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?

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

jeff jeffy answered 8 months ago

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