Business Math: Annuities Homework

Section I • Future Value of an Annuity: Ordinary and Annuity Due
 Ta b l e 1 2 – 1
383
Future Value (Amount) of an Ordinary Annuity of
1
%
2
1%
112%
2%
3%
4%
5%
6%
7%
8%
Periods
1
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1
2
2.00500
2.01000
2.01500
2.02000
2.03000
2.04000
2.05000
2.06000
2.07000
2.08000
2
3
3.01502
3.03010
3.04522
3.06040
3.09090
3.12160
3.15250
3.18360
3.21490
3.24640
3
4
4.03010
4.06040
4.09090
4.12161
4.18363
4.24646
4.31013
4.37462
4.43994
4.50611
4
5
5.05025
5.10101
5.15227
5.20404
5.30914
5.41632
5.52563
5.63709
5.75074
5.86660
5
6
6.07550
6.15202
6.22955
6.30812
6.46841
6.63298
6.80191
6.97532
7.15329
7.33593
6
7
7.10588
7.21354
7.32299
7.43428
7.66246
7.89829
8.14201
8.39384
8.65402
8.92280
7
8
8.14141
8.28567
8.43284
8.58297
8.89234
9.21423
9.54911
9.89747
10.25980
10.63663
8
9.36853
9.55933
9
9.18212
9.75463 10.15911 10.58280 11.02656 11.49132
11.97799
12.48756
9
10
10.22803 10.46221 10.70272 10.94972 11.46388 12.00611 12.57789 13.18079
13.81645
14.48656
10
11
11.27917 11.56683 11.86326 12.16872 12.80780 13.48635 14.20679 14.97164
15.78360
16.64549
11
12
12.33556 12.68250 13.04121 13.41209 14.19203 15.02581 15.91713 16.86994
17.88845
18.97713
12
13
13.39724 13.80933 14.23683 14.68033 15.61779 16.62684 17.71298 18.88214
20.14064
21.49530
13
14
14.46423 14.94742 15.45038 15.97394 17.08632 18.29191 19.59863 21.01507
22.55049
24.21492
14
15
15.53655 16.09690 16.68214 17.29342 18.59891 20.02359 21.57856 23.27597
25.12902
27.15211
15
16
16.61423 17.25786 17.93237 18.63929 20.15688 21.82453 23.65749 25.67253
27.88805
30.32428
16
17
17.69730 18.43044 19.20136 20.01207 21.76159 23.69751 25.84037 28.21288
30.84022
33.75023
17
18
18.78579 19.61475 20.48938 21.41231 23.41444 25.64541 28.13238 30.90565
33.99903
37.45024
18
19
19.87972 20.81090 21.79672 22.84056 25.11687 27.67123 30.53900 33.75999
37.37896
41.44626
19
20
20.97912 22.01900 23.12367 24.29737 26.87037 29.77808 33.06595 36.78559
40.99549
45.76196
20
21
22.08401 23.23919 24.47052 25.78332 28.67649 31.96920 35.71925 39.99273
44.86518
50.42292
21
22
23.19443 24.47159 25.83758 27.29898 30.53678 34.24797 38.50521 43.39229
49.00574
55.45676
22
23
24.31040 25.71630 27.22514 28.84496 32.45288 36.61789 41.43048 46.99583
53.43614
60.89330
23
24
25.43196 26.97346 28.63352 30.42186 34.42647 39.08260 44.50200 50.81558
58.17667
66.76476
24
25
26.55912 28.24320 30.06302 32.03030 36.45926 41.64591 47.72710 54.86451
63.24904
73.10594
25
26
27.69191 29.52563 31.51397 33.67091 38.55304 44.31174 51.11345 59.15638
68.67647
79.95442
26
27
28.83037 30.82089 32.98668 35.34432 40.70963 47.08421 54.66913 63.70577
74.48382
87.35077
27
28
29.97452 32.12910 34.48148 37.05121 42.93092 49.96758 58.40258 68.52811
80.69769
95.33883
28
29
31.12439 33.45039 35.99870 38.79223 45.21885 52.96629 62.32271 73.63980
87.34653
103.96594
29
30
32.28002 34.78489 37.53868 40.56808 47.57542 56.08494 66.43885 79.05819
94.46079
113.28321
30
31
33.44142 36.13274 39.10176 42.37944 50.00268 59.32834 70.76079 84.80168 102.07304 123.34587
31
32
34.60862 37.49407 40.68829 44.22703 52.50276 62.70147 75.29883 90.88978 110.21815 134.21354
32
33
35.78167 38.86901 42.29861 46.11157 55.07784 66.20953 80.06377 97.34316 118.93343 145.95062
33
34
36.96058 40.25770 43.93309 48.03380 57.73018 69.85791 85.06696 104.18375 128.25876 158.62667
34
35
38.14538 41.66028 45.59209 49.99448 60.46208 73.65222 90.32031 111.43478 138.23688 172.31680
35
36
39.33610 43.07688 47.27597 51.99437 63.27594 77.59831 95.83632 119.12087 148.91346 187.10215
36
The values in Table 12-1 were generated by the formula
rate per period and n is the total number of periods.
26441_ch12_hr_380-419_1.indd 383
© Cengage Learning, Inc. This content is not final and may not match the published product.
Periods
(1 + i) n − 1
and rounded to five decimal places, where i is the interest
i
10/12/18 2:52 PM
384 Chapter 12 • Annuities
© Cengage Learning, Inc. This content is not final and may not match the published product.
 Ta b l e 1 2 – 1
Future Value (Amount) of an Ordinary Annuity of $1
(Continued )
Periods
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
Periods
1
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1
2
2.09000
2.10000
2.11000
2.12000
2.13000
2.14000
2.15000
2.16000
2.17000
2.18000
2
3
3.27810
3.31000
3.34210
3.37440
3.40690
3.43960
3.47250
3.50560
3.53890
3.57240
3
4
4.57313
4.64100
4.70973
4.77933
4.84980
4.92114
4.99338
5.06650
5.14051
5.21543
4
5
5.98471
6.10510
6.22780
6.35285
6.48027
6.61010
6.74238
6.87714
7.01440
7.15421
5
6
7.52333
7.71561
7.91286
8.11519
8.32271
8.53552
8.75374
8.97748
9.20685
9.44197
6
7
9.20043
9.48717
9.78327
10.08901 10.40466 10.73049
11.06680
11.41387
11.77201
12.14152
7
8
11.02847 11.43589 11.85943 12.29969 12.75726 13.23276
13.72682
14.24009
14.77325
15.32700
8
9
9
13.02104 13.57948 14.16397 14.77566 15.41571 16.08535
16.78584
17.51851
18.28471
19.08585
10
15.19293 15.93742 16.72201 17.54874 18.41975 19.33730
20.30372
21.32147
22.39311
23.52131 10
11
17.56029 18.53117 19.56143 20.65458 21.81432 23.04452
24.34928
25.73290
27.19994
28.75514 11
12
20.14072 21.38428 22.71319 24.13313 25.65018 27.27075
29.00167
30.85017
32.82393
34.93107 12
13
22.95338 24.52271 26.21164 28.02911 29.98470 32.08865
34.35192
36.78620
39.40399
42.21866 13
14
26.01919 27.97498 30.09492 32.39260 34.88271 37.58107
40.50471
43.67199
47.10267
50.81802 14
15
29.36092 31.77248 34.40536 37.27971 40.41746 43.84241
47.58041
51.65951
56.11013
60.96527 15
16
33.00340 35.94973 39.18995 42.75328 46.67173 50.98035
55.71747
60.92503
66.64885
72.93901 16
17
36.97370 40.54470 44.50084 48.88367 53.73906 59.11760
65.07509
71.67303
78.97915
87.06804 17
18
41.30134 45.59917 50.39594 55.74971 61.72514 68.39407
75.83636
84.14072
93.40561 103.74028 18
19
46.01846 51.15909 56.93949 63.43968 70.74941 78.96923
88.21181
98.60323
110.28456 123.41353 19
20
51.16012 57.27500 64.20283 72.05244 80.94683 91.02493 102.44358 115.37975
130.03294 146.62797 20
21
56.76453 64.00250 72.26514 81.69874 92.46992 104.76842 118.81012 134.84051
153.13854 174.02100 21
22
62.87334 71.40275 81.21431 92.50258 105.49101 120.43600 137.63164 157.41499
180.17209 206.34479 22
23
69.53194 79.54302 91.14788 104.60289 120.20484 138.29704 159.27638 183.60138
211.80134 244.48685 23
24
76.78981 88.49733 102.17415 118.15524 136.83147 158.65862 184.16784 213.97761
248.80757 289.49448 24
25
84.70090 98.34706 114.41331 133.33387 155.61956 181.87083 212.79302 249.21402
292.10486 342.60349 25
26
93.32398 109.18177 127.99877 150.33393 176.85010 208.33274 245.71197 290.08827
342.76268 405.27211 26
27
102.72313 121.09994 143.07864 169.37401 200.84061 238.49933 283.56877 337.50239
402.03234 479.22109 27
28
112.96822 134.20994 159.81729 190.69889 227.94989 272.88923 327.10408 392.50277
471.37783 566.48089 28
29
124.13536 148.63093 178.39719 214.58275 258.58338 312.09373 377.16969 456.30322
552.51207 669.44745 29
30
136.30754 164.49402 199.02088 241.33268 293.19922 356.78685 434.74515 530.31173
647.43912 790.94799 30
31
149.57522 181.94342 221.91317 271.29261 332.31511 407.73701 500.95692 616.16161
758.50377 934.31863 31
32
164.03699 201.13777 247.32362 304.84772 376.51608 465.82019 577.10046 715.74746
888.44941 1103.49598 32
33
179.80032 222.25154 275.52922 342.42945 426.46317 532.03501 664.66552 831.26706 1040.48581 1303.12526 33
34
196.98234 245.47670 306.83744 384.52098 482.90338 607.51991 765.36535 965.26979 1218.36839 1538.68781 34
35
215.71075 271.02437 341.58955 431.66350 546.68082 693.57270 881.17016 1120.71295 1426.49102 1816.65161 35
36
236.12472 299.12681 380.16441 484.46312 618.74933 791.67288 1014.34568 1301.02703 1669.99450 2144.64890 36
The values in Table 12-1 were generated by the formula
rate per period and n is the total number of periods.
(1 + i) n − 1
and rounded to five decimal places, where i is the interest
i
Not For Sale
26441_ch12_hr_380-419_1.indd 384
10/12/18 2:52 PM
394
Chapter 12 • Annuities
© Cengage Learning, Inc. This content is not final and may not match the published product.
Ta b l e 1 2 – 2
Present Value (Amount) of an Ordinary Annuity of $1
Periods
1
%
2
1%
112%
2%
3%
4%
5%
6%
7%
8%
Periods
1
0.99502
0.99010
0.98522
0.98039
0.97087
0.96154
0.95238
0.94340
0.93458
0.92593
1
2
1.98510
1.97040
1.95588
1.94156
1.91347
1.88609
1.85941
1.83339
1.80802
1.78326
2
3
2.97025
2.94099
2.91220
2.88388
2.82861
2.77509
2.72325
2.67301
2.62432
2.57710
3
4
3.95050
3.90197
3.85438
3.80773
3.71710
3.62990
3.54595
3.46511
3.38721
3.31213
4
5
4.92587
4.85343
4.78264
4.71346
4.57971
4.45182
4.32948
4.21236
4.10020
3.99271
5
6
5.89638
5.79548
5.69719
5.60143
5.41719
5.24214
5.07569
4.91732
4.76654
4.62288
6
7
6.86207
6.72819
6.59821
6.47199
6.23028
6.00205
5.78637
5.58238
5.38929
5.20637
7
8
7.82296
7.65168
7.48593
7.32548
7.01969
6.73274
6.46321
6.20979
5.97130
5.74664
8
9
8.77906
8.56602
8.36052
8.16224
7.78611
7.43533
7.10782
6.80169
6.51523
6.24689
9
10
9.73041
9.47130
9.22218
8.98259
8.53020
8.11090
7.72173
7.36009
7.02358
6.71008
10
11
10.67703 10.36763 10.07112
9.78685
9.25262
8.76048
8.30641
7.88687
7.49867
7.13896
11
12
11.61893 11.25508 10.90751
10.57534
9.95400
9.38507
8.86325
8.38384
7.94269
7.53608
12
13
12.55615 12.13374 11.73153
11.34837 10.63496
9.98565
9.39357
8.85268
8.35765
7.90378
13
14
13.48871 13.00370 12.54338
12.10625 11.29607 10.56312
9.89864
9.29498
8.74547
8.24424
14
15
14.41662 13.86505 13.34323
12.84926 11.93794 11.11839 10.37966
9.71225
9.10791
8.55948
15
16
15.33993 14.71787 14.13126
13.57771 12.56110 11.65230 10.83777 10.10590
9.44665
8.85137
16
17
16.25863 15.56225 14.90765
14.29187 13.16612 12.16567 11.27407 10.47726
9.76322
9.12164
17
18
17.17277 16.39827 15.67256
14.99203 13.75351 12.65930 11.68959 10.82760 10.05909
9.37189
18
19
18.08236 17.22601 16.42617
15.67846 14.32380 13.13394 12.08532 11.15812 10.33560
9.60360
19
20
18.98742 18.04555 17.16864
16.35143 14.87747 13.59033 12.46221 11.46992 10.59401
9.81815
20
21
19.88798 18.85698 17.90014
17.01121 15.41502 14.02916 12.82115 11.76408 10.83553 10.01680
21
22
20.78406 19.66038 18.62082
17.65805 15.93692 14.45112 13.16300 12.04158 11.06124 10.20074
22
23
21.67568 20.45582 19.33086
18.29220 16.44361 14.85684 13.48857 12.30338 11.27219 10.37106
23
24
22.56287 21.24339 20.03041
18.91393 16.93554 15.24696 13.79864 12.55036 11.46933 10.52876
24
25
23.44564 22.02316 20.71961
19.52346 17.41315 15.62208 14.09394 12.78336 11.65358 10.67478
25
26
24.32402 22.79520 21.39863
20.12104 17.87684 15.98277 14.37519 13.00317 11.82578 10.80998
26
27
25.19803 23.55961 22.06762
20.70690 18.32703 16.32959 14.64303 13.21053 11.98671 10.93516
27
28
26.06769 24.31644 22.72672
21.28127 18.76411 16.66306 14.89813 13.40616 12.13711 11.05108
28
29
26.93302 25.06579 23.37608
21.84438 19.18845 16.98371 15.14107 13.59072 12.27767 11.15841
29
30
27.79405 25.80771 24.01584
22.39646 19.60044 17.29203 15.37245 13.76483 12.40904 11.25778
30
31
28.65080 26.54229 24.64615
22.93770 20.00043 17.58849 15.59281 13.92909 12.53181 11.34980
31
32
29.50328 27.26959 25.26714
23.46833 20.38877 17.87355 15.80268 14.08404 12.64656 11.43500
32
33
30.35153 27.98969 25.87895
23.98856 20.76579 18.14765 16.00255 14.23023 12.75379 11.51389
33
34
31.19555 28.70267 26.48173
24.49859 21.13184 18.41120 16.19290 14.36814 12.85401 11.58693
34
35
32.03537 29.40858 27.07559
24.99862 21.48722 18.66461 16.37419 14.49825 12.94767 11.65457
35
36
32.87102 30.10751 27.66068
25.48884 21.83225 18.90828 16.54685 14.62099 13.03521 11.71719
36
The values in Table 12-2 were generated by the formula
rate per period and n is the total number of periods.
(1 + i) n − 1
and rounded to five decimal places, where i is the interest
i(1 + i) n
Not For Sale
26441_ch12_hr_380-419_2.indd 394
10/10/18 3:50 PM
Section II • Present Value of an Annuity: Ordinary and Annuity Due
Ta b l e 1 2 – 2
9%
(Continued )
10%
11%
12%
13%
14%
15%
16%
17%
18%
Periods
1
0.91743 0.90909
0.90090
0.89286
0.88496
0.87719
0.86957
0.86207
0.85470
0.84746
1
2
1.75911 1.73554
1.71252
1.69005
1.66810
1.64666
1.62571
1.60523
1.58521
1.56564
2
3
2.53129 2.48685
2.44371
2.40183
2.36115
2.32163
2.28323
2.24589
2.20958
2.17427
3
4
3.23972 3.16987
3.10245
3.03735
2.97447
2.91371
2.85498
2.79818
2.74324
2.69006
4
5
3.88965 3.79079
3.69590
3.60478
3.51723
3.43308
3.35216
3.27429
3.19935
3.12717
5
6
4.48592 4.35526
4.23054
4.11141
3.99755
3.88867
3.78448
3.68474
3.58918
3.49760
6
7
5.03295 4.86842
4.71220
4.56376
4.42261
4.28830
4.16042
4.03857
3.92238
3.81153
7
8
5.53482 5.33493
5.14612
4.96764
4.79877
4.63886
4.48732
4.34359
4.20716
4.07757
8
9
5.99525 5.75902
5.53705
5.32825
5.13166
4.94637
4.77158
4.60654
4.45057
4.30302
9
10
6.41766 6.14457
5.88923
5.65022
5.42624
5.21612
5.01877
4.83323
4.65860
4.49409
10
11
6.80519 6.49506
6.20652
5.93770
5.68694
5.45273
5.23371
5.02864
4.83641
4.65601
11
12
7.16073 6.81369
6.49236
6.19437
5.91765
5.66029
5.42062
5.19711
4.98839
4.79322
12
13
7.48690 7.10336
6.74987
6.42355
6.12181
5.84236
5.58315
5.34233
5.11828
4.90951
13
14
7.78615 7.36669
6.98187
6.62817
6.30249
6.00207
5.72448
5.46753
5.22930
5.00806
14
15
8.06069 7.60608
7.19087
6.81086
6.46238
6.14217
5.84737
5.57546
5.32419
5.09158
15
16
8.31256 7.82371
7.37916
6.97399
6.60388
6.26506
5.95423
5.66850
5.40529
5.16235
16
17
8.54363 8.02155
7.54879
7.11963
6.72909
6.37286
6.04716
5.74870
5.47461
5.22233
17
18
8.75563 8.20141
7.70162
7.24967
6.83991
6.46742
6.12797
5.81785
5.53385
5.27316
18
19
8.95011 8.36492
7.83929
7.36578
6.93797
6.55037
6.19823
5.87746
5.58449
5.31624
19
20
9.12855 8.51356
7.96333
7.46944
7.02475
6.62313
6.25933
5.92884
5.62777
5.35275
20
21
9.29224 8.64869
8.07507
7.56200
7.10155
6.68696
6.31246
5.97314
5.66476
5.38368
21
22
9.44243 8.77154
8.17574
7.64465
7.16951
6.74294
6.35866
6.01133
5.69637
5.40990
22
23
9.58021 8.88322
8.26643
7.71843
7.22966
6.79206
6.39884
6.04425
5.72340
5.43212
23
24
9.70661 8.98474
8.34814
7.78432
7.28288
6.83514
6.43377
6.07263
5.74649
5.45095
24
25
9.82258 9.07704
8.42174
7.84314
7.32998
6.87293
6.46415
6.09709
5.76623
5.46691
25
26
9.92897 9.16095
8.48806
7.89566
7.37167
6.90608
6.49056
6.11818
5.78311
5.48043
26
27
10.02658 9.23722
8.54780
7.94255
7.40856
6.93515
6.51353
6.13636
5.79753
5.49189
27
28
10.11613 9.30657
8.60162
7.98442
7.44120
6.96066
6.53351
6.15204
5.80985
5.50160
28
29
10.19828 9.36961
8.65011
8.02181
7.47009
6.98304
6.55088
6.16555
5.82039
5.50983
29
30
10.27365 9.42691
8.69379
8.05518
7.49565
7.00266
6.56598
6.17720
5.82939
5.51681
30
31
10.34280 9.47901
8.73315
8.08499
7.51828
7.01988
6.57911
6.18724
5.83709
5.52272
31
32
10.40624 9.52638
8.76860
8.11159
7.53830
7.03498
6.59053
6.19590
5.84366
5.52773
32
33
10.46444 9.56943
8.80054
8.13535
7.55602
7.04823
6.60046
6.20336
5.84928
5.53197
33
34
10.51784 9.60857
8.82932
8.15656
7.57170
7.05985
6.60910
6.20979
5.85409
5.53557
34
35
10.56682 9.64416
8.85524
8.17550
7.58557
7.07005
6.61661
6.21534
5.85820
5.53862
35
36
10.61176 9.67651
8.87859
8.19241
7.59785
7.07899
6.62314
6.22012
5.86171
5.54120
36
The values in Table 12-2 were generated by the formula
rate per period and n is the total number of periods.
26441_ch12_hr_380-419_2.indd 395
© Cengage Learning, Inc. This content is not final and may not match the published product.
Periods
Present Value (Amount) of an Ordinary Annuity of $1
395
(1 + i) n − 1
and rounded to five decimal places, where i is the interest
i(1 + i) n
10/10/18 3:50 PM