Question

In: Finance

Charlie, who is just 16 years old, won a lottery. However, the lottery does not pay...

Charlie, who is just 16 years old, won a lottery. However, the lottery does not pay out money until a person is at least 25 years old. Charlie hires a financial consultant and this consultant suggests that Charlie invest the money and then begin receiving monthly payments of 2500$ once he reaches age 25. The consultant also suggests that Charlie should protect himself from inflation by having his payments increase by 2.3% each year. Thus, the 12 monthly payments in year 1 will be 2500$ (age 25 until age 25+11months), the 12 monthly payments for year 2 will be 2500(1.023)$ (age 26 to age 26+11months), the 12 payments for year 3 will be 2500(1.023)2$ and so on.(NOTE: this is a situation where payments are monthly, but the percentage increase is annually.) It turns out that Charlie has won enough money for this payment scheme to last for a total of 25 years after he turns 25. If Charlie can earn j1 = 8% on his lottery winnings and the consultant charges 1.5% of the winnings as a fee (payable upfront when charlie is 16), how much did Charlie win in the lottery?

Solutions

Expert Solution

Monthly interest rate=(8/12)% 0.6667%
N A B
Year Monthly Payment Present Valueat Beginning of year of 12 months payment (Using PV function of excel with Rate=0.6667%,Nper=12,Pmt=-A)
1 $2,500 $28,739.45 (Using PV function of excel with Rate=0.6667%,Nper=12,Pmt=-2500)
(1.023*2500) 2 $2,557.50 $29,400.46
(1.023*2557.50) 3 $2,616.32 $30,076.67 (Using PV function of excel with Rate=0.6667%,Nper=12,Pmt=-2616.32)
4 $2,676.50 $30,768.44
5 $2,738.06 $31,476.11
6 $2,801.03 $32,200.06
7 $2,865.46 $32,940.66
8 $2,931.36 $33,698.30
9 $2,998.78 $34,473.36
10 $3,067.76 $35,266.25
11 $3,138.31 $36,077.37
12 $3,210.49 $36,907.15
13 $3,284.34 $37,756.01
14 $3,359.88 $38,624.40
15 $3,437.15 $39,512.76
16 $3,516.21 $40,421.56
17 $3,597.08 $41,351.25
18 $3,679.81 $42,302.33
19 $3,764.45 $43,275.28
20 $3,851.03 $44,270.62
21 $3,939.61 $45,288.84
22 $4,030.22 $46,330.48
23 $4,122.91 $47,396.08
24 $4,217.74 $48,486.19
25 $4,314.75 $49,601.38

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