In 2004 Geraldine Williams won a $294 million MegaMillions lottery. She had the
ID: 1096595 • Letter: I
Question
In 2004 Geraldine Williams won a $294 million MegaMillions lottery. She had the option of receiving her winnings in 26 payments of $11.3 million or an immediate payoff of $168 million. The calculations in the table below show that $11.3 million in 26 annual installments has a present value of $168 million (at a 4.47 percent rate of interest).
Assuming Ms. Williams took the immediate payoff, how much interest accrued each day on the cash payoff of the MegaMillions jacpot?
, where r is the prevailing rate.
Explanation / Answer
In the fourth column, the interest for each annual period is calculated. To calculate how much the individual has earned daily as interest, divide the interest incurred with 365 days
Bitmap Bitmap Bitmap
Years
Annual Payment at the beginning of the year
Present value of flow
Interest accrued between each period ($)
Interest incurred each day ($)
0
11.3
11.30
0.00
0
1
11.3
10.82
0.48
0.001
2
11.3
10.35
0.95
0.003
3
11.3
9.91
1.39
0.004
4
11.3
9.49
1.81
0.005
5
11.3
9.08
2.22
0.006
6
11.3
8.69
2.61
0.007
7
11.3
8.32
2.98
0.008
8
11.3
7.96
3.34
0.009
9
11.3
7.62
3.68
0.010
10
11.3
7.30
4.00
0.011
11
11.3
6.99
4.31
0.012
12
11.3
6.69
4.61
0.013
13
11.3
6.40
4.90
0.013
14
11.3
6.13
5.17
0.014
15
11.3
5.86
5.44
0.015
16
11.3
5.61
5.69
0.016
17
11.3
5.37
5.93
0.016
18
11.3
5.14
6.16
0.017
19
11.3
4.92
6.38
0.017
20
11.3
4.71
6.59
0.018
21
11.3
4.51
6.79
0.019
22
11.3
4.32
6.98
0.019
23
11.3
4.13
7.17
0.020
24
11.3
3.96
7.34
0.020
25
11.3
3.79
7.51
0.021
In the table above, the numbers the last column is the interest accrued on each day.
Bitmap Bitmap Bitmap
Years
Annual Payment at the beginning of the year
Present value of flow
Interest accrued between each period ($)
Interest incurred each day ($)
0
11.3
11.30
0.00
0
1
11.3
10.82
0.48
0.001
2
11.3
10.35
0.95
0.003
3
11.3
9.91
1.39
0.004
4
11.3
9.49
1.81
0.005
5
11.3
9.08
2.22
0.006
6
11.3
8.69
2.61
0.007
7
11.3
8.32
2.98
0.008
8
11.3
7.96
3.34
0.009
9
11.3
7.62
3.68
0.010
10
11.3
7.30
4.00
0.011
11
11.3
6.99
4.31
0.012
12
11.3
6.69
4.61
0.013
13
11.3
6.40
4.90
0.013
14
11.3
6.13
5.17
0.014
15
11.3
5.86
5.44
0.015
16
11.3
5.61
5.69
0.016
17
11.3
5.37
5.93
0.016
18
11.3
5.14
6.16
0.017
19
11.3
4.92
6.38
0.017
20
11.3
4.71
6.59
0.018
21
11.3
4.51
6.79
0.019
22
11.3
4.32
6.98
0.019
23
11.3
4.13
7.17
0.020
24
11.3
3.96
7.34
0.020
25
11.3
3.79
7.51
0.021
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