1. Today, Mark invested $5,000 into an account that guarantees 7.75% p.a. compounded monthly and Madonna invested $5,000 into account guaranteeing 8.25% p.a. compounded semiannually.

How long will it take (in years) for the value of Madonna's investment to be two times as much as
Mark's?

It will take 114 YEARS.

SEE WORKINGS:-

MARK MADONNA

1 5,000.00 5,388.17 10,776.33 5,000.00 5,421.01
2 5,388.17 5,806.46 11,612.93 5,421.01 5,877.47
3 5,806.46 6,257.24 12,514.48 5,877.47 6,372.36
4 6,257.24 6,743.01 13,486.01 6,372.36 6,908.93
5 6,743.01 7,266.49 14,532.97 6,908.93 7,490.68
6 7,266.49 7,830.60 15,661.21 7,490.68 8,121.41
7 7,830.60 8,438.52 16,877.04 8,121.41 8,805.24
8 8,438.52 9,093.63 18,187.25 8,805.24 9,546.66
9 9,093.63 9,799.59 19,599.18 9,546.66 10,350.51
10 9,799.59 10,560.36 21,120.72 10,350.51 11,222.05
11 10,560.36 11,380.20 22,760.39 11,222.05 12,166.96
12 11,380.20 12,263.67 24,527.35 12,166.96 13,191.45
13 12,263.67 13,215.74 26,431.48 13,191.45 14,302.19
14 13,215.74 14,241.72 28,483.43 14,302.19 15,506.47
15 14,241.72 15,347.34 30,694.69 15,506.47 16,812.14
16 15,347.34 16,538.80 33,077.61 16,812.14 18,227.76
17 16,538.80 17,822.76 35,645.52 18,227.76 19,762.57
18 17,822.76 19,206.40 38,412.79 19,762.57 21,426.62
19 19,206.40 20,697.45 41,394.89 21,426.62 23,230.78
20 20,697.45 22,304.25 44,608.50 23,230.78 25,186.86
21 22,304.25 24,035.80 48,071.59 25,186.86 27,307.65
22 24,035.80 25,901.77 51,803.54 27,307.65 29,607.01
23 25,901.77 27,912.60 55,825.20 29,607.01 32,099.98
24 27,912.60 30,079.54 60,159.08 32,099.98 34,802.86
25 30,079.54 32,414.70 64,829.41 34,802.86 37,733.33
26 32,414.70 34,931.15 69,862.31 37,733.33 40,910.55
27 34,931.15 37,642.96 75,285.93 40,910.55 44,355.30
28 37,642.96 40,565.30 81,130.60 44,355.30 48,090.10
29 40,565.30 43,714.51 87,429.01 48,090.10 52,139.39
30 43,714.51 47,108.20 94,216.39 52,139.39 56,529.63
31 47,108.20 50,765.35 101,530.69 56,529.63 61,289.54
32 50,765.35 54,706.41 109,412.82 61,289.54 66,450.24
33 54,706.41 58,953.44 117,906.87 66,450.24 72,045.48
34 58,953.44 63,530.17 127,060.33 72,045.48 78,111.85
35 63,530.17 68,462.20 136,924.41 78,111.85 84,689.03
36 68,462.20 73,777.13 147,554.26 84,689.03 91,820.01
37 73,777.13 79,504.67 159,009.34 91,820.01 99,551.44
38 79,504.67 85,676.86 171,353.71 99,551.44 107,933.87
39 85,676.86 92,328.21 184,656.42 107,933.87 117,022.12
40 92,328.21 99,495.92 198,991.85 117,022.12 126,875.62
41 99,495.92 107,220.09 214,440.18 126,875.62 137,558.80
42 107,220.09 115,543.91 231,087.82 137,558.80 149,141.52
43 115,543.91 124,513.93 249,027.86 149,141.52 161,699.54
44 124,513.93 134,180.32 268,360.64 161,699.54 175,314.96
45 134,180.32 144,597.14 289,194.28 175,314.96 190,076.83
46 144,597.14 155,822.65 311,645.30 190,076.83 206,081.68
47 155,822.65 167,919.63 335,839.26 206,081.68 223,434.17
48 167,919.63 180,955.73 361,911.47 223,434.17 242,247.78
49 180,955.73 195,003.87 390,007.74 242,247.78 262,645.52
50 195,003.87 210,142.61 420,285.21 262,645.52 284,760.80
51 210,142.61 226,456.61 452,913.21 284,760.80 308,738.23
52 226,456.61 244,037.11 488,074.22 308,738.23 334,734.61
53 244,037.11 262,982.45 525,964.89 334,734.61 362,919.93
54 262,982.45 283,398.56 566,797.12 362,919.93 393,478.52
55 283,398.56 305,399.64 610,799.28 393,478.52 426,610.19
56 305,399.64 329,108.73 658,217.47 426,610.19 462,531.63
57 329,108.73 354,658.43 709,316.86 462,531.63 501,477.71
58 354,658.43 382,191.63 764,383.26 501,477.71 543,703.14
59 382,191.63 411,862.31 823,724.62 543,703.14 589,484.03
60 411,862.31 443,836.42 887,672.84 589,484.03 639,119.77
61 443,836.42 478,292.77 956,585.54 639,119.77 692,934.93
62 478,292.77 515,424.07 1,030,848.15 692,934.93 751,281.44
63 515,424.07 555,437.99 1,110,875.98 751,281.44 814,540.83
64 555,437.99 598,558.31 1,197,116.62 814,540.83 883,126.80
65 598,558.31 645,026.19 1,290,052.37 883,126.80 957,487.84
66 645,026.19 695,101.50 1,390,203.01 957,487.84 1,038,110.24
67 695,101.50 749,064.32 1,498,128.64 1,038,110.24 1,125,521.19
68 749,064.32 807,216.43 1,614,432.86 1,125,521.19 1,220,292.33
69 807,216.43 869,883.06 1,739,766.12 1,220,292.33 1,323,043.38
70 869,883.06 937,414.69 1,874,829.39 1,323,043.38 1,434,446.28
71 937,414.69 1,010,189.01 2,020,378.02 1,434,446.28 1,555,229.53
72 1,010,189.01 1,088,613.01 2,177,226.02 1,555,229.53 1,686,182.97
73 1,088,613.01 1,173,125.31 2,346,250.61 1,686,182.97 1,828,162.94
74 1,173,125.31 1,264,198.54 2,528,397.09 1,828,162.94 1,982,097.92
75 1,264,198.54 1,362,342.07 2,724,684.14 1,982,097.92 2,148,994.53
76 1,362,342.07 1,468,104.77 2,936,209.54 2,148,994.53 2,329,944.17
77 1,468,104.77 1,582,078.15 3,164,156.29 2,329,944.17 2,526,130.13
78 1,582,078.15 1,704,899.62 3,409,799.24 2,526,130.13 2,738,835.34
79 1,704,899.62 1,837,256.09 3,674,512.18 2,738,835.34 2,969,450.75
80 1,837,256.09 1,979,887.79 3,959,775.59 2,969,450.75 3,219,484.44
81 1,979,887.79 2,133,592.42 4,267,184.85 3,219,484.44 3,490,571.47
82 2,133,592.42 2,299,229.60 4,598,459.21 3,490,571.47 3,784,484.57
83 2,299,229.60 2,477,725.70 4,955,451.39 3,784,484.57 4,103,145.74
84 2,477,725.70 2,670,078.98 5,340,157.95 4,103,145.74 4,448,638.82
85 2,670,078.98 2,877,365.22 5,754,730.43 4,448,638.82 4,823,223.10
86 2,877,365.22 3,100,743.71 6,201,487.42 4,823,223.10 5,229,348.13
87 3,100,743.71 3,341,463.75 6,682,927.49 5,229,348.13 5,669,669.70
88 3,341,463.75 3,600,871.60 7,201,743.20 5,669,669.70 6,147,067.23
89 3,600,871.60 3,880,418.07 7,760,836.13 6,147,067.23 6,664,662.59
90 3,880,418.07 4,181,666.56 8,363,333.12 6,664,662.59 7,225,840.51
91 4,181,666.56 4,506,301.88 9,012,603.77 7,225,840.51 7,834,270.73
92 4,506,301.88 4,856,139.62 9,712,279.23 7,834,270.73 8,493,931.99
93 4,856,139.62 5,233,136.30 10,466,272.61 8,493,931.99 9,209,138.05
94 5,233,136.30 5,639,400.37 11,278,800.75 9,209,138.05 9,984,565.90
95 5,639,400.37 6,077,203.94 12,154,407.89 9,984,565.90 10,825,286.31
96 6,077,203.94 6,548,995.52 13,097,991.03 10,825,286.31 11,736,797.07
97 6,548,995.52 7,057,413.69 14,114,827.37 11,736,797.07 12,725,058.86
98 7,057,413.69 7,605,301.88 15,210,603.77 12,725,058.86 13,796,534.27
99 7,605,301.88 8,195,724.28 16,391,448.57 13,796,534.27 14,958,230.04
100 8,195,724.28 8,831,982.95 17,663,965.89 14,958,230.04 16,217,742.93
101 8,831,982.95 9,517,636.28 19,035,272.56 16,217,742.93 17,583,309.32
102 9,517,636.28 10,256,518.94 20,513,037.87 17,583,309.32 19,063,859.13
103 10,256,518.94 11,052,763.27 22,105,526.54 19,063,859.13 20,669,074.20
104 11,052,763.27 11,910,822.44 23,821,644.89 20,669,074.20 22,409,451.58
105 11,910,822.44 12,835,495.32 25,670,990.64 22,409,451.58 24,296,372.23
106 12,835,495.32 13,831,953.33 27,663,906.66 24,296,372.23 26,342,175.36
107 13,831,953.33 14,905,769.36 29,811,538.72 26,342,175.36 28,560,239.21
108 14,905,769.36 16,062,948.96 32,125,897.91 28,560,239.21 30,965,068.47
109 16,062,948.96 17,309,963.87 34,619,927.74 30,965,068.47 33,572,389.17
110 17,309,963.87 18,653,788.30 37,307,576.59 33,572,389.17 36,399,251.48
111 18,653,788.30 20,101,937.84 40,203,875.69 36,399,251.48 39,464,141.25
112 20,101,937.84 21,662,511.58 43,325,023.17 39,464,141.25 42,787,100.88
113 21,662,511.58 23,344,237.35 46,688,474.69 42,787,100.88 46,389,860.34
114 23,344,237.35 25,156,520.52 50,313,041.05 46,389,860.34 50,295,979.36

Please acknowledge understanding.

Effective Rates:-

MARK

1 1.000000 1.006250
2 1.006250 1.012539
3 1.012539 1.018867
4 1.018867 1.025235
5 1.025235 1.031643
6 1.031643 1.038091
7 1.038091 1.044579
8 1.044579 1.051108
9 1.051108 1.057677
10 1.057677 1.064287
11 1.064287 1.070939
12 1.070939 1.077633

MADONNA

1 1.000000 1.041250
2 1.041250 1.084202


Rolcam