Question

James just won the Georgia State lottery prize of $30,000,000. he has decided to take a lump sum payment, even though taxes will reduce his prize by 45%. James feels safer with his money in a bank, where he will receive an annual return of 0.95%, and where he will have ready access to cash when he needs it. If he withdraws $100,000 at the end of each month, approximately how long will it be until his lottery winnings are exhausted?

		14 years
		15 years
		13 years
		16 years

Answer 1

After tax winning = pre tax winning*(1-tax rate) = 30000000*(1-0.45) = 16500000

PVOrdinary Annuity = C*[(1-(1+i/(f*100))^(-n*f))/(i/(f*100))]

C = Cash flow per period

i = interest rate

n = number of years I f = frequency of payment

16500000= 100000*((1-(1+ 0.95/1200)^(-n*12))/(0.95/1200))

n(in years) = 14.74 = 15 years

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-16500000

PMT =100000

I/Y =0.95/12

FV = 0

CPT N

Number of years = N/12

Using Excel

=NPER(rate,pmt,pv,fv,type)/no. of payments per year

=NPER(0.95/(12*100),-100000,,16500000,)/12