You have just invested $60,000. What is the maximum dollar amount you can withdraw at the
end of each month for the next 10 years if the annual rate of return is 6.5%, and at the end of the
10^th year, the account balance is to be zero?
Solution
Amount Month interest balance Withdrawal balance 60,000.00 1 325.00
60,325.00 681.00 59,644.00 59,644.00 2 323.07 59,967.07 681.00
59,286.07 59,286.07 3 321.13 59,607.20 681.00 58,926.20 58,926.20
4 319.18 59,245.39 681.00 58,564.39 58,564.39 5 317.22
58,881.61 681.00 58,200.61 58,200.61 6 315.25 58,515.87 681.00
57,834.87 57,834.87 7 313.27 58,148.14 681.00 57,467.14 57,467.14
8 311.28 57,778.42 681.00 57,097.42 57,097.42 9 309.28
57,406.70 681.00 56,725.70 56,725.70 10 307.26 57,032.96 681.00
56,351.96 56,351.96 11 305.24 56,657.20 681.00 55,976.20 55,976.20
12 303.20 56,279.40 681.00 55,598.40 55,598.40 13 301.16 55,899.56
681.00 55,218.56 55,218.56 14 299.10 55,517.66 681.00 54,836.66
54,836.66 15 297.03 55,133.69 681.00 54,452.69 54,452.69 16
294.95 54,747.65 681.00 54,066.65 54,066.65 17 292.86 54,359.51
681.00 53,678.51 53,678.51 18 290.76 53,969.27 681.00 53,288.27
53,288.27 19 288.64 53,576.91 681.00 52,895.91 52,895.91 20
286.52 53,182.43 681.00 52,501.43 52,501.43 21 284.38 52,785.81
681.00 52,104.81 52,104.81 22 282.23 52,387.05 681.00 51,706.05
51,706.05 23 280.07 51,986.12 681.00 51,305.12 51,305.12 24
277.90 51,583.02 681.00 50,902.02 50,902.02 25 275.72 51,177.74
681.00 50,496.74 50,496.74 26 273.52 50,770.27 681.00 50,089.27
50,089.27 27 271.32 50,360.58 681.00 49,679.58 49,679.58 28
269.10 49,948.68 681.00 49,267.68 49,267.68 29 266.87 49,534.55
681.00 48,853.55 48,853.55 30 264.62 49,118.17 681.00 48,437.17
48,437.17 31 262.37 48,699.54 681.00 48,018.54 48,018.54 32
260.10 48,278.64 681.00 47,597.64 47,597.64 33 257.82 47,855.46
681.00 47,174.46 47,174.46 34 255.53 47,429.99 681.00 46,748.99
46,748.99 35 253.22 47,002.21 681.00 46,321.21 46,321.21 36
250.91 46,572.12 681.00 45,891.12 45,891.12 37 248.58 46,139.70
681.00 45,458.70 45,458.70 38 246.23 45,704.93 681.00 45,023.93
45,023.93 39 243.88 45,267.81 681.00 44,586.81 44,586.81 40
241.51 44,828.32 681.00 44,147.32 44,147.32 41 239.13 44,386.45

681.00 43,705.45 43,705.45 42 236.74 43,942.19 681.00 43,261.19
43,261.19 43 234.33 43,495.52 681.00 42,814.52 42,814.52 44
231.91 43,046.44 681.00 42,365.44 42,365.44 45 229.48 42,594.92
681.00 41,913.92 41,913.92 46 227.03 42,140.95 681.00 41,459.95
41,459.95 47 224.57 41,684.52 681.00 41,003.52 41,003.52 48
222.10 41,225.63 681.00 40,544.63 40,544.63 49 219.62 40,764.24
681.00 40,083.24 40,083.24 50 217.12 40,300.36 681.00 39,619.36
39,619.36 51 214.60 39,833.97 681.00 39,152.97 39,152.97 52
212.08 39,365.04 681.00 38,684.04 38,684.04 53 209.54 38,893.58
681.00 38,212.58 38,212.58 54 206.98 38,419.57 681.00 37,738.57
37,738.57 55 204.42 37,942.98 681.00 37,261.98 37,261.98 56
201.84 37,463.82 681.00 36,782.82 36,782.82 57 199.24 36,982.06
681.00 36,301.06 36,301.06 58 196.63 36,497.69 681.00 35,816.69
35,816.69 59 194.01 36,010.70 681.00 35,329.70 35,329.70 60
191.37 35,521.07 681.00 34,840.07 34,840.07 61 188.72 35,028.78
681.00 34,347.78 34,347.78 62 186.05 34,533.84 681.00 33,852.84
33,852.84 63 183.37 34,036.20 681.00 33,355.20 33,355.20 64
180.67 33,535.88 681.00 32,854.88 32,854.88 65 177.96 33,032.84
681.00 32,351.84 32,351.84 66 175.24 32,527.08 681.00 31,846.08
31,846.08 67 172.50 32,018.58 681.00 31,337.58 31,337.58 68
169.75 31,507.33 681.00 30,826.33 30,826.33 69 166.98 30,993.30
681.00 30,312.30 30,312.30 70 164.19 30,476.49 681.00 29,795.49
29,795.49 71 161.39 29,956.89 681.00 29,275.89 29,275.89 72
158.58 29,434.46 681.00 28,753.46 28,753.46 73 155.75 28,909.21
681.00 28,228.21 28,228.21 74 152.90 28,381.11 681.00 27,700.11
27,700.11 75 150.04 27,850.16 681.00 27,169.16 27,169.16 76
147.17 27,316.32 681.00 26,635.32 26,635.32 77 144.27 26,779.60
681.00 26,098.60 26,098.60 78 141.37 26,239.97 681.00 25,558.97
25,558.97 79 138.44 25,697.41 681.00 25,016.41 25,016.41 80
135.51 25,151.92 681.00 24,470.92 24,470.92 81 132.55 24,603.47
681.00 23,922.47 23,922.47 82 129.58 24,052.05 681.00 23,371.05
23,371.05 83 126.59 23,497.64 681.00 22,816.64 22,816.64 84
123.59 22,940.23 681.00 22,259.23 22,259.23 85 120.57 22,379.80
681.00 21,698.80 21,698.80 86 117.54 21,816.34 681.00 21,135.34
21,135.34 87 114.48 21,249.82 681.00 20,568.82 20,568.82 88
111.41 20,680.23 681.00 19,999.23 19,999.23 89 108.33 20,107.56

681.00 19,426.56 19,426.56 90 105.23 19,531.79 681.00 18,850.79
18,850.79 91 102.11 18,952.90 681.00 18,271.90 18,271.90 92
98.97 18,370.87 681.00 17,689.87 17,689.87 93 95.82 17,785.69
681.00 17,104.69 17,104.69 94 92.65 17,197.34 681.00 16,516.34
16,516.34 95 89.46 16,605.80 681.00 15,924.80 15,924.80 96
86.26 16,011.06 681.00 15,330.06 15,330.06 97 83.04 15,413.10
681.00 14,732.10 14,732.10 98 79.80 14,811.90 681.00 14,130.90
14,130.90 99 76.54 14,207.44 681.00 13,526.44 13,526.44 100
73.27 13,599.71 681.00 12,918.71 12,918.71 101 69.98 12,988.69
681.00 12,307.69 12,307.69 102 66.67 12,374.35 681.00 11,693.35
11,693.35 103 63.34 11,756.69 681.00 11,075.69 11,075.69 104
59.99 11,135.69 681.00 10,454.69 10,454.69 105 56.63 10,511.32
681.00 9,830.32 9,830.32 106 53.25 9,883.56 681.00 9,202.56
9,202.56 107 49.85 9,252.41 681.00 8,571.41 8,571.41 108
46.43 8,617.84 681.00 7,936.84 7,936.84 109 42.99 7,979.83
681.00 7,298.83 7,298.83 110 39.54 7,338.37 681.00
6,657.37 6,657.37 111 36.06 6,693.43 681.00 6,012.43 6,012.43
112 32.57 6,044.99 681.00 5,363.99 5,363.99 113 29.05
5,393.05 681.00 4,712.05 4,712.05 114 25.52 4,737.57 681.00
4,056.57 4,056.57 115 21.97 4,078.55 681.00 3,397.55 3,397.55
116 18.40 3,415.95 681.00 2,734.95 2,734.95 117 14.81
2,749.76 681.00 2,068.76 2,068.76 118 11.21 2,079.97 681.00
1,398.97 1,398.97 119 7.58 1,406.55 681.00 725.55 725.55
120 3.93 729.48 681.00 48.48