part 2-1 評價
DESCRIPTION
Part 2-1 評價. 貨幣時間價值. 大綱. 終值 現值 年金終值 年金現值 連續複利與折現 貸款的攤銷. 複利. 複利與單利的差異 本金 $100 元,利率為 14% 複利與單利間本利和的差距越來越大,這是因為複利每一期以上一期本利和為計算利息的基礎。. 圖 5-1 複利與單利之差異. 複利與單利的差異. 終值. 將某特定時點的金錢價值複利成為未來特定時點之金錢價值(複利就是將今天價值轉換成為終值的過程) 一般而言我們可以利用以下的複利公式來計算終值 - PowerPoint PPT PresentationTRANSCRIPT
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Part 2-1
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$10014%
-
010010011141142129.961283148.15441424168.8961565192.54151706219.49731847250.22691988285.25862129325.194922610370.7221240
-
(Future Value Interest Factor)
-
5% 1 10,500 500($10,000 0.05)10,000 ($10,000 1) 10,500 $10,500 = $10,000(1.05)
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5,000 10% 1
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12 5 5,000 12 5
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Excel
-
Chart1
1092727115762512597121331000
1159274.07431276281.56251469328.07681610510
1266770.081387621477455.443789061850930.210281882143588.81
1343916.379344121628894.626777442158924.997272792593742.4601
2093777.929654213386354.940899396848475.1962193310834705.9433884
2813862.454371525516015.3675922514785344.294320628102436.8480643
3%
5%
8%
10%
Sheet1
PV
3510,000,000=$1,000,000
3%5%8%10%
6.75%
3$915,141.66$863,837.60$793,832.24$751,314.80
10,000,000(1+0.0675)35=$1,016,539.065$862,608.78$783,526.17$680,583.20$620,921.32
8$789,409.23$676,839.36$540,268.88$466,507.38
10$744,093.91$613,913.25$463,193.49$385,543.29
25$477,605.57$295,302.77$146,017.90$92,296.00
35$355,383.40$181,290.29$67,634.54$35,584.10
FV
1,000,000=$1,000,000
8%3%5%8%10%
1,000,000(1+0.08)3 =$1,259,712.003$1,092,727.00$1,157,625.00$1,259,712.00$1,331,000.00
5$1,159,274.07$1,276,281.56$1,469,328.08$1,610,510.00
8$1,266,770.08$1,477,455.44$1,850,930.21$2,143,588.81
10$1,343,916.38$1,628,894.63$2,158,925.00$2,593,742.46
25$2,093,777.93$3,386,354.94$6,848,475.20$10,834,705.94
35$2,813,862.45$5,516,015.37$14,785,344.29$28,102,436.85
185601,000,8%=8%12
1,000,8%=8%12
8%=8%12
8%=8%12
1000[SUM(1+8%12)t , t=2~N]=$49,318.43
560
10,000,
8%=8%12
10000[SUM(1+8%12)t , t=1~60]X (1+8%12)=$496,472.23
100,000,
8%420
100,0008%=$1,250,000
6035
20,000420
6.8%=6.8%12
20,000[SUM(1+6.8%12)^t-1 , t=1~420]=$34,350,208.81
672
10,000,
8%=8%12
10,000[SUM(1+8%12)^t-1 , t=1~60]X (1+8%12)=$926,388.27
1000300
8%=8%12
301360700
[1SUM(1+8%12)^t , t=1~360] 7,000,000=$51,363.52
100030
130 $ 1,060,793
1,060,793 = [1SUM(1+R%)^t , t=1~30] 10,000,000
R=10%
Sheet1
0000
0000
0000
0000
0000
0000
3%
5%
8%
10%
Sheet2
0000
0000
0000
0000
0000
0000
3%
5%
8%
10%
Sheet3
-
Present Value(Discounting)
-
{Ct}
-
Chart2
915141.65935316863837.598531476793832.24102017751314.800901578
862608.784384164783526.166468459680583.197033753620921.323059155
789409.234313936676839.362028687540268.884501976466507.380209733
744093.914896725613913.253540759463193.488084684385543.289429531
477605.56926166295302.771697762146017.90491291492295.9981770641
355383.397808387181290.28535257767634.542699430235584.1027383673
3%
5%
8%
10%
Sheet1
PV=1000000
3510,000,0003%5%8%10%
6.75%3$915,141.66$863,837.60$793,832.24$751,314.80
5$862,608.78$783,526.17$680,583.20$620,921.32
10,000,000(1+0.0675)35=$1,016,539.068$789,409.23$676,839.36$540,268.88$466,507.38
10$744,093.91$613,913.25$463,193.49$385,543.29
25$477,605.57$295,302.77$146,017.90$92,296.00
35$355,383.40$181,290.29$67,634.54$35,584.10
FV
1,000,000
8%
1,000,000(1+0.08)3 =$1,259,712.00
Sheet1
0000
0000
0000
0000
0000
0000
3%
5%
8%
10%
Sheet2
Sheet3
-
Future Value Interest FactorFVIF:
Present Value Interest FactorPVIF :
-
Basic Present Value Equation
1 (FVIFi , n) (PVIFi ,n) = 1
-
Annuity$1,000PMT
-
Ordinary Annuity
-
(Perpetuity)n
-
9% 100 4
-
$323.97$297.22
-
200 200 12%
-
(Perpetuity)
-
12% 50 3
-
(Continuous Compounding)
-
(Continuous Compounding)
-
(Effective Annual Interest RateEAR)im
-
12% 50 3
-
18% 1.5%
19.56%
-
Chart1
1
1
1.1
1.1
1.21
1.21
1.331
1.331
1.4641
1.4641
1.61051
1.6105
Sheet1
1.2510%01
3.9406420791111
11.111.1
1.166666666721.2121.1
1821.33121.21
14.431.33131.21
31.464131.331
41.464141.331
41.6105141.4641
51.6105151.4641
51.61051
01
0.51
0.51.05
11.05
11.1025
1.51.1025
1.51.157625
21.157625
21.21550625
2.51.21550625
2.51.276281562501
31.276281562511.1051709181
31.340095640621.2214027582
3.51.340095640631.3498588076
3.51.407100422741.4918246976
41.407100422751.6487212707
41.4774554438
4.51.4774554438
4.51.551328216
51.551328216
51.6288946268
Sheet1
0
0
0
0
0
0
0
0
0
0
0
1.6105
Sheet2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.6289
Sheet3
0
0
0
0
0
0
1.6487
-
Chart2
1
1
1.05
1.05
1.1025
1.1025
1.157625
1.157625
1.21550625
1.21550625
1.2762815625
1.2762815625
1.3400956406
1.3400956406
1.4071004227
1.4071004227
1.4774554438
1.4774554438
1.551328216
1.551328216
1.6288946268
1.6289
Sheet1
1.2510%01
3.9406420791111
11.111.1
1.166666666721.2121.1
1821.33121.21
14.431.33131.21
31.464131.331
41.464141.331
41.6105141.4641
51.6105151.4641
51.61051
01
0.51
0.51.05
11.05
11.1025
1.51.1025
1.51.157625
21.157625
21.21550625
2.51.21550625
2.51.276281562501
31.276281562511.1051709181
31.340095640621.2214027582
3.51.340095640631.3498588076
3.51.407100422741.4918246976
41.407100422751.6487212707
41.4774554438
4.51.4774554438
4.51.551328216
51.551328216
51.6288946268
Sheet1
0
0
0
0
0
0
0
0
0
0
0
1.6105
Sheet2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.6289
Sheet3
0
0
0
0
0
0
1.6487
-
Chart3
1
1.1051709181
1.2214027582
1.3498588076
1.4918246976
1.6487212707
1.6487
Sheet1
1.2510%01
3.9406420791111
11.111.1
1.166666666721.2121.1
1821.33121.21
14.431.33131.21
31.464131.331
41.464141.331
41.6105141.4641
51.6105151.4641
51.61051
01
0.51
0.51.05
11.05
11.1025
1.51.1025
1.51.157625
21.157625
21.21550625
2.51.21550625
2.51.276281562501
31.276281562511.1051709181
31.340095640621.2214027582
3.51.340095640631.3498588076
3.51.407100422741.4918246976
41.407100422751.6487212707
41.4774554438
4.51.4774554438
4.51.551328216
51.551328216
51.6288946268
Sheet1
0
0
0
0
0
0
0
0
0
0
0
1.6105
Sheet2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.6289
Sheet3
0
0
0
0
0
0
1.6487
-
(Payment)
-
Chart1
5250010480.8169095119
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52342.198200406210638.6187091057
52262.408560087910718.408349424
52182.020497467210798.7964120447
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51602.166955317611378.6499541943
51516.827080661111463.9898288508
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51344.222383800511636.5945257114
51256.947924857611723.8689846542
51169.018907472711811.7980020391
51080.430422457411900.3864870544
50991.177523804511989.6393857073
50901.255228411712079.5616811002
50810.658515803512170.1583937084
50719.382327850712261.4345816612
50627.421568488212353.3953410237
50534.771103430512446.0458060814
50441.425759884912539.391149627
50347.380326262712633.4365832492
50252.629551888312728.1873576235
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50060.990780985112919.8261285267
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49768.109021882413212.7078876294
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49569.175188749313411.6417207625
49468.587875843613512.2290336683
49367.246158091113613.5707514208
49265.144377455413715.6725320564
49162.27683346513818.5400760469
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45429.734055244917551.082854267
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45031.865541429117948.9513680827
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42138.779209922920842.037699589
41982.46392717620998.3529823359
41824.976279808521155.8406297034
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39315.838697959623664.9782115523
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38597.862411938424382.9544975735
38414.990253206624565.8266563053
38230.746553284324750.0703562276
38045.121025612624935.6958838993
37858.103306483425122.7136030285
37669.682954460725311.1339550512
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37095.900508482425884.9164010294
36901.763635474726079.0532740371
36706.170735919426274.6461735924
36509.110889617526471.7060198944
36310.573094468326670.2438150436
36110.546265855526870.2706436564
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35705.980753476927274.8361560349
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35087.682804793327893.1341047186
34878.484299007928102.332610504
34667.716804429128313.1001050827
34455.36855364128525.4483558709
34241.42769097228739.3892185399
34025.882271832928954.9346376789
33808.720262050329172.0966474615
33589.929537194429390.8873723175
33369.49788190229611.3190276099
33147.412989194929833.403920317
32923.662459792530057.1544497193
32698.233801419630282.5831080922
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32242.291659498430738.5252500134
32011.752720123330969.0641893885
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31545.474747421831435.34216209
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2309.556757686860671.260151825
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menu
CHAPTER
2
Introduction
1FVPV2Excel3 Excel Excel XY
FV
PV1,000,000
i8%
1.
2.
3.
Future value of $1,000,000 at 8%
yearBeginning amountinterest earnedEnding AmountFormulaFunction
01000000
110000008000010800001080000$1,080,000
210800008640011664001166400$1,166,400
311664009331212597121259712$1,259,712
41259712100776.961360488.961360488.96$1,360,489
51360488.96108839.11681469328.07681469328.0768$1,469,328
1.FV
1,080,000.00
$31,259,712.00
$51,469,328.08
$81,850,930.21
$102,158,925.00
$256,848,475.20
$3514,785,344.29
2.FV
$1,259,712
3%1092727
5%1157625
8%1259712
10%1331000
20%1728000
30%2197000
3.FV
Sensitivity analysis (period v.s. interest rate)
$1,080,0003%5%8%10%15%
31,092,727.001,157,625.001,259,712.001,331,000.001,520,875.00
51,159,274.071,276,281.561,469,328.081,610,510.002,011,357.19
81,266,770.081,477,455.441,850,930.212,143,588.813,059,022.86
101,343,916.381,628,894.632,158,925.002,593,742.464,045,557.74
151,557,967.422,078,928.183,172,169.114,177,248.178,137,061.63
n420
discount rate0.0056666667=6.8%/12
payment20000
pv0
FV$34,350,208.81=FV(E148,E147,-E149,E150)
FV
0000
0000
0000
0000
0000
3%
5%
8%
10%
,
PV
FV1,000,000
i6.75%
n35
Excel
PV101,653.91$101,653.91
Discount rate10%
Payment1,000
year5
Year012345
Payment1,0001,0001,0001,0001,000
Present value factor100%91%83%75%68%62%
PV of payment909826751683621
PV of all payments3,791
$3,791
1.
discount rate$3,791
3%4,579.71
5%4,329.48
8%3,992.71
10%3,790.79
12%3,604.78
2.
payment$3,791
5001,895.39
10003,790.79
15005,686.18
20007,581.57
25009,476.97
3.
year$3,791
32,486.85
53,790.79
85,334.93
106,144.57
157,606.08
4.
$3,7913%5%8%10%12%
32,828.612,723.252,577.102,486.852,401.83
54,579.714,329.483,992.713,790.793,604.78
87,019.696,463.215,746.645,334.934,967.64
108,530.207,721.736,710.086,144.575,650.22
2517,413.1514,093.9410,674.789,077.047,843.14
3521,487.2216,374.1911,654.579,644.168,175.50
5.
(Future values)(Compounding)
PVFVin FVIF=(1+i)^n
key in
a.TableYear 0Ending amount D59)PV1000000b.Beginning amountEnding amount B60D59c.interest earned=Benginning amount*iC60=B60 * $E$28d.Eending amount=Beginning amount+interest earnedD60 B60+C60e.Eending amountB60:D60 64Eending amount
E60=$E$27*(1+$E$28)^A60
FV(i, T,,PV) iTPVPVCFVCF60FV($E$28,A60,,-$E$27)ExcelfxFVFV
1,000,0008%Excel
D79:D84E78F60D78:E84 A60('8%)
D89:D94E88F62D88:E94E28(3)
A104:A108B103:F103A103F60A103:F108E28A60
B104:F108XY3%,5%,8%,10%,15%XY
603520,0004206.8%=6.8%12
FV=(, , , )FVE151=FV(E148,E147,-E149,E150)Excel /FV/
1,000,0008%
Step1
Future Values
Step2
Sensitivity analysis
$Excel$$E$28A1A2+A3A1B1B1B2+B3B1A1$A$2+A3B1B1$A$2+B3A2
$A1A$1$A1AA$1A2$A1+B1B2B2$A1+C1
F4F4F4F4 A1F4$A$1F4A$1F4$A1F4A1
Back
()A1B1+C1A1A3A2B2+C2A3B3+C3
A1A10110A11A22A1A2A10A3A10310
Back
1. A60
2.
Back
PV
00000
00000
00000
00000
00000
00000
3%
5%
8%
10%
12%
,
Mortgage
Interest rate8%
Payment2,000
Amount borrowed7,985
BeginningPlusLessEnding
YearBalanceInterestPaymentBalance
17,985.00638.80(2,000)6,623.80
26,623.80529.90(2,000)5,153.70
35,153.70412.30(2,000)3,566.00
43,566.00285.28(2,000)1,851.28
51,851.28148.10(2,000)(0.62)(0)
0.0
0.0
0.0
0.0
0.0
Mortgage amortization schedule
Principal7,000,000.00
period24020 years
discount rate0.0075i=9%
payment$62,980.82
periodbeginning balancepaymentinterest paidprincipal paidending balance
07,000,000.00
17,000,000.00$62,980.82$52,500.00$10,480.82$6,989,519.18
26,989,519.18$62,980.82$52,421.39$10,559.42$6,978,959.76
36,978,959.76$62,980.82$52,342.20$10,638.62$6,968,321.14
46,968,321.14$62,980.82$52,262.41$10,718.41$6,957,602.73
56,957,602.73$62,980.82$52,182.02$10,798.80$6,946,803.94
66,946,803.94$62,980.82$52,101.03$10,879.79$6,935,924.15
76,935,924.15$62,980.82$52,019.43$10,961.39$6,924,962.76
86,924,962.76$62,980.82$51,937.22$11,043.60$6,913,919.17
96,913,919.17$62,980.82$51,854.39$11,126.42$6,902,792.74
106,902,792.74$62,980.82$51,770.95$11,209.87$6,891,582.87
116,891,582.87$62,980.82$51,686.87$11,293.95$6,880,288.93
126,880,288.93$62,980.82$51,602.17$11,378.65$6,868,910.28
136,868,910.28$62,980.82$51,516.83$11,463.99$6,857,446.29
146,857,446.29$62,980.82$51,430.85$11,549.97$6,845,896.32
156,845,896.32$62,980.82$51,344.22$11,636.59$6,834,259.72
166,834,259.72$62,980.82$51,256.95$11,723.87$6,822,535.85
176,822,535.85$62,980.82$51,169.02$11,811.80$6,810,724.06
186,810,724.06$62,980.82$51,080.43$11,900.39$6,798,823.67
196,798,823.67$62,980.82$50,991.18$11,989.64$6,786,834.03
206,786,834.03$62,980.82$50,901.26$12,079.56$6,774,754.47
216,774,754.47$62,980.82$50,810.66$12,170.16$6,762,584.31
226,762,584.31$62,980.82$50,719.38$12,261.43$6,750,322.88
236,750,322.88$62,980.82$50,627.42$12,353.40$6,737,969.48
246,737,969.48$62,980.82$50,534.77$12,446.05$6,725,523.43
256,725,523.43$62,980.82$50,441.43$12,539.39$6,712,984.04
266,712,984.04$62,980.82$50,347.38$12,633.44$6,700,350.61
276,700,350.61$62,980.82$50,252.63$12,728.19$6,687,622.42
286,687,622.42$62,980.82$50,157.17$12,823.65$6,674,798.77
296,674,798.77$62,980.82$50,060.99$12,919.83$6,661,878.94
306,661,878.94$62,980.82$49,964.09$13,016.72$6,648,862.22
316,648,862.22$62,980.82$49,866.47$13,114.35$6,635,747.87
326,635,747.87$62,980.82$49,768.11$13,212.71$6,622,535.16
336,622,535.16$62,980.82$49,669.01$13,311.80$6,609,223.36
346,609,223.36$62,980.82$49,569.18$13,411.64$6,595,811.72
356,595,811.72$62,980.82$49,468.59$13,512.23$6,582,299.49
366,582,299.49$62,980.82$49,367.25$13,613.57$6,568,685.92
376,568,685.92$62,980.82$49,265.14$13,715.67$6,554,970.24
386,554,970.24$62,980.82$49,162.28$13,818.54$6,541,151.70
396,541,151.70$62,980.82$49,058.64$13,922.18$6,527,229.53
406,527,229.53$62,980.82$48,954.22$14,026.60$6,513,202.93
416,513,202.93$62,980.82$48,849.02$14,131.79$6,499,071.13
426,499,071.13$62,980.82$48,743.03$14,237.78$6,484,833.35
436,484,833.35$62,980.82$48,636.25$14,344.57$6,470,488.78
446,470,488.78$62,980.82$48,528.67$14,452.15$6,456,036.63
456,456,036.63$62,980.82$48,420.27$14,560.54$6,441,476.09
466,441,476.09$62,980.82$48,311.07$14,669.75$6,426,806.35
476,426,806.35$62,980.82$48,201.05$14,779.77$6,412,026.58
486,412,026.58$62,980.82$48,090.20$14,890.62$6,397,135.96
496,397,135.96$62,980.82$47,978.52$15,002.30$6,382,133.66
506,382,133.66$62,980.82$47,866.00$15,114.81$6,367,018.85
516,367,018.85$62,980.82$47,752.64$15,228.18$6,351,790.67
526,351,790.67$62,980.82$47,638.43$15,342.39$6,336,448.28
536,336,448.28$62,980.82$47,523.36$15,457.45$6,320,990.83
546,320,990.83$62,980.82$47,407.43$15,573.39$6,305,417.44
556,305,417.44$62,980.82$47,290.63$15,690.19$6,289,727.26
566,289,727.26$62,980.82$47,172.95$15,807.86$6,273,919.40
576,273,919.40$62,980.82$47,054.40$15,926.42$6,257,992.97
586,257,992.97$62,980.82$46,934.95$16,045.87$6,241,947.10
596,241,947.10$62,980.82$46,814.60$16,166.21$6,225,780.89
606,225,780.89$62,980.82$46,693.36$16,287.46$6,209,493.43
616,209,493.43$62,980.82$46,571.20$16,409.62$6,193,083.81
626,193,083.81$62,980.82$46,448.13$16,532.69$6,176,551.13
636,176,551.13$62,980.82$46,324.13$16,656.68$6,159,894.44
646,159,894.44$62,980.82$46,199.21$16,781.61$6,143,112.83
656,143,112.83$62,980.82$46,073.35$16,907.47$6,126,205.36
666,126,205.36$62,980.82$45,946.54$17,034.28$6,109,171.09
676,109,171.09$62,980.82$45,818.78$17,162.03$6,092,009.05
686,092,009.05$62,980.82$45,690.07$17,290.75$6,074,718.30
696,074,718.30$62,980.82$45,560.39$17,420.43$6,057,297.87
706,057,297.87$62,980.82$45,429.73$17,551.08$6,039,746.79
716,039,746.79$62,980.82$45,298.10$17,682.72$6,022,064.08
726,022,064.08$62,980.82$45,165.48$17,815.34$6,004,248.74
736,004,248.74$62,980.82$45,031.87$17,948.95$5,986,299.79
745,986,299.79$62,980.82$44,897.25$18,083.57$5,968,216.22
755,968,216.22$62,980.82$44,761.62$18,219.20$5,949,997.02
765,949,997.02$62,980.82$44,624.98$18,355.84$5,931,641.18
775,931,641.18$62,980.82$44,487.31$18,493.51$5,913,147.68
785,913,147.68$62,980.82$44,348.61$18,632.21$5,894,515.47
795,894,515.47$62,980.82$44,208.87$18,771.95$5,875,743.52
805,875,743.52$62,980.82$44,068.08$18,912.74$5,856,830.78
815,856,830.78$62,980.82$43,926.23$19,054.59$5,837,776.19
825,837,776.19$62,980.82$43,783.32$19,197.50$5,818,578.69
835,818,578.69$62,980.82$43,639.34$19,341.48$5,799,237.22
845,799,237.22$62,980.82$43,494.28$19,486.54$5,779,750.68
855,779,750.68$62,980.82$43,348.13$19,632.69$5,760,117.99
865,760,117.99$62,980.82$43,200.88$19,779.93$5,740,338.06
875,740,338.06$62,980.82$43,052.54$19,928.28$5,720,409.78
885,720,409.78$62,980.82$42,903.07$20,077.74$5,700,332.04
895,700,332.04$62,980.82$42,752.49$20,228.33$5,680,103.71
905,680,103.71$62,980.82$42,600.78$20,380.04$5,659,723.67
915,659,723.67$62,980.82$42,447.93$20,532.89$5,639,190.78
925,639,190.78$62,980.82$42,293.93$20,686.89$5,618,503.89
935,618,503.89$62,980.82$42,138.78$20,842.04$5,597,661.86
945,597,661.86$62,980.82$41,982.46$20,998.35$5,576,663.50
955,576,663.50$62,980.82$41,824.98$21,155.84$5,555,507.66
965,555,507.66$62,980.82$41,666.31$21,314.51$5,534,193.15
975,534,193.15$62,980.82$41,506.45$21,474.37$5,512,718.79
985,512,718.79$62,980.82$41,345.39$21,635.43$5,491,083.36
995,491,083.36$62,980.82$41,183.13$21,797.69$5,469,285.67
1005,469,285.67$62,980.82$41,019.64$21,961.17$5,447,324.49
1015,447,324.49$62,980.82$40,854.93$22,125.88$5,425,198.61
1025,425,198.61$62,980.82$40,688.99$22,291.83$5,402,906.78
1035,402,906.78$62,980.82$40,521.80$22,459.02$5,380,447.77
1045,380,447.77$62,980.82$40,353.36$22,627.46$5,357,820.31
1055,357,820.31$62,980.82$40,183.65$22,797.16$5,335,023.14
1065,335,023.14$62,980.82$40,012.67$22,968.14$5,312,055.00
1075,312,055.00$62,980.82$39,840.41$23,140.40$5,288,914.60
1085,288,914.60$62,980.82$39,666.86$23,313.96$5,265,600.64
1095,265,600.64$62,980.82$39,492.00$23,488.81$5,242,111.83
1105,242,111.83$62,980.82$39,315.84$23,664.98$5,218,446.85
1115,218,446.85$62,980.82$39,138.35$23,842.47$5,194,604.38
1125,194,604.38$62,980.82$38,959.53$24,021.28$5,170,583.10
1135,170,583.10$62,980.82$38,779.37$24,201.44$5,146,381.65
1145,146,381.65$62,980.82$38,597.86$24,382.95$5,121,998.70
1155,121,998.70$62,980.82$38,414.99$24,565.83$5,097,432.87
1165,097,432.87$62,980.82$38,230.75$24,750.07$5,072,682.80
1175,072,682.80$62,980.82$38,045.12$24,935.70$5,047,747.11
1185,047,747.11$62,980.82$37,858.10$25,122.71$5,022,624.39
1195,022,624.39$62,980.82$37,669.68$25,311.13$4,997,313.26
1204,997,313.26$62,980.82$37,479.85$25,500.97$4,971,812.29
1214,971,812.29$62,980.82$37,288.59$25,692.22$4,946,120.07
1224,946,120.07$62,980.82$37,095.90$25,884.92$4,920,235.15
1234,920,235.15$62,980.82$36,901.76$26,079.05$4,894,156.10
1244,894,156.10$62,980.82$36,706.17$26,274.65$4,867,881.45
1254,867,881.45$62,980.82$36,509.11$26,471.71$4,841,409.75
1264,841,409.75$62,980.82$36,310.57$26,670.24$4,814,739.50
1274,814,739.50$62,980.82$36,110.55$26,870.27$4,787,869.23
1284,787,869.23$62,980.82$35,909.02$27,071.80$4,760,797.43
1294,760,797.43$62,980.82$35,705.98$27,274.84$4,733,522.60
1304,733,522.60$62,980.82$35,501.42$27,479.40$4,706,043.20
1314,706,043.20$62,980.82$35,295.32$27,685.49$4,678,357.71
1324,678,357.71$62,980.82$35,087.68$27,893.13$4,650,464.57
1334,650,464.57$62,980.82$34,878.48$28,102.33$4,622,362.24
1344,622,362.24$62,980.82$34,667.72$28,313.10$4,594,049.14
1354,594,049.14$62,980.82$34,455.37$28,525.45$4,565,523.69
1364,565,523.69$62,980.82$34,241.43$28,739.39$4,536,784.30
1374,536,784.30$62,980.82$34,025.88$28,954.93$4,507,829.37
1384,507,829.37$62,980.82$33,808.72$29,172.10$4,478,657.27
1394,478,657.27$62,980.82$33,589.93$29,390.89$4,449,266.38
1404,449,266.38$62,980.82$33,369.50$29,611.32$4,419,655.07
1414,419,655.07$62,980.82$33,147.41$29,833.40$4,389,821.66
1424,389,821.66$62,980.82$32,923.66$30,057.15$4,359,764.51
1434,359,764.51$62,980.82$32,698.23$30,282.58$4,329,481.92
1444,329,481.92$62,980.82$32,471.11$30,509.70$4,298,972.22
1454,298,972.22$62,980.82$32,242.29$30,738.53$4,268,233.70
1464,268,233.70$62,980.82$32,011.75$30,969.06$4,237,264.63
1474,237,264.63$62,980.82$31,779.48$31,201.33$4,206,063.30
1484,206,063.30$62,980.82$31,545.47$31,435.34$4,174,627.96
1494,174,627.96$62,980.82$31,309.71$31,671.11$4,142,956.85
1504,142,956.85$62,980.82$31,072.18$31,908.64$4,111,048.21
1514,111,048.21$62,980.82$30,832.86$32,147.96$4,078,900.25
1524,078,900.25$62,980.82$30,591.75$32,389.07$4,046,511.19
1534,046,511.19$62,980.82$30,348.83$32,631.98$4,013,879.21
1544,013,879.21$62,980.82$30,104.09$32,876.72$3,981,002.48
1553,981,002.48$62,980.82$29,857.52$33,123.30$3,947,879.19
1563,947,879.19$62,980.82$29,609.09$33,371.72$3,914,507.46
1573,914,507.46$62,980.82$29,358.81$33,622.01$3,880,885.45
1583,880,885.45$62,980.82$29,106.64$33,874.18$3,847,011.28
1593,847,011.28$62,980.82$28,852.58$34,128.23$3,812,883.04
1603,812,883.04$62,980.82$28,596.62$34,384.19$3,778,498.85
1613,778,498.85$62,980.82$28,338.74$34,642.08$3,743,856.77
1623,743,856.77$62,980.82$28,078.93$34,901.89$3,708,954.88
1633,708,954.88$62,980.82$27,817.16$35,163.66$3,673,791.23
1643,673,791.23$62,980.82$27,553.43$35,427.38$3,638,363.84
1653,638,363.84$62,980.82$27,287.73$35,693.09$3,602,670.76
1663,602,670.76$62,980.82$27,020.03$35,960.79$3,566,709.97
1673,566,709.97$62,980.82$26,750.32$36,230.49$3,530,479.48
1683,530,479.48$62,980.82$26,478.60$36,502.22$3,493,977.26
1693,493,977.26$62,980.82$26,204.83$36,775.99$3,457,201.27
1703,457,201.27$62,980.82$25,929.01$37,051.81$3,420,149.46
1713,420,149.46$62,980.82$25,651.12$37,329.70$3,382,819.77
1723,382,819.77$62,980.82$25,371.15$37,609.67$3,345,210.10
1733,345,210.10$62,980.82$25,089.08$37,891.74$3,307,318.36
1743,307,318.36$62,980.82$24,804.89$38,175.93$3,269,142.43
1753,269,142.43$62,980.82$24,518.57$38,462.25$3,230,680.18
1763,230,680.18$62,980.82$24,230.10$38,750.72$3,191,929.46
1773,191,929.46$62,980.82$23,939.47$39,041.35$3,152,888.12
1783,152,888.12$62,980.82$23,646.66$39,334.16$3,113,553.96
1793,113,553.96$62,980.82$23,351.65$39,629.16$3,073,924.80
1803,073,924.80$62,980.82$23,054.44$39,926.38$3,033,998.42
1813,033,998.42$62,980.82$22,754.99$40,225.83$2,993,772.59
1822,993,772.59$62,980.82$22,453.29$40,527.52$2,953,245.07
1832,953,245.07$62,980.82$22,149.34$40,831.48$2,912,413.59
1842,912,413.59$62,980.82$21,843.10$41,137.72$2,871,275.87
1852,871,275.87$62,980.82$21,534.57$41,446.25$2,829,829.62
1862,829,829.62$62,980.82$21,223.72$41,757.09$2,788,072.53
1872,788,072.53$62,980.82$20,910.54$42,070.27$2,746,002.26
1882,746,002.26$62,980.82$20,595.02$42,385.80$2,703,616.46
1892,703,616.46$62,980.82$20,277.12$42,703.69$2,660,912.76
1902,660,912.76$62,980.82$19,956.85$43,023.97$2,617,888.79
1912,617,888.79$62,980.82$19,634.17$43,346.65$2,574,542.14
1922,574,542.14$62,980.82$19,309.07$43,671.75$2,530,870.39
1932,530,870.39$62,980.82$18,981.53$43,999.29$2,486,871.10
1942,486,871.10$62,980.82$18,651.53$44,329.28$2,442,541.82
1952,442,541.82$62,980.82$18,319.06$44,661.75$2,397,880.06
1962,397,880.06$62,980.82$17,984.10$44,996.72$2,352,883.35
1972,352,883.35$62,980.82$17,646.63$45,334.19$2,307,549.16
1982,307,549.16$62,980.82$17,306.62$45,674.20$2,261,874.96
1992,261,874.96$62,980.82$16,964.06$46,016.75$2,215,858.20
2002,215,858.20$62,980.82$16,618.94$46,361.88$2,169,496.32
2012,169,496.32$62,980.82$16,271.22$46,709.59$2,122,786.73
2022,122,786.73$62,980.82$15,920.90$47,059.92$2,075,726.81
2032,075,726.81$62,980.82$15,567.95$47,412.87$2,028,313.95
2042,028,313.95$62,980.82$15,212.35$47,768.46$1,980,545.48
2051,980,545.48$62,980.82$14,854.09$48,126.73$1,932,418.76
2061,932,418.76$62,980.82$14,493.14$48,487.68$1,883,931.08
2071,883,931.08$62,980.82$14,129.48$48,851.33$1,835,079.75
2081,835,079.75$62,980.82$13,763.10$49,217.72$1,785,862.03
2091,785,862.03$62,980.82$13,393.97$49,586.85$1,736,275.18
2101,736,275.18$62,980.82$13,022.06$49,958.75$1,686,316.42
2111,686,316.42$62,980.82$12,647.37$50,333.44$1,635,982.98
2121,635,982.98$62,980.82$12,269.87$50,710.94$1,585,272.04
2131,585,272.04$62,980.82$11,889.54$51,091.28$1,534,180.76
2141,534,180.76$62,980.82$11,506.36$51,474.46$1,482,706.30
2151,482,706.30$62,980.82$11,120.30$51,860.52$1,430,845.78
2161,430,845.78$62,980.82$10,731.34$52,249.47$1,378,596.31
2171,378,596.31$62,980.82$10,339.47$52,641.34$1,325,954.96
2181,325,954.96$62,980.82$9,944.66$53,036.15$1,272,918.81
2191,272,918.81$62,980.82$9,546.89$53,433.93$1,219,484.88
2201,219,484.88$62,980.82$9,146.14$53,834.68$1,165,650.20
2211,165,650.20$62,980.82$8,742.38$54,238.44$1,111,411.76
2221,111,411.76$62,980.82$8,335.59$54,645.23$1,056,766.53
2231,056,766.53$62,980.82$7,925.75$55,055.07$1,001,711.46
2241,001,711.46$62,980.82$7,512.84$55,467.98$946,243.48
225946,243.48$62,980.82$7,096.83$55,883.99$890,359.49
226890,359.49$62,980.82$6,677.70$56,303.12$834,056.37
227834,056.37$62,980.82$6,255.42$56,725.39$777,330.98
228777,330.98$62,980.82$5,829.98$57,150.83$720,180.14
229720,180.14$62,980.82$5,401.35$57,579.47$662,600.68
230662,600.68$62,980.82$4,969.51$58,011.31$604,589.36
231604,589.36$62,980.82$4,534.42$58,446.40$546,142.97
232546,142.97$62,980.82$4,096.07$58,884.74$487,258.22
233487,258.22$62,980.82$3,654.44$59,326.38$427,931.84
234427,931.84$62,980.82$3,209.49$59,771.33$368,160.51
235368,160.51$62,980.82$2,761.20$60,219.61$307,940.90
236307,940.90$62,980.82$2,309.56$60,671.26$247,269.64
237247,269.64$62,980.82$1,854.52$61,126.29$186,143.35
238186,143.35$62,980.82$1,396.08$61,584.74$124,558.60
239124,558.60$62,980.82$934.19$62,046.63$62,511.98
24062,511.98$62,980.82$468.84$62,511.98$0.00
(Present values)(discount)
3510,000,0006.75%
1.PV PVFV/(1+i)^nC45C32/(1+C33)^C342.PV a.PV(,,,) D45-PV(C33,C34,,C32) b. /PV/
Excel1. a. TableC68G68Payment 1000C68$C$49D68G68 b.PV Factor=100%/(1+i)^nB69100%C69PV Factor$B$69/(1+$C$48)^C67D69G69 c.PV of Payment=Payment*PV FactorC70C68*C69 D70G70 d.B71SUM(B70G70)
2.Excel a.PV=(,,) B72-PV(C48,C50,C49) b. /PV/
E88:E92F87B72E87:F92C48
E96:E100F95B72E95:F100C49
E105:E109F104B72E104:F109C50
A119:A124B118:F118A118B72A118:F124C48C50
B119:F124XY3%,5%,8%,10%,12%XY
Present Values
Step1
Step2
Sensitivity analysis
1.L12L7M12=L12*$L$5N12=-$L$6O12=SUM(L12:N12)2.L13=O12M12M13N12N13O12O133.L13O1316
1.F41=B34B42=F41C42 =$B$37D42=B42*$B$36 E42=C42-D42F42B42-E42 2.B42F42281 240
20240
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interest paid
principal paid
HOMEWORKS
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1.()XY 2.A42A281D42D281E42E281 InterestPrincipal paid 3.XY/
Amortization Table
$1,000,0008%20$50,000
1-4"3510,000,0006.75%"1. 1-3510,000,0006.75% 2. 3. 4.
1.
MBD00490F5E.unknown
MBD00FB503C.unknown
MBD00B8B376.unknown