In: Finance
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?
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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