Time Value of Money
Time Value of Money
Understanding the time value of money is essential to finance. The value of something is not a static but dynamic thing. Dating back as far as 5000 BC, this concept is the foundation of modern day finance (https://www.encyclopedia.com/finance/encyclopedias-almanacs-transcripts-and-maps/time-value-money). Thankfully R makes calculations for TVM easy and efficient. TVM calculations are broken down into 4 topicsL Future Value, Present Value, Rates of Return and Amortization.
#install.packages("modelr")
#install.packages("FinCal")
#install.packages("dplyr")
#install.packages("FinancialMath")
library("modelr")
library("FinCal")
library("dplyr")
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library("FinancialMath")
library("ggplot2")
Future Value and Present Value
#Below is random cash flow data I have added for these exercises. We are going to assume our invesment period is 8 years, interest is 10%, and this is an ordinary annunity
cash_flow <- c(-10023,-84949,-84940,-83838,-93838,-73839,-83383,-102939)
i = 1.10
#Manual calculation of FV
(cash_flow[1] * i ^ 7) + (cash_flow[2] * i ^ 6) + (cash_flow[3] * i ^ 5) + (cash_flow[4] * i ^ 4) + (cash_flow[5] * i ^ 3) + (cash_flow[6] * i ^ 2) + (cash_flow[7] * i ^ 1) + (cash_flow[8])
## [1] -838472.1
#R makes this calculation much easier
fv.uneven(.1,cash_flow)
## [1] 838472.1
#FV of Annuity Due. Int = 10%, T = 8, type = 1 which means payment at the beginning of each period
fv(.10,8,pv = 0, pmt = 1000, 1)
## [1] -12579.48
#Manual Calculation of PV
(cash_flow[1]/ (i) ^ 1) + (cash_flow[2] / i ^ 2) + (cash_flow[3] / i ^ 3) + (cash_flow[4] / i ^ 4) + (cash_flow[5] / i ^ 5) + (cash_flow[6] / i ^ 6) + (cash_flow[7] / i ^ 7) + (cash_flow[8]
/ i ^ 8)
## [1] -391153.4
#Again R makes PV calculation easier
pv.uneven(.1, cash_flow)
## [1] 391153.4
#PV of Annuity Due. Int = 10%, T = 8, type = 1 which means payment at the beginning of each period
pv(.1,8, fv = 0, pmt = 1000, type = 1)
## [1] -5868.419
Rates of Return
#Calculating Rates of Return in R
FV = 149374838
PV = 84933
N = 89
M = 4 # number of compounding periods
Iper = .1
#Calculating annualized returns manually. Couldnt find a function for this in R
return = (FV/PV) ^ 1/N - 1
return
## [1] 18.76109
#Finding the EAR.
EAR = (1 + Iper/M)^M - 1
EAR
## [1] 0.1038129
#Amortization Tablesin R
#Add Numbers to Values to Quick Calculations
FV = 0
PV = 300000
N = 30
M = 12 # frequency of payments per year
Iper = .023
#Step 1 find the PMT
PMT = -pmt(Iper/M,N*M,PV,FV,type = 0)
PMT
## [1] 1154.404
#Step 2 create the data frame
Amort <- data.frame(payment = 1:360)
#Step 3 assign beginning value to start loop
Amort[1,2] <- PV
#Step 4 Create for loop to fill in amortization table
for(i in 1:360){ #number of periods is 360
Amort[i,3] <- Amort[i,2] * Iper/12 #Interest Paid is Beginning Balance x Interest Rate
Amort[i,4] <- PMT - Amort[i,3] #Priciple Paid is equal to the Payment minus Interest Paid
Amort[i,5] <- Amort[i,2] - Amort[i,4] #Ending Balance is equal to the Beginning Balance minus the Principle Paid
Amort[i + 1,2]<- Amort[i,5] #Assign Beginning Balance as last payments Ending Balance
}
#Add column names
names(Amort)[2]<- 'Beginning Balance'
names(Amort)[3]<- 'Interest Paid'
names(Amort)[4]<- 'Principle Paid'
names(Amort)[5]<- 'Ending Balance'
#View the finished table
head(Amort)
## payment Beginning Balance Interest Paid Principle Paid Ending Balance
## 1 1 300000.0 575.0000 579.4039 299420.6
## 2 2 299420.6 573.8895 580.5144 298840.1
## 3 3 298840.1 572.7768 581.6270 298258.5
## 4 4 298258.5 571.6620 582.7418 297675.7
## 5 5 297675.7 570.5451 583.8588 297091.9
## 6 6 297091.9 569.4261 584.9778 296506.9
#I created this amortization using a for loop, but fortunately R has a package for this
#Amort.table function in R
amort_table <- amort.table(Loan=PV,n=360,i=Iper,ic=12,pf=12)
head(amort_table["Schedule"], n = 10L)
## $Schedule
## Year Payment Interest Paid Principal Paid Balance
## 1 0.08 1154.4 575.00 579.40 299420.60
## 2 0.17 1154.4 573.89 580.51 298840.08
## 3 0.25 1154.4 572.78 581.63 298258.45
## 4 0.33 1154.4 571.66 582.74 297675.71
## 5 0.42 1154.4 570.55 583.86 297091.85
## 6 0.50 1154.4 569.43 584.98 296506.88
## 7 0.58 1154.4 568.30 586.10 295920.78
## 8 0.67 1154.4 567.18 587.22 295333.55
## 9 0.75 1154.4 566.06 588.35 294745.21
## 10 0.83 1154.4 564.93 589.48 294155.73
## 11 0.92 1154.4 563.80 590.61 293565.13
## 12 1.00 1154.4 562.67 591.74 292973.39
## 13 1.08 1154.4 561.53 592.87 292380.52
## 14 1.17 1154.4 560.40 594.01 291786.51
## 15 1.25 1154.4 559.26 595.15 291191.36
## 16 1.33 1154.4 558.12 596.29 290595.08
## 17 1.42 1154.4 556.97 597.43 289997.65
## 18 1.50 1154.4 555.83 598.58 289399.07
## 19 1.58 1154.4 554.68 599.72 288799.35
## 20 1.67 1154.4 553.53 600.87 288198.48
## 21 1.75 1154.4 552.38 602.02 287596.45
## 22 1.83 1154.4 551.23 603.18 286993.28
## 23 1.92 1154.4 550.07 604.33 286388.94
## 24 2.00 1154.4 548.91 605.49 285783.45
## 25 2.08 1154.4 547.75 606.65 285176.80
## 26 2.17 1154.4 546.59 607.82 284568.98
## 27 2.25 1154.4 545.42 608.98 283960.00
## 28 2.33 1154.4 544.26 610.15 283349.86
## 29 2.42 1154.4 543.09 611.32 282738.54
## 30 2.50 1154.4 541.92 612.49 282126.05
## 31 2.58 1154.4 540.74 613.66 281512.39
## 32 2.67 1154.4 539.57 614.84 280897.55
## 33 2.75 1154.4 538.39 616.02 280281.53
## 34 2.83 1154.4 537.21 617.20 279664.34
## 35 2.92 1154.4 536.02 618.38 279045.96
## 36 3.00 1154.4 534.84 619.57 278426.39
## 37 3.08 1154.4 533.65 620.75 277805.64
## 38 3.17 1154.4 532.46 621.94 277183.69
## 39 3.25 1154.4 531.27 623.14 276560.56
## 40 3.33 1154.4 530.07 624.33 275936.23
## 41 3.42 1154.4 528.88 625.53 275310.70
## 42 3.50 1154.4 527.68 626.73 274683.98
## 43 3.58 1154.4 526.48 627.93 274056.05
## 44 3.67 1154.4 525.27 629.13 273426.92
## 45 3.75 1154.4 524.07 630.34 272796.59
## 46 3.83 1154.4 522.86 631.54 272165.04
## 47 3.92 1154.4 521.65 632.75 271532.29
## 48 4.00 1154.4 520.44 633.97 270898.32
## 49 4.08 1154.4 519.22 635.18 270263.14
## 50 4.17 1154.4 518.00 636.40 269626.74
## 51 4.25 1154.4 516.78 637.62 268989.12
## 52 4.33 1154.4 515.56 638.84 268350.28
## 53 4.42 1154.4 514.34 640.07 267710.21
## 54 4.50 1154.4 513.11 641.29 267068.92
## 55 4.58 1154.4 511.88 642.52 266426.40
## 56 4.67 1154.4 510.65 643.75 265782.65
## 57 4.75 1154.4 509.42 644.99 265137.66
## 58 4.83 1154.4 508.18 646.22 264491.43
## 59 4.92 1154.4 506.94 647.46 263843.97
## 60 5.00 1154.4 505.70 648.70 263195.27
## 61 5.08 1154.4 504.46 649.95 262545.32
## 62 5.17 1154.4 503.21 651.19 261894.13
## 63 5.25 1154.4 501.96 652.44 261241.69
## 64 5.33 1154.4 500.71 653.69 260588.00
## 65 5.42 1154.4 499.46 654.94 259933.06
## 66 5.50 1154.4 498.21 656.20 259276.86
## 67 5.58 1154.4 496.95 657.46 258619.40
## 68 5.67 1154.4 495.69 658.72 257960.69
## 69 5.75 1154.4 494.42 659.98 257300.71
## 70 5.83 1154.4 493.16 661.24 256639.46
## 71 5.92 1154.4 491.89 662.51 255976.95
## 72 6.00 1154.4 490.62 663.78 255313.17
## 73 6.08 1154.4 489.35 665.05 254648.12
## 74 6.17 1154.4 488.08 666.33 253981.79
## 75 6.25 1154.4 486.80 667.61 253314.18
## 76 6.33 1154.4 485.52 668.89 252645.30
## 77 6.42 1154.4 484.24 670.17 251975.13
## 78 6.50 1154.4 482.95 671.45 251303.68
## 79 6.58 1154.4 481.67 672.74 250630.94
## 80 6.67 1154.4 480.38 674.03 249956.91
## 81 6.75 1154.4 479.08 675.32 249281.59
## 82 6.83 1154.4 477.79 676.61 248604.98
## 83 6.92 1154.4 476.49 677.91 247927.07
## 84 7.00 1154.4 475.19 679.21 247247.86
## 85 7.08 1154.4 473.89 680.51 246567.34
## 86 7.17 1154.4 472.59 681.82 245885.53
## 87 7.25 1154.4 471.28 683.12 245202.40
## 88 7.33 1154.4 469.97 684.43 244517.97
## 89 7.42 1154.4 468.66 685.74 243832.23
## 90 7.50 1154.4 467.35 687.06 243145.17
## 91 7.58 1154.4 466.03 688.38 242456.79
## 92 7.67 1154.4 464.71 689.70 241767.10
## 93 7.75 1154.4 463.39 691.02 241076.08
## 94 7.83 1154.4 462.06 692.34 240383.74
## 95 7.92 1154.4 460.74 693.67 239690.07
## 96 8.00 1154.4 459.41 695.00 238995.07
## 97 8.08 1154.4 458.07 696.33 238298.74
## 98 8.17 1154.4 456.74 697.66 237601.08
## 99 8.25 1154.4 455.40 699.00 236902.08
## 100 8.33 1154.4 454.06 700.34 236201.74
## 101 8.42 1154.4 452.72 701.68 235500.05
## 102 8.50 1154.4 451.38 703.03 234797.02
## 103 8.58 1154.4 450.03 704.38 234092.65
## 104 8.67 1154.4 448.68 705.73 233386.92
## 105 8.75 1154.4 447.32 707.08 232679.84
## 106 8.83 1154.4 445.97 708.43 231971.41
## 107 8.92 1154.4 444.61 709.79 231261.61
## 108 9.00 1154.4 443.25 711.15 230550.46
## 109 9.08 1154.4 441.89 712.52 229837.95
## 110 9.17 1154.4 440.52 713.88 229124.07
## 111 9.25 1154.4 439.15 715.25 228408.82
## 112 9.33 1154.4 437.78 716.62 227692.20
## 113 9.42 1154.4 436.41 717.99 226974.20
## 114 9.50 1154.4 435.03 719.37 226254.83
## 115 9.58 1154.4 433.66 720.75 225534.08
## 116 9.67 1154.4 432.27 722.13 224811.95
## 117 9.75 1154.4 430.89 723.51 224088.44
## 118 9.83 1154.4 429.50 724.90 223363.54
## 119 9.92 1154.4 428.11 726.29 222637.25
## 120 10.00 1154.4 426.72 727.68 221909.57
## 121 10.08 1154.4 425.33 729.08 221180.49
## 122 10.17 1154.4 423.93 730.47 220450.01
## 123 10.25 1154.4 422.53 731.87 219718.14
## 124 10.33 1154.4 421.13 733.28 218984.86
## 125 10.42 1154.4 419.72 734.68 218250.18
## 126 10.50 1154.4 418.31 736.09 217514.09
## 127 10.58 1154.4 416.90 737.50 216776.59
## 128 10.67 1154.4 415.49 738.92 216037.67
## 129 10.75 1154.4 414.07 740.33 215297.34
## 130 10.83 1154.4 412.65 741.75 214555.59
## 131 10.92 1154.4 411.23 743.17 213812.42
## 132 11.00 1154.4 409.81 744.60 213067.82
## 133 11.08 1154.4 408.38 746.02 212321.79
## 134 11.17 1154.4 406.95 747.45 211574.34
## 135 11.25 1154.4 405.52 748.89 210825.45
## 136 11.33 1154.4 404.08 750.32 210075.13
## 137 11.42 1154.4 402.64 751.76 209323.37
## 138 11.50 1154.4 401.20 753.20 208570.17
## 139 11.58 1154.4 399.76 754.64 207815.53
## 140 11.67 1154.4 398.31 756.09 207059.44
## 141 11.75 1154.4 396.86 757.54 206301.90
## 142 11.83 1154.4 395.41 758.99 205542.91
## 143 11.92 1154.4 393.96 760.45 204782.46
## 144 12.00 1154.4 392.50 761.90 204020.55
## 145 12.08 1154.4 391.04 763.36 203257.19
## 146 12.17 1154.4 389.58 764.83 202492.36
## 147 12.25 1154.4 388.11 766.29 201726.07
## 148 12.33 1154.4 386.64 767.76 200958.31
## 149 12.42 1154.4 385.17 769.23 200189.07
## 150 12.50 1154.4 383.70 770.71 199418.36
## 151 12.58 1154.4 382.22 772.19 198646.18
## 152 12.67 1154.4 380.74 773.67 197872.51
## 153 12.75 1154.4 379.26 775.15 197097.37
## 154 12.83 1154.4 377.77 776.63 196320.73
## 155 12.92 1154.4 376.28 778.12 195542.61
## 156 13.00 1154.4 374.79 779.61 194763.00
## 157 13.08 1154.4 373.30 781.11 193981.89
## 158 13.17 1154.4 371.80 782.61 193199.28
## 159 13.25 1154.4 370.30 784.11 192415.18
## 160 13.33 1154.4 368.80 785.61 191629.57
## 161 13.42 1154.4 367.29 787.11 190842.45
## 162 13.50 1154.4 365.78 788.62 190053.83
## 163 13.58 1154.4 364.27 790.13 189263.70
## 164 13.67 1154.4 362.76 791.65 188472.05
## 165 13.75 1154.4 361.24 793.17 187678.88
## 166 13.83 1154.4 359.72 794.69 186884.20
## 167 13.92 1154.4 358.19 796.21 186087.99
## 168 14.00 1154.4 356.67 797.74 185290.25
## 169 14.08 1154.4 355.14 799.26 184490.99
## 170 14.17 1154.4 353.61 800.80 183690.19
## 171 14.25 1154.4 352.07 802.33 182887.86
## 172 14.33 1154.4 350.54 803.87 182083.99
## 173 14.42 1154.4 348.99 805.41 181278.58
## 174 14.50 1154.4 347.45 806.95 180471.63
## 175 14.58 1154.4 345.90 808.50 179663.13
## 176 14.67 1154.4 344.35 810.05 178853.08
## 177 14.75 1154.4 342.80 811.60 178041.48
## 178 14.83 1154.4 341.25 813.16 177228.32
## 179 14.92 1154.4 339.69 814.72 176413.61
## 180 15.00 1154.4 338.13 816.28 175597.33
## 181 15.08 1154.4 336.56 817.84 174779.49
## 182 15.17 1154.4 334.99 819.41 173960.08
## 183 15.25 1154.4 333.42 820.98 173139.09
## 184 15.33 1154.4 331.85 822.55 172316.54
## 185 15.42 1154.4 330.27 824.13 171492.41
## 186 15.50 1154.4 328.69 825.71 170666.70
## 187 15.58 1154.4 327.11 827.29 169839.41
## 188 15.67 1154.4 325.53 828.88 169010.53
## 189 15.75 1154.4 323.94 830.47 168180.06
## 190 15.83 1154.4 322.35 832.06 167348.00
## 191 15.92 1154.4 320.75 833.65 166514.35
## 192 16.00 1154.4 319.15 835.25 165679.10
## 193 16.08 1154.4 317.55 836.85 164842.25
## 194 16.17 1154.4 315.95 838.46 164003.79
## 195 16.25 1154.4 314.34 840.06 163163.73
## 196 16.33 1154.4 312.73 841.67 162322.05
## 197 16.42 1154.4 311.12 843.29 161478.77
## 198 16.50 1154.4 309.50 844.90 160633.86
## 199 16.58 1154.4 307.88 846.52 159787.34
## 200 16.67 1154.4 306.26 848.14 158939.20
## 201 16.75 1154.4 304.63 849.77 158089.43
## 202 16.83 1154.4 303.00 851.40 157238.03
## 203 16.92 1154.4 301.37 853.03 156385.00
## 204 17.00 1154.4 299.74 854.67 155530.33
## 205 17.08 1154.4 298.10 856.30 154674.03
## 206 17.17 1154.4 296.46 857.95 153816.08
## 207 17.25 1154.4 294.81 859.59 152956.49
## 208 17.33 1154.4 293.17 861.24 152095.25
## 209 17.42 1154.4 291.52 862.89 151232.37
## 210 17.50 1154.4 289.86 864.54 150367.82
## 211 17.58 1154.4 288.20 866.20 149501.63
## 212 17.67 1154.4 286.54 867.86 148633.77
## 213 17.75 1154.4 284.88 869.52 147764.24
## 214 17.83 1154.4 283.21 871.19 146893.05
## 215 17.92 1154.4 281.55 872.86 146020.20
## 216 18.00 1154.4 279.87 874.53 145145.66
## 217 18.08 1154.4 278.20 876.21 144269.46
## 218 18.17 1154.4 276.52 877.89 143391.57
## 219 18.25 1154.4 274.83 879.57 142512.00
## 220 18.33 1154.4 273.15 881.26 141630.74
## 221 18.42 1154.4 271.46 882.94 140747.80
## 222 18.50 1154.4 269.77 884.64 139863.16
## 223 18.58 1154.4 268.07 886.33 138976.83
## 224 18.67 1154.4 266.37 888.03 138088.80
## 225 18.75 1154.4 264.67 889.73 137199.06
## 226 18.83 1154.4 262.96 891.44 136307.62
## 227 18.92 1154.4 261.26 893.15 135414.48
## 228 19.00 1154.4 259.54 894.86 134519.62
## 229 19.08 1154.4 257.83 896.57 133623.04
## 230 19.17 1154.4 256.11 898.29 132724.75
## 231 19.25 1154.4 254.39 900.01 131824.73
## 232 19.33 1154.4 252.66 901.74 130922.99
## 233 19.42 1154.4 250.94 903.47 130019.53
## 234 19.50 1154.4 249.20 905.20 129114.33
## 235 19.58 1154.4 247.47 906.93 128207.39
## 236 19.67 1154.4 245.73 908.67 127298.72
## 237 19.75 1154.4 243.99 910.41 126388.30
## 238 19.83 1154.4 242.24 912.16 125476.14
## 239 19.92 1154.4 240.50 913.91 124562.24
## 240 20.00 1154.4 238.74 915.66 123646.58
## 241 20.08 1154.4 236.99 917.41 122729.16
## 242 20.17 1154.4 235.23 919.17 121809.99
## 243 20.25 1154.4 233.47 920.93 120889.05
## 244 20.33 1154.4 231.70 922.70 119966.35
## 245 20.42 1154.4 229.94 924.47 119041.89
## 246 20.50 1154.4 228.16 926.24 118115.65
## 247 20.58 1154.4 226.39 928.02 117187.63
## 248 20.67 1154.4 224.61 929.79 116257.84
## 249 20.75 1154.4 222.83 931.58 115326.26
## 250 20.83 1154.4 221.04 933.36 114392.90
## 251 20.92 1154.4 219.25 935.15 113457.75
## 252 21.00 1154.4 217.46 936.94 112520.80
## 253 21.08 1154.4 215.66 938.74 111582.06
## 254 21.17 1154.4 213.87 940.54 110641.53
## 255 21.25 1154.4 212.06 942.34 109699.19
## 256 21.33 1154.4 210.26 944.15 108755.04
## 257 21.42 1154.4 208.45 945.96 107809.08
## 258 21.50 1154.4 206.63 947.77 106861.31
## 259 21.58 1154.4 204.82 949.59 105911.73
## 260 21.67 1154.4 203.00 951.41 104960.32
## 261 21.75 1154.4 201.17 953.23 104007.09
## 262 21.83 1154.4 199.35 955.06 103052.03
## 263 21.92 1154.4 197.52 956.89 102095.14
## 264 22.00 1154.4 195.68 958.72 101136.42
## 265 22.08 1154.4 193.84 960.56 100175.86
## 266 22.17 1154.4 192.00 962.40 99213.46
## 267 22.25 1154.4 190.16 964.24 98249.22
## 268 22.33 1154.4 188.31 966.09 97283.13
## 269 22.42 1154.4 186.46 967.94 96315.18
## 270 22.50 1154.4 184.60 969.80 95345.38
## 271 22.58 1154.4 182.75 971.66 94373.72
## 272 22.67 1154.4 180.88 973.52 93400.20
## 273 22.75 1154.4 179.02 975.39 92424.82
## 274 22.83 1154.4 177.15 977.26 91447.56
## 275 22.92 1154.4 175.27 979.13 90468.43
## 276 23.00 1154.4 173.40 981.01 89487.42
## 277 23.08 1154.4 171.52 982.89 88504.54
## 278 23.17 1154.4 169.63 984.77 87519.77
## 279 23.25 1154.4 167.75 986.66 86533.11
## 280 23.33 1154.4 165.86 988.55 85544.56
## 281 23.42 1154.4 163.96 990.44 84554.12
## 282 23.50 1154.4 162.06 992.34 83561.78
## 283 23.58 1154.4 160.16 994.24 82567.53
## 284 23.67 1154.4 158.25 996.15 81571.38
## 285 23.75 1154.4 156.35 998.06 80573.32
## 286 23.83 1154.4 154.43 999.97 79573.35
## 287 23.92 1154.4 152.52 1001.89 78571.46
## 288 24.00 1154.4 150.60 1003.81 77567.66
## 289 24.08 1154.4 148.67 1005.73 76561.92
## 290 24.17 1154.4 146.74 1007.66 75554.26
## 291 24.25 1154.4 144.81 1009.59 74544.67
## 292 24.33 1154.4 142.88 1011.53 73533.14
## 293 24.42 1154.4 140.94 1013.47 72519.68
## 294 24.50 1154.4 139.00 1015.41 71504.27
## 295 24.58 1154.4 137.05 1017.35 70486.92
## 296 24.67 1154.4 135.10 1019.30 69467.61
## 297 24.75 1154.4 133.15 1021.26 68446.36
## 298 24.83 1154.4 131.19 1023.22 67423.14
## 299 24.92 1154.4 129.23 1025.18 66397.96
## 300 25.00 1154.4 127.26 1027.14 65370.82
## 301 25.08 1154.4 125.29 1029.11 64341.71
## 302 25.17 1154.4 123.32 1031.08 63310.63
## 303 25.25 1154.4 121.35 1033.06 62277.57
## 304 25.33 1154.4 119.37 1035.04 61242.53
## 305 25.42 1154.4 117.38 1037.02 60205.51
## 306 25.50 1154.4 115.39 1039.01 59166.50
## 307 25.58 1154.4 113.40 1041.00 58125.50
## 308 25.67 1154.4 111.41 1043.00 57082.50
## 309 25.75 1154.4 109.41 1045.00 56037.51
## 310 25.83 1154.4 107.41 1047.00 54990.51
## 311 25.92 1154.4 105.40 1049.01 53941.50
## 312 26.00 1154.4 103.39 1051.02 52890.49
## 313 26.08 1154.4 101.37 1053.03 51837.46
## 314 26.17 1154.4 99.36 1055.05 50782.41
## 315 26.25 1154.4 97.33 1057.07 49725.34
## 316 26.33 1154.4 95.31 1059.10 48666.24
## 317 26.42 1154.4 93.28 1061.13 47605.11
## 318 26.50 1154.4 91.24 1063.16 46541.95
## 319 26.58 1154.4 89.21 1065.20 45476.76
## 320 26.67 1154.4 87.16 1067.24 44409.52
## 321 26.75 1154.4 85.12 1069.29 43340.23
## 322 26.83 1154.4 83.07 1071.34 42268.89
## 323 26.92 1154.4 81.02 1073.39 41195.51
## 324 27.00 1154.4 78.96 1075.45 40120.06
## 325 27.08 1154.4 76.90 1077.51 39042.55
## 326 27.17 1154.4 74.83 1079.57 37962.98
## 327 27.25 1154.4 72.76 1081.64 36881.34
## 328 27.33 1154.4 70.69 1083.71 35797.62
## 329 27.42 1154.4 68.61 1085.79 34711.83
## 330 27.50 1154.4 66.53 1087.87 33623.96
## 331 27.58 1154.4 64.45 1089.96 32534.00
## 332 27.67 1154.4 62.36 1092.05 31441.95
## 333 27.75 1154.4 60.26 1094.14 30347.81
## 334 27.83 1154.4 58.17 1096.24 29251.58
## 335 27.92 1154.4 56.07 1098.34 28153.24
## 336 28.00 1154.4 53.96 1100.44 27052.80
## 337 28.08 1154.4 51.85 1102.55 25950.24
## 338 28.17 1154.4 49.74 1104.67 24845.58
## 339 28.25 1154.4 47.62 1106.78 23738.79
## 340 28.33 1154.4 45.50 1108.90 22629.89
## 341 28.42 1154.4 43.37 1111.03 21518.86
## 342 28.50 1154.4 41.24 1113.16 20405.70
## 343 28.58 1154.4 39.11 1115.29 19290.41
## 344 28.67 1154.4 36.97 1117.43 18172.98
## 345 28.75 1154.4 34.83 1119.57 17053.40
## 346 28.83 1154.4 32.69 1121.72 15931.69
## 347 28.92 1154.4 30.54 1123.87 14807.82
## 348 29.00 1154.4 28.38 1126.02 13681.80
## 349 29.08 1154.4 26.22 1128.18 12553.62
## 350 29.17 1154.4 24.06 1130.34 11423.27
## 351 29.25 1154.4 21.89 1132.51 10290.76
## 352 29.33 1154.4 19.72 1134.68 9156.08
## 353 29.42 1154.4 17.55 1136.85 8019.23
## 354 29.50 1154.4 15.37 1139.03 6880.19
## 355 29.58 1154.4 13.19 1141.22 5738.98
## 356 29.67 1154.4 11.00 1143.40 4595.57
## 357 29.75 1154.4 8.81 1145.60 3449.98
## 358 29.83 1154.4 6.61 1147.79 2302.19
## 359 29.92 1154.4 4.41 1149.99 1152.20
## 360 30.00 1154.4 2.21 1152.20 0.00
amort_schedule <- as.data.frame(amort_table["Schedule"])
amort_schedule$period <- c(1:360)
#From graph,
ggplot(data = amort_schedule, aes(x = period, y = Schedule.Principal.Paid)) +
geom_bar(stat = "identity", color="blue") +
labs (title = "Amount of Priciple Paid Over Life of Loan", x = "Payment Period", y = "Dollars")