Question

Two friends, Kyle and Wes, graduated college and started working on their career at the same time. Both friends were 25 at the time. As soon as Kyle was eligible for the 401K benefit he started depositing $100 per month for the next ten years. Wes decided he so enjoyed having a real income that he wanted to spend it on fast cars, awesome threads, the most recent smart phone and video game system, and clubbing every weekend. Wes chose not to invest in his 401K for a while. After ten years, Kyle decided to buy a house and couldn't afford to invest in his 401K anymore, so he stopped with his $100 per month deposit, but never touched his balance. After ten years, Wes's party days were slowing down, he no longer needed the fancy clothes, and didn't need the newest gadgets as much, so he started investing $100 per month in his 401K for the next twenty years. Both friends averaged 8% over the life of their investment in a mixed mutual fund. At age 55, the friends decided to see where they stood for retirement savings.

Calculate the following:

1. How much did each friend invest in their 401K (no interest, just $100 X number of months invested).

2. How much will Kyle have after 10 years of investing $100/month at 8%?

3. Since Kyle is going to leave his balance after ten years remain in the account and accumulate interest, what will be his balance after 20 more years. HINT: Lump sum using balance after ten years for a twenty year term.

4. How much did Kyle’s investment grow in those twenty years with no additional investment?

5. What is Wes' total investment after investing $100 per month for 20 years?

6. Who has the higher balance?

7. What does this tell us about the time value of money?

Answer 1

1. Kyle total Investment - $100*10 years *12 Months = 12000$
Wes total Investment - $100*20 Years *12 Months = 24000$
2. After ten year Kyle have : 18416.57
here is the Calculation -
Month Before Interest   Interest Total
1   100.00   0.67   100.67
2   200.67   1.34   202.00
3   302.00   2.01   304.02
4   404.02   2.69   406.71
5   506.71   3.38   510.09
6   610.09   4.07   614.16
7   714.16   4.76   718.92
8   818.92   5.46   824.38
9   924.38   6.16   930.54
10   1,030.54   6.87   1,037.41
11   1,137.41   7.58   1,144.99
12   1,244.99   8.30   1,253.29
13   1,353.29   9.02   1,362.31
14   1,462.31   9.75   1,472.06
15   1,572.06   10.48   1,582.54
16   1,682.54   11.22   1,693.76
17   1,793.76   11.96   1,805.72
18   1,905.72   12.70   1,918.42
19   2,018.42   13.46   2,031.88
20   2,131.88   14.21   2,146.09
21   2,246.09   14.97   2,261.07
22   2,361.07   15.74   2,376.81
23   2,476.81   16.51   2,493.32
24   2,593.32   17.29   2,610.61
25   2,710.61   18.07   2,728.68
26   2,828.68   18.86   2,847.54
27   2,947.54   19.65   2,967.19
28   3,067.19   20.45   3,087.63
29   3,187.63   21.25   3,208.89
30   3,308.89   22.06   3,330.94
31   3,430.94   22.87   3,453.82
32   3,553.82   23.69   3,577.51
33   3,677.51   24.52   3,702.03
34   3,802.03   25.35   3,827.37
35   3,927.37   26.18   3,953.56
36   4,053.56   27.02   4,080.58
37   4,180.58   27.87   4,208.45
38   4,308.45   28.72   4,337.17
39   4,437.17   29.58   4,466.75
40   4,566.75   30.45   4,597.20
41   4,697.20   31.31   4,728.51
42   4,828.51   32.19   4,860.70
43   4,960.70   33.07   4,993.78
44   5,093.78   33.96   5,127.73
45   5,227.73   34.85   5,262.59
46   5,362.59   35.75   5,398.34
47   5,498.34   36.66   5,534.99
48   5,634.99   37.57   5,672.56
49   5,772.56   38.48   5,811.04
50   5,911.04   39.41   5,950.45
51   6,050.45   40.34   6,090.79
52   6,190.79   41.27   6,232.06
53   6,332.06   42.21   6,374.27
54   6,474.27   43.16   6,517.43
55   6,617.43   44.12   6,661.55
56   6,761.55   45.08   6,806.63
57   6,906.63   46.04   6,952.67
58   7,052.67   47.02   7,099.69
59   7,199.69   48.00   7,247.69
60   7,347.69   48.98   7,396.67
61   7,496.67   49.98   7,546.65
62   7,646.65   50.98   7,697.63
63   7,797.63   51.98   7,849.61
64   7,949.61   53.00   8,002.61
65   8,102.61   54.02   8,156.62
66   8,256.62   55.04   8,311.67
67   8,411.67   56.08   8,467.75
68   8,567.75   57.12   8,624.86
69   8,724.86   58.17   8,783.03
70   8,883.03   59.22   8,942.25
71   9,042.25   60.28   9,102.53
72   9,202.53   61.35   9,263.88
73   9,363.88   62.43   9,426.31
74   9,526.31   63.51   9,589.82
75   9,689.82   64.60   9,754.42
76   9,854.42   65.70   9,920.11
77   10,020.11   66.80   10,086.91
78   10,186.91   67.91   10,254.83
79   10,354.83   69.03   10,423.86
80   10,523.86   70.16   10,594.02
81   10,694.02   71.29   10,765.31
82   10,865.31   72.44   10,937.75
83   11,037.75   73.58   11,111.33
84   11,211.33   74.74   11,286.07
85   11,386.07   75.91   11,461.98
86   11,561.98   77.08   11,639.06
87   11,739.06   78.26   11,817.32
88   11,917.32   79.45   11,996.77
89   12,096.77   80.65   12,177.41
90   12,277.41   81.85   12,359.26
91   12,459.26   83.06   12,542.33
92   12,642.33   84.28   12,726.61
93   12,826.61   85.51   12,912.12
94   13,012.12   86.75   13,098.87
95   13,198.87   87.99   13,286.86
96   13,386.86   89.25   13,476.10
97   13,576.10   90.51   13,666.61
98   13,766.61   91.78   13,858.39
99   13,958.39   93.06   14,051.44
100   14,151.44   94.34   14,245.79
101   14,345.79   95.64   14,441.43
102   14,541.43   96.94   14,638.37
103   14,738.37   98.26   14,836.62
104   14,936.62   99.58   15,036.20
105   15,136.20   100.91   15,237.11
106   15,337.11   102.25   15,439.36
107   15,539.36   103.60   15,642.95
108   15,742.95   104.95   15,847.91
109   15,947.91   106.32   16,054.23
110   16,154.23   107.69   16,261.92
111   16,361.92   109.08   16,471.00
112   16,571.00   110.47   16,681.47
113   16,781.47   111.88   16,893.35
114   16,993.35   113.29   17,106.64
115   17,206.64   114.71   17,321.35
116   17,421.35   116.14   17,537.49
117   17,637.49   117.58   17,755.08
118   17,855.08   119.03   17,974.11
119   18,074.11   120.49   18,194.60
120   18,294.60   121.96   18,416.57

3. After 20 more years kyle balance is :

(18416.57*(1.08)20 = 85838.83$
After more 10 Years his balance was - 85838.83*(1.08)10= 185319.6 $ OR 18416.57*(1.08)30 = 185319.6 $

4. Kyle Balance was at the end of 10th year - 18416.57
Kyle balance was at the end of 30th Year - 85838.83
Kyle Balance was at the end of 40th Year - 185319.6 $
His investment grow by at the end of 30th Year - 85838.83-18416.57 = $67422.26

  His investment grow by at the end of 40th Year - 185319.6-18416.57 = $166903.03

5. Wes total Investment after investing 20 years : 59294.72 $
Here is the Calculation : ( 120 Months calculation given in Point No. 2)   
Month Before Interest   Interest Total
121   18,516.57   123.44   18,640.01
122   18,740.01   124.93   18,864.94
123   18,964.94   126.43   19,091.38
124   19,191.38   127.94   19,319.32
125   19,419.32   129.46   19,548.78
126   19,648.78   130.99   19,779.77
127   19,879.77   132.53   20,012.31
128   20,112.31   134.08   20,246.39
129   20,346.39   135.64   20,482.03
130   20,582.03   137.21   20,719.24
131   20,819.24   138.79   20,958.04
132   21,058.04   140.39   21,198.43
133   21,298.43   141.99   21,440.42
134   21,540.42   143.60   21,684.02
135   21,784.02   145.23   21,929.25
136   22,029.25   146.86   22,176.11
137   22,276.11   148.51   22,424.61
138   22,524.61   150.16   22,674.78
139   22,774.78   151.83   22,926.61
140   23,026.61   153.51   23,180.12
141   23,280.12   155.20   23,435.32
142   23,535.32   156.90   23,692.22
143   23,792.22   158.61   23,950.84
144   24,050.84   160.34   24,211.18
145   24,311.18   162.07   24,473.25
146   24,573.25   163.82   24,737.07
147   24,837.07   165.58   25,002.65
148   25,102.65   167.35   25,270.01
149   25,370.01   169.13   25,539.14
150   25,639.14   170.93   25,810.07
151   25,910.07   172.73   26,082.80
152   26,182.80   174.55   26,357.35
153   26,457.35   176.38   26,633.73
154   26,733.73   178.22   26,911.96
155   27,011.96   180.08   27,192.04
156   27,292.04   181.95   27,473.99
157   27,573.99   183.83   27,757.81
158   27,857.81   185.72   28,043.53
159   28,143.53   187.62   28,331.15
160   28,431.15   189.54   28,620.70
161   28,720.70   191.47   28,912.17
162   29,012.17   193.41   29,205.58
163   29,305.58   195.37   29,500.95
164   29,600.95   197.34   29,798.29
165   29,898.29   199.32   30,097.61
166   30,197.61   201.32   30,398.93
167   30,498.93   203.33   30,702.26
168   30,802.26   205.35   31,007.61
169   31,107.61   207.38   31,314.99
170   31,414.99   209.43   31,624.42
171   31,724.42   211.50   31,935.92
172   32,035.92   213.57   32,249.49
173   32,349.49   215.66   32,565.16
174   32,665.16   217.77   32,882.92
175   32,982.92   219.89   33,202.81
176   33,302.81   222.02   33,524.83
177   33,624.83   224.17   33,848.99
178   33,948.99   226.33   34,175.32
179   34,275.32   228.50   34,503.82
180   34,603.82   230.69   34,834.51
181   34,934.51   232.90   35,167.41
182   35,267.41   235.12   35,502.53
183   35,602.53   237.35   35,839.88
184   35,939.88   239.60   36,179.48
185   36,279.48   241.86   36,521.34
186   36,621.34   244.14   36,865.48
187   36,965.48   246.44   37,211.92
188   37,311.92   248.75   37,560.66
189   37,660.66   251.07   37,911.74
190   38,011.74   253.41   38,265.15
191   38,365.15   255.77   38,620.91
192   38,720.91   258.14   38,979.05
193   39,079.05   260.53   39,339.58
194   39,439.58   262.93   39,702.51
195   39,802.51   265.35   40,067.86
196   40,167.86   267.79   40,435.65
197   40,535.65   270.24   40,805.89
198   40,905.89   272.71   41,178.59
199   41,278.59   275.19   41,553.78
200   41,653.78   277.69   41,931.47
201   42,031.47   280.21   42,311.68
202   42,411.68   282.74   42,694.43
203   42,794.43   285.30   43,079.72
204   43,179.72   287.86   43,467.59
205   43,567.59   290.45   43,858.04
206   43,958.04   293.05   44,251.09
207   44,351.09   295.67   44,646.77
208   44,746.77   298.31   45,045.08
209   45,145.08   300.97   45,446.05
210   45,546.05   303.64   45,849.69
211   45,949.69   306.33   46,256.02
212   46,356.02   309.04   46,665.06
213   46,765.06   311.77   47,076.83
214   47,176.83   314.51   47,491.34
215   47,591.34   317.28   47,908.61
216   48,008.61   320.06   48,328.67
217   48,428.67   322.86   48,751.53
218   48,851.53   325.68   49,177.20
219   49,277.20   328.51   49,605.72
220   49,705.72   331.37   50,037.09
221   50,137.09   334.25   50,471.34
222   50,571.34   337.14   50,908.48
223   51,008.48   340.06   51,348.54
224   51,448.54   342.99   51,791.53
225   51,891.53   345.94   52,237.47
226   52,337.47   348.92   52,686.39
227   52,786.39   351.91   53,138.30
228   53,238.30   354.92   53,593.22
229   53,693.22   357.95   54,051.17
230   54,151.17   361.01   54,512.18
231   54,612.18   364.08   54,976.26
232   55,076.26   367.18   55,443.44
233   55,543.44   370.29   55,913.73
234   56,013.73   373.42   56,387.15
235   56,487.15   376.58   56,863.73
236   56,963.73   379.76   57,343.49
237   57,443.49   382.96   57,826.45
238   57,926.45   386.18   58,312.62
239   58,412.62   389.42   58,802.04
240   58,902.04   392.68   59,294.72

7. There is no reason for any rational person to delay taking an amount owed to him or her. More than financial principles, this is basic instinct. The money you have in hand at the moment is worth more than the same amount you ‘may’ get in future. One reason for this is inflation and another is possible earning capacity. The fundamental code of finance maintains that, given money can generate interest, the value of a certain sum is more if you receive it sooner. This is why it is called as the present value.6. Kyle has the Higher balance at the age of 55 Years.
Basically, the time value of money validates that it is more beneficial to have cash now than later. Say, if you invest a Rs. 100 today – the returns will be more compared to the same investment made 2 months from now.
Kyle started his investment in the earlier age. So he got the benefit of time value of money more than Wes.