Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges
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B (32 points) For each of the following annuities, find the present value, the amount of the periodic
payment, or the total amount of interest paid. Round answers to the nearest cent. (4 points for each
correct answer)
8.
An annuity consists of quarterly payments of $1,200 each for 10 years at an interest rate of 5%
compounded quarterly. Determine the present value of the annuity.
9. Compute the amount of each payment in an annuity that has a present value of $10,000 with 9 years of
semiannual payments at an interest rate of 16% compounded semiannually.
10. In a 40-year annuity, the annual payments are $10,000 each and the interest rate is 6% compounded
annually. What is the present value of the annuity?
11. What is the total interest earned by an annuity that has a present value of $16,000 with monthly
payments over a 2-year period at an interest rate of 9% compounded monthly?
12. Calculate the size of the regular quarterly payments in a 10-year annuity that has a present value of
$100,000 and an interest rate of 8% compounded quarterly.
13. An annuity has a present value of $75,000. Compute the total interest earned by the annuity if there are
annual payments over 10 years at an interest rate of 12% compounded annually.
14. Find the present value of a 15-year annuity with semiannual payments of $8,000 each, which earns
interest at a rate of 6% compounded semiannually.
$156,803.52
$57,738.20
$3,655.57
$1,543.04
$150,463.00
$1,067.02
$37,592.32
484 Part 6 Corporate and Special Applications
Assignment 23.2 Continued
5% 4 4 5 1.25%
4 3 10 5 40 payments $1,200 3 31.32693 5 $37,592.32
16% 4 2 5 8%
2 3 9 5 18 payments $10,000 4 9.37189 5 $1,067.02
6% 4 1 5 6%
1 3 40 5 40 payments $10,000 3 15.04630 5 $150,463.00
9% 4 12 5 0.75% $16,000 4 21.88915 5 $730.96
12 3 2 5 24 payments ($730.96 3 24) 2 $16,000 5 $1,543.04
8% 4 4 5 2%
4 3 10 5 40 payments $100,000 4 27.35548 5 $3,655.57
12% 4 1 5 12% $75,000 4 5.65022 5 $13,273.82
1 3 10 5 10 payments ($13,273.82 3 10) 2 $75,000 5 $57,738.20
6% 4 2 5 3%
2 3 15 years 5 30 payments $8,000 3 19.60044 5 $156,803.52
15. Compute the amount of the regular monthly payments in a 1-year annuity that has a present value of
$20,000 and an interest rate of 12% compounded monthly.
Score for B (32)
C (28 points) In each of the following applications, find the present value of the annuity, the amount
of the periodic payment, or the total amount of interest earned. Round answers to the nearest cent.
(4 points for each correct answer)
16.
Walt Pierce is making a budget for the next 18 months. He estimates that his rent will be about $650 per
month. For calculations, Walt considers his housing expense to be an annuity of 18 payments. If he uses
an interest rate of 9% compounded monthly, what will be the present value of the annuity?
17. After their children moved away from home, Barbara Cain and her husband sold their large house and
bought a smaller condominium. Barbara invested $25,000 of their after-tax profit in an annuity that would
give them equal quarterly payments for 10 years. The fund will pay a return of 8% compounded quarterly.
At the end of the 10 years, their annuity will be finished. What amount will they receive each quarter?
18. Joe Littrell is considering an investment that is somewhat like a bond. The investment is an annuity that
would pay Joe $2,400 every 6 months for 16 years. He is trying to determine how much the investment is
worth today. If he uses an interest rate of 10% compounded semiannually, what is the present value of
the annuity?
19. Bonnie Bomar will receive a retirement bonus of $80,000. She has the option of either receiving the
$80,000 now in one lump sum or having it invested and then receiving 15 equal annual annuity pay-
ments, the first payment arriving 1 year after retirement. If she selects payments over 15 years, the
$80,000 is invested at a guaranteed rate of 8% compounded annually. Compute the amount of interest
that Bonnie would earn by choosing the payments over 15 years instead of the lump sum.
20. Nellie Van Calcar inherited money from her grandfather. Nellie’s daughter is in her second year of
college, and Nellie wants to give her $1,600 every quarter for 3 years. Nellie can invest the money for her
daughter at 6% compounded quarterly. How much should she invest now to provide for all the quarterly
withdrawals and have an empty account after the last withdrawal?
$17,452.02
$60,195.40
$37,926.43
$913.89
$10,906.47
$1,776.98
Chapter 23 Annuities 485
Assignment 23.2 Continued
12% 4 12 5 1%
1 3 12 5 12 payments $20,000 4 11.25508 5 $1,776.98
9% 4 12 5 0.75%
18 payments $650 3 16.77918 5 $10,906.47
8% 4 4 5 2%
4 3 10 5 40 payments $25,000 4 27.35548 5 $913.89
10% 4 2 5 5%
2 3 16 5 32 payments $2,400 3 15.80268 5 $37,926.43
8% 4 1 5 8% $80,000 4 8.55948 5 $9,346.36
1 3 15 5 15 payments ($9,346.36 3 15) 2 $80,000 5 $60,195.40
6% 4 4 5 1.5%
4 3 3 5 12 payments $1,600 3 10.90751 5 $17,452.02
21. Joyce Bodley plans to buy a pre-owned car. She can either finance the car through the dealer or borrow
the money from the bank. Either way, the amount borrowed will be amortized in equal payments over
4 years. If the bank’s 12% annual interest rate for pre-owned cars is compounded monthly, compute
Joyce’s monthly payments for a bank loan of $15,000.
22. Sonny Hansen wanted to protect his home from fire and burglars, so he purchased a home security sys-
tem. The total price including installation was $4,460. The alarm company convinced Sonny to amortize
the cost over 30 months at an interest rate of 9% compounded monthly. Determine the amount of each
of the equal monthly payments.
Score for C (28)
D (12 points) Gary Robinson purchased some new equipment and furniture for his office. Instead of
charging it on a credit card, which had an 18% interest rate, Gary negotiated financing with the office
supply dealer. The total purchase amount was $6,450 and it was amortized over 4 months.The interest
rate was 6% per year, or 0.5% per month.The first three monthly payments were each $1,632.70.
Complete the first three lines of the following amortization schedule. Round answers to the nearest
cent.(1 point for each correct answer)
Unpaid InterestPrincipal Total New
Month Balance Payment Payment Payment Balance
23. 1 $1,632.70
24. 2 $1,632.70
25. 3 $1,632.70
Score for D (12)
$1,624.61$1,616.49$16. 21$3,241.10
$3,241.10$1,608.45$24. 25$4,849.55
$4,849.55$1,600.45$32. 25$6,450.00
$166.57
$395.01
486 Part 6 Corporate and Special Applications
Assignment 23.2 Continued
12% 4 12 5 1%
12 3 4 5 48 payments $15,000 4 37.97396 5 $395.01
9% 4 12 5 0.75%
30 months 5 30 payments $4,460 4 26.77508 5 $166.57
Month 1:
$6,450.00 3 0.005 5 $32.25
$1,632.70 2 $32.25 5 $1,600.45
$6,450.00 2 $1,600.45 5 $4,849.55
Month 2:
$4,849.55 3 0.005 5 $24.25
$1,632.70 2 $24.25 5 $1,608.45
$4,849.55 2 $1,608.45 5 $3,241.10
Month 3:
$3,241.10 3 0.005 5 $16.21
$1,632.70 2 $16.21 5 $1,616.49
$3,241.10 2 $1,616.49 5 $1,624.61
Notes
Chapter 23 Annuities 487
488 Part 6 Corporate and Special Applications
Period 0.50% 0.75% 1.00% 1.25% 1.50% 2.00% 3.00% 4.00% 5.00% 6.00% 8.00% 9.00% 10.00% 12.00%
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00500 2.00750 2.01000 2.01250 2.01500 2.02000 2.03000 2.04000 2.05000 2.06000 2.08000 2.09000 2.10000 2.12000
3 3.01502 3.02256 3.03010 3.03766 3.04522 3.06040 3.09090 3.12160 3.15250 3.18360 3.24640 3.27810 3.31000 3.37440
4 4.03010 4.04523 4.06040 4.07563 4.09090 4.12161 4.18363 4.24646 4.31013 4.37462 4.50611 4.57313 4.64100 4.77933
5 5.05025 5.07556 5.10101 5.12657 5.15227 5.20404 5.30914 5.41632 5.52563 5.63709 5.86660 5.98471 6.10510 6.35285
6 6.07550 6.11363 6.15202 6.19065 6.22955 6.30812 6.46841 6.63298 6.80191 6.97532 7.33593 7.52333 7.71561 8.11519
7 7.10588 7.15948 7.21354 7.26804 7.32299 7.43428 7.66246 7.89829 8.14201 8.39384 8.92280 9.20043 9.48717 10.08901
8 8.14141 8.21318 8.28567 8.35889 8.43284 8.58297 8.89234 9.21423 9.54911 9.89747 10.63663 11.02847 11.43589 12.29969
9 9.18212 9.27478 9.36853 9.46337 9.55933 9.75463 10.15911 10.58280 11.02656 11.49132 12.48756 13.02104 13.57948 14.77566
10 10.22803 10.34434 10.46221 10.58167 10.70272 10.94972 11.46388 12.00611 12.57789 13.18079 14.48656 15.19293 15.93742 17.54874
11 11.27917 11.42192 11.56683 11.71394 11.86326 12.16872 12.80780 13.48635 14.20679 14.97164 16.64549 17.56029 18.53117 20.65458
12 12.33556 12.50759 12.68250 12.86036 13.04121 13.41209 14.19203 15.02581 15.91713 16.86994 18.97713 20.14072 21.38428 24.13313
13 13.39724 13.60139 13.80933 14.02112 14.23683 14.68033 15.61779 16.62684 17.71298 18.88214 21.49530 22.95338 24.52271 28.02911
14 14.46423 14.70340 14.94742 15.19638 15.45038 15.97394 17.08632 18.29191 19.59863 21.01507 24.21492 26.01919 27.97498 32.39260
15 15.53655 15.81368 16.09690 16.38633 16.68214 17.29342 18.59891 20.02359 21.57856 23.27597 27.15211 29.36092 31.77248 37.27971
16 16.61423 16.93228 17.25786 17.59116 17.93237 18.63929 20.15688 21.82453 23.65749 25.67253 30.32428 33.00340 35.94973 42.75328
17 17.69730 18.05927 18.43044 18.81105 19.20136 20.01207 21.76159 23.69751 25.84037 28.21288 33.75023 36.97370 40.54470 48.88367
18 18.78579 19.19472 19.61475 20.04619 20.48938 21.41231 23.41444 25.64541 28.13238 30.90565 37.45024 41.30134 45.59917 55.74971
19 19.87972 20.33868 20.81090 21.29677 21.79672 22.84056 25.11687 27.67123 30.53900 33.75999 41.44626 46.01846 51.15909 63.43968
20 20.97912 21.49122 22.01900 22.56298 23.12367 24.29737 26.87037 29.77808 33.06595 36.78559 45.76196 51.16012 57.27500 72.05244
21 22.08401 22.65240 23.23919 23.84502 24.47052 25.78332 28.67649 31.96920 35.71925 39.99273 50.42292 56.76453 64.00250 81.69874
22 23.19443 23.82230 24.47159 25.14308 25.83758 27.29898 30.53678 34.24797 38.50521 43.39229 55.45676 62.87334 71.40275 92.50258
23 24.31040 25.00096 25.71630 26.45737 27.22514 28.84496 32.45288 36.61789 41.43048 46.99583 60.89330 69.53194 79.54302 104.60289
24 25.43196 26.18847 26.97346 27.78808 28.63352 30.42186 34.42647 39.08260 44.50200 50.81558 66.76476 76.78981 88.49733 118.15524
25 26.55912 27.38488 28.24320 29.13544 30.06302 32.03030 36.45926 41.64591 47.72710 54.86451 73.10594 84.70090 98.34706 133.33387
Table 23-1 Future Value Annuity Factors
Chapter 23 Annuities 489
Period 0.50% 0.75% 1.00% 1.25% 1.50% 2.00% 3.00% 4.00% 5.00% 6.00% 8.00% 9.00% 10.00% 12.00%
26 27.69191 28.59027 29.52563 30.49963 31.51397 33.67091 38.55304 44.31174 51.11345 59.15638 79.95442 93.32398 109.18177 150.33393
27 28.83037 29.80470 30.82089 31.88087 32.98668 35.34432 40.70963 47.08421 54.66913 63.70577 87.35077 102.72313 121.09994 169.37401
28 29.97452 31.02823 32.12910 33.27938 34.48148 37.05121 42.93092 49.96758 58.40258 68.52811 95.33883 112.96822 134.20994 190.69889
29 31.12439 32.26094 33.45039 34.69538 35.99870 38.79223 45.21885 52.96629 62.32271 73.63980 103.96594 124.13536 148.63093 214.58275
30 32.28002 33.50290 34.78489 36.12907 37.53868 40.56808 47.57542 56.08494 66.43885 79.05819 113.28321 136.30754 164.49402 241.33268
31 33.44142 34.75417 36.13274 37.58068 39.10176 42.37944 50.00268 59.32834 70.76079 84.80168 123.34587 149.57522 181.94342 271.29261
32 34.60862 36.01483 37.49407 39.05044 40.68829 44.22703 52.50276 62.70147 75.29883 90.88978 134.21354 164.03699 201.13777 304.84772
33 35.78167 37.28494 38.86901 40.53857 42.29861 46.11157 55.07784 66.20953 80.06377 97.34316 145.95062 179.80032 222.25154 342.42945
34 36.96058 38.56458 40.25770 42.04530 43.93309 48.03380 57.73018 69.85791 85.06696 104.18375 158.62667 196.98234 245.47670 384.52098
35 38.14538 39.85381 41.66028 43.57087 45.59209 49.99448 60.46208 73.65222 90.32031 111.43478 172.31680 215.71075 271.02437 431.66350
36 39.33610 41.15272 43.07688 45.11551 47.27597 51.99437 63.27594 77.59831 95.83632 119.12087 187.10215 236.12472 299.12681 484.46312
37 40.53279 42.46136 44.50765 46.67945 48.98511 54.03425 66.17422 81.70225 101.62814 127.26812 203.07032 258.37595 330.03949 543.59869
38 41.73545 43.77982 45.95272 48.26294 50.71989 56.11494 69.15945 85.97034 107.70955 135.90421 220.31595 282.62978 364.04343 609.83053
39 42.94413 45.10817 47.41225 49.86623 52.48068 58.23724 72.23423 90.40915 114.09502 145.05846 238.94122 309.06646 401.44778 684.01020
40 44.15885 46.44648 48.88637 51.48956 54.26789 60.40198 75.40126 95.02552 120.79977 154.76197 259.05652 337.88245 442.59256 767.09142
41 45.37964 47.79483 50.37524 53.13318 56.08191 62.61002 78.66330 99.82654 127.83976 165.04768 280.78104 369.29187 487.85181 860.14239
42 46.60654 49.15329 51.87899 54.79734 57.92314 64.86222 82.02320 104.81960 135.23175 175.95054 304.24352 403.52813 537.63699 964.35948
43 47.83957 50.52194 53.39778 56.48231 59.79199 67.15947 85.48389 110.01238 142.99334 187.50758 329.58301 440.84566 592.40069 1081.08262
44 49.07877 51.90086 54.93176 58.18834 61.68887 69.50266 89.04841 115.41288 151.14301 199.75803 356.94965 481.52177 652.64076 1211.81253
45 50.32416 53.29011 56.48107 59.91569 63.61420 71.89271 92.71986 121.02939 159.70016 212.74351 386.50562 525.85873 718.90484 1358.23003
46 51.57578 54.68979 58.04589 61.66464 65.56841 74.33056 96.50146 126.87057 168.68516 226.50812 418.42607 574.18602 791.79532 1522.21764
47 52.83366 56.09996 59.62634 63.43545 67.55194 76.81718 100.39650 132.94539 178.11942 241.09861 452.90015 626.86276 871.97485 1705.88375
48 54.09783 57.52071 61.22261 65.22839 69.56522 79.35352 104.40840 139.26321 188.02539 256.56453 490.13216 684.28041 960.17234 1911.58980
49 55.36832 58.95212 62.83483 67.04374 71.60870 81.94059 108.54065 145.83373 198.42666 272.95840 530.34274 746.86565 1057.18957 2141.98058
50 56.64516 60.39426 64.46318 68.88179 73.68283 84.57940 112.79687 152.66708 209.34800 290.33590 573.77016 815.08356 1163.90853 2400.01825
Table 23-1 Future Value Annuity Factors (continued)
490 Part 6 Corporate and Special Applications
Period 0.50% 0.75% 1.00% 1.25% 1.50% 2.00% 3.00% 4.00% 5.00% 6.00% 8.00% 9.00% 10.00% 12.00%
1 0.99502 0.99256 0.99010 0.98765 0.98522 0.98039 0.97087 0.96154 0.95238 0.94340 0.92593 0.91743 0.90909 0.89286
2 1.98510 1.97772 1.97040 1.96312 1.95588 1.94156 1.91347 1.88609 1.85941 1.83339 1.78326 1.75911 1.73554 1.69005
3 2.97025 2.95556 2.94099 2.92653 2.91220 2.88388 2.82861 2.77509 2.72325 2.67301 2.57710 2.53129 2.48685 2.40183
4 3.95050 3.92611 3.90197 3.87806 3.85438 3.80773 3.71710 3.62990 3.54595 3.46511 3.31213 3.23972 3.16987 3.03735
5 4.92587 4.88944 4.85343 4.81784 4.78264 4.71346 4.57971 4.45182 4.32948 4.21236 3.99271 3.88965 3.79079 3.60478
6 5.89638 5.84560 5.79548 5.74601 5.69719 5.60143 5.41719 5.24214 5.07569 4.91732 4.62288 4.48592 4.35526 4.11141
7 6.86207 6.79464 6.72819 6.66273 6.59821 6.47199 6.23028 6.00205 5.78637 5.58238 5.20637 5.03295 4.86842 4.56376
8 7.82296 7.73661 7.65168 7.56812 7.48593 7.32548 7.01969 6.73274 6.46321 6.20979 5.74664 5.53482 5.33493 4.96764
9 8.77906 8.67158 8.56602 8.46234 8.36052 8.16224 7.78611 7.43533 7.10782 6.80169 6.24689 5.99525 5.75902 5.32825
10 9.73041 9.59958 9.47130 9.34553 9.22218 8.98259 8.53020 8.11090 7.72173 7.36009 6.71008 6.41766 6.14457 5.65022
11 10.67703 10.52067 10.36763 10.21780 10.07112 9.78685 9.25262 8.76048 8.30641 7.88687 7.13896 6.80519 6.49506 5.93770
12 11.61893 11.43491 11.25508 11.07931 10.90751 10.57534 9.95400 9.38507 8.86325 8.38384 7.53608 7.16073 6.81369 6.19437
13 12.55615 12.34235 12.13374 11.93018 11.73153 11.34837 10.63496 9.98565 9.39357 8.85268 7.90378 7.48690 7.10336 6.42355
14 13.48871 13.24302 13.00370 12.77055 12.54338 12.10625 11.29607 10.56312 9.89864 9.29498 8.24424 7.78615 7.36669 6.62817
15 14.41662 14.13699 13.86505 13.60055 13.34323 12.84926 11.93794 11.11839 10.37966 9.71225 8.55948 8.06069 7.60608 6.81086
16 15.33993 15.02431 14.71787 14.42029 14.13126 13.57771 12.56110 11.65230 10.83777 10.10590 8.85137 8.31256 7.82371 6.97399
17 16.25863 15.90502 15.56225 15.22992 14.90765 14.29187 13.16612 12.16567 11.27407 10.47726 9.12164 8.54363 8.02155 7.11963
18 17.17277 16.77918 16.39827 16.02955 15.67256 14.99203 13.75351 12.65930 11.68959 10.82760 9.37189 8.75563 8.20141 7.24967
19 18.08236 17.64683 17.22601 16.81931 16.42617 15.67846 14.32380 13.13394 12.08532 11.15812 9.60360 8.95011 8.36492 7.36578
20 18.98742 18.50802 18.04555 17.59932 17.16864 16.35143 14.87747 13.59033 12.46221 11.46992 9.81815 9.12855 8.51356 7.46944
21 19.88798 19.36280 18.85698 18.36969 17.90014 17.01121 15.41502 14.02916 12.82115 11.76408 10.01680 9.29224 8.64869 7.56200
22 20.78406 20.21121 19.66038 19.13056 18.62082 17.65805 15.93692 14.45112 13.16300 12.04158 10.20074 9.44243 8.77154 7.64465
23 21.67568 21.05331 20.45582 19.88204 19.33086 18.29220 16.44361 14.85684 13.48857 12.30338 10.37106 9.58021 8.88322 7.71843
24 22.56287 21.88915 21.24339 20.62423 20.03041 18.91393 16.93554 15.24696 13.79864 12.55036 10.52876 9.70661 8.98474 7.78432
25 23.44564 22.71876 22.02316 21.35727 20.71961 19.52346 17.41315 15.62208 14.09394 12.78336 10.67478 9.82258 9.07704 7.84314
Table 23-2 Present Value Annuity Factors
Chapter 23 Annuities 491
Period 0.50% 0.75% 1.00% 1.25% 1.50% 2.00% 3.00% 4.00% 5.00% 6.00% 8.00% 9.00% 10.00% 12.00%
26 24.32402 23.54219 22.79520 22.08125 21.39863 20.12104 17.87684 15.98277 14.37519 13.00317 10.80998 9.92897 9.16095 7.89566
27 25.19803 24.35949 23.55961 22.79630 22.06762 20.70690 18.32703 16.32959 14.64303 13.21053 10.93516 10.02658 9.23722 7.94255
28 26.06769 25.17071 24.31644 23.50252 22.72672 21.28127 18.76411 16.66306 14.89813 13.40616 11.05108 10.11613 9.30657 7.98442
29 26.93302 25.97589 25.06579 24.20002 23.37608 21.84438 19.18845 16.98371 15.14107 13.59072 11.15841 10.19828 9.36961 8.02181
30 27.79405 26.77508 25.80771 24.88891 24.01584 22.39646 19.60044 17.29203 15.37245 13.76483 11.25778 10.27365 9.42691 8.05518
31 28.65080 27.56832 26.54229 25.56929 24.64615 22.93770 20.00043 17.58849 15.59281 13.92909 11.34980 10.34280 9.47901 8.08499
32 29.50328 28.35565 27.26959 26.24127 25.26714 23.46833 20.38877 17.87355 15.80268 14.08404 11.43500 10.40624 9.52638 8.11159
33 30.35153 29.13712 27.98969 26.90496 25.87895 23.98856 20.76579 18.14765 16.00255 14.23023 11.51389 10.46444 9.56943 8.13535
34 31.19555 29.91278 28.70267 27.56046 26.48173 24.49859 21.13184 18.41120 16.19290 14.36814 11.58693 10.51784 9.60857 8.15656
35 32.03537 30.68266 29.40858 28.20786 27.07559 24.99862 21.48722 18.66461 16.37419 14.49825 11.65457 10.56682 9.64416 8.17550
36 32.87102 31.44681 30.10751 28.84727 27.66068 25.48884 21.83225 18.90828 16.54685 14.62099 11.71719 10.61176 9.67651 8.19241
37 33.70250 32.20527 30.79951 29.47878 28.23713 25.96945 22.16724 19.14258 16.71129 14.73678 11.77518 10.65299 9.70592 8.20751
38 34.52985 32.95808 31.48466 30.10250 28.80505 26.44064 22.49246 19.36786 16.86789 14.84602 11.82887 10.69082 9.73265 8.22099
39 35.35309 33.70529 32.16303 30.71852 29.36458 26.90259 22.80822 19.58448 17.01704 14.94907 11.87858 10.72552 9.75696 8.23303
40 36.17223 34.44694 32.83469 31.32693 29.91585 27.35548 23.11477 19.79277 17.15909 15.04630 11.92461 10.75736 9.77905 8.24378
41 36.98729 35.18307 33.49969 31.92784 30.45896 27.79949 23.41240 19.99305 17.29437 15.13802 11.96723 10.78657 9.79914 8.25337
42 37.79830 35.91371 34.15811 32.52132 30.99405 28.23479 23.70136 20.18563 17.42321 15.22454 12.00670 10.81337 9.81740 8.26194
43 38.60527 36.63892 34.81001 33.10748 31.52123 28.66156 23.98190 20.37079 17.54591 15.30617 12.04324 10.83795 9.83400 8.26959
44 39.40823 37.35873 35.45545 33.68640 32.04062 29.07996 24.25427 20.54884 17.66277 15.38318 12.07707 10.86051 9.84909 8.27642
45 40.20720 38.07318 36.09451 34.25817 32.55234 29.49016 24.51871 20.72004 17.77407 15.45583 12.10840 10.88120 9.86281 8.28252
46 41.00219 38.78231 36.72724 34.82288 33.05649 29.89231 24.77545 20.88465 17.88007 15.52437 12.13741 10.90018 9.87528 8.28796
47 41.79322 39.48617 37.35370 35.38062 33.55319 30.28658 25.02471 21.04294 17.98102 15.58903 12.16427 10.91760 9.88662 8.29282
48 42.58032 40.18478 37.97396 35.93148 34.04255 30.67312 25.26671 21.19513 18.07716 15.65003 12.18914 10.93358 9.89693 8.29716
49 43.36350 40.87820 38.58808 36.47554 34.52468 31.05208 25.50166 21.34147 18.16872 15.70757 12.21216 10.94823 9.90630 8.30104
50 44.14279 41.56645 39.19612 37.01288 34.99969 31.42361 25.72976 21.48218 18.25593 15.76186 12.23348 10.96168 9.91481 8.30450
Table 23-2 Present Value Annuity Factors (continued)
492 Part 6 Corporate and Special Applications
Notes
Business
Statistics
Chapter 24 Business Statistics 493
Learning Objectives
By studying this chapter and completing all assignments, you will be able to:
Learning Objective
Compute the mean.
Determine the median.
Determine the mode.
Construct frequency tables.
Construct histograms.
Construct bar graphs.
Construct line graphs.
Construct pie charts.
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