 Page A-7
TABL
E4
(Pla
ce a
clip
on
this
pag
e fo
r eas
y re
fere
nce.
)Pr
esen
t Val
ue o
f Ann
uity
$1.
00 in
Arr
ears
.*
P n=
[1 −
]1
(1 +
r)n
1 r
Per
iods
2%4%
6%8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
30%
32%
40%
Per
iods
10.
980
0.96
20.
943
0.92
60.
909
0.89
30.
877
0.86
20.
847
0.83
30.
820
0.80
60.
794
0.78
10.
769
0.75
80.
714
12
1.94
21.
886
1.83
31.
783
1.73
61.
690
1.64
71.
605
1.56
61.
528
1.49
21.
457
1.42
41.
392
1.36
11.
331
1.22
42
32.
884
2.77
52.
673
2.57
72.
487
2.40
22.
322
2.24
62.
174
2.10
62.
042
1.98
11.
923
1.86
81.
816
1.76
61.
589
34
3.80
83.
630
3.46
53.
312
3.17
03.
037
2.91
42.
798
2.69
02.
589
2.49
42.
404
2.32
02.
241
2.16
62.
096
1.84
94
54.
713
4.45
24.
212
3.99
33.
791
3.60
53.
433
3.27
43.
127
2.99
12.
864
2.74
52.
635
2.53
22.
436
2.34
52.
035
56
5.60
15.
242
4.91
74.
623
4.35
54.
111
3.88
93.
685
3.49
83.
326
3.16
73.
020
2.88
52.
759
2.64
32.
534
2.16
86
76.
472
6.00
25.
582
5.20
64.
868
4.56
44.
288
4.03
93.
812
3.60
53.
416
3.24
23.
083
2.93
72.
802
2.67
72.
263
78
7.32
56.
733
6.21
05.
747
5.33
54.
968
4.63
94.
344
4.07
83.
837
3.61
93.
421
3.24
13.
076
2.92
52.
786
2.33
18
98.
162
7.43
56.
802
6.24
75.
759
5.32
84.
946
4.60
74.
303
4.03
13.
786
3.56
63.
366
3.18
43.
019
2.86
82.
379
910
8.98
38.
111
7.36
06.
710
6.14
55.
650
5.21
64.
833
4.49
44.
192
3.92
33.
682
3.46
53.
269
3.09
22.
930
2.41
410
119.
787
8.76
07.
887
7.13
96.
495
5.93
85.
453
5.02
94.
656
4.32
74.
035
3.77
63.
543
3.33
53.
147
2.97
82.
438
1112
10.5
759.
385
8.38
47.
536
6.81
46.
194
5.66
05.
197
4.79
34.
439
4.12
73.
851
3.60
63.
387
3.19
03.
013
2.45
612
1311
,348
9.98
68.
853
7.90
47.
103
6.42
45.
842
5.34
24.
910
4.53
34.
203
3.91
23.
656
3.42
73.
223
3.04
02.
469
1314
12.1
0610
.563
9.29
58.
244
7.36
76.
628
6.00
25.
468
5.00
84.
611
4.26
53.
962
3.69
53.
459
3.24
93.
061
2.47
814
1512
.849
11.1
189.
712
8.55
97.
606
6.81
16.
142
5.57
55.
092
4.67
54.
315
4.00
13.
726
3.48
33.
268
3.07
62.
484
1516
13.5
7811
.652
10.1
068.
851
7.82
46.
974
6.26
55.
668
5.16
24.
730
4.35
74.
033
3.75
13.
503
3.28
33.
088
2.48
916
1714
.292
12.1
6610
.477
9.12
28.
022
7.12
06.
373
5.74
95.
222
4.77
54.
391
4.05
93.
771
3.51
83.
295
3.09
72.
492
1718
14.9
9212
.659
10.8
289.
372
8.20
17.
250
6.46
75.
818
5.27
34.
812
4.41
94.
080
3.78
63.
529
3.30
43.
104
2.49
418
1915
.678
13.1
3411
.158
9.60
48.
365
7.36
66.
550
5.87
75.
316
4.84
34.
442
4.09
73.
799
3.53
93.
311
3.10
92.
496
1920
16.3
5113
.590
11.4
709.
818
8.51
47.
469
6.62
35.
929
5.35
34.
870
4.46
04.
110
3.80
83.
546
3.31
63.
113
2.49
720
2117
.011
14.0
2911
.764
10.0
178.
649
7.56
26.
687
5.97
35.
384
4.89
14.
476
4.12
13.
816
3.55
13.
320
3.11
62.
498
2122
17.6
5814
.451
12.0
4210
.201
8.77
27.
645
6.74
36.
011
5.41
04.
909
4.48
84.
130
3.82
23.
556
3.32
33.
118
2.49
822
2318
.292
14.8
5712
.303
10.3
718.
883
7.71
86.
792
6.04
45.
432
4.92
54.
499
4.13
73.
827
3.55
93.
325
3.12
02.
499
2324
18.9
1415
.247
12.5
5010
.529
8.98
57.
784
6.83
56.
073
5.45
14.
937
4.50
74.
143
3.83
13.
562
3.32
73.
121
2.49
924
2519
.523
15.6
2212
.783
10.6
759.
077
7.84
36.
873
6.09
75.
467
4.94
84.
514
4.14
73.
834
3.56
43.
329
3.12
22.
499
2526
20.1
2115
.983
13.0
0310
.810
9.16
17.
896
6.90
66.
118
5.48
04.
956
4.52
04.
151
3.83
73.
566
3.33
03.
123
2.50
026
2720
.707
16.3
3013
.211
10.9
359.
237
7.94
36.
935
6.13
65.
492
4.96
44.
524
4.15
43.
839
3.56
73.
331
3.12
32.
500
2728
21.2
8116
.663
13.4
0611
.051
9.30
77.
984
6.96
16.
152
5.50
24.
970
4.52
84.
157
3.84
03.
568
3.33
13.
124
2.50
028
2921
.844
16.9
8413
.591
11.1
589.
370
8.02
26.
983
6.16
65.
510
4.97
54.
531
4.15
93.
841
3.56
93.
332
3.12
42.
500
2930
22.3
9617
.292
13.7
6511
.258
9.42
78.
055
7.00
36.
177
5.51
74.
979
4.53
44.
160
3.84
23.
569
3.33
23.
124
2.50
030
3524
.999
18.6
6514
.498
11.6
559.
644
8.17
67.
070
6.21
55.
539
4.99
24.
541
4.16
43.
845
3.57
13.
333
3.12
52.
500
3540
27.3
5519
.793
15.0
4611
.925
9.77
98.
244
7.10
56.
233
5.54
84.
997
4.54
44.
166
3.84
63.
571
3.33
33.
125
2.50
040
*Pay
men
ts (o
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ts) a
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end
of e
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peri
od.
Horngren APP A.QXD 07/06/06 17:57 Page A-8
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