Question

Suppose a state lottery prize of $2 million is to be paid in 5 payments of $400,000 each at the end of each of the next 5 years. If money is worth 8%, compounded annually, what is the present value of the prize? (Round your answer to the nearest cent.)

Answer 1

Annual Payment=$400,000

Number of years=5

Annually compounded worth =8%=0.08

Present Worth factor(PWF)=(P/A,i,N)=(((1+i)^N)-1)/(i*((1+i)^N))

i=annual compounded worth (Interest Rate)=0.08

N=Number of years=5

PWF=(P/A,8%,5)=(((1+0.08)^5)-1)/(0.08*((1+0.08)^5))=3.99271

Present value of the prize=400000*3.99271=$1,597,084

Present Value of the Prize

$1,597,084

Alternative Method of Calculation is also given below

Present Value (PV) of Cash Flow:
(Cash Flow)/((1+i)^N)
i=Discount Rate=0.08
N=Year of Cash Flow

		N	A	PV=A/(1.08^N)
		Year	Cash flow	PV of Cash flow
		1	$400,000	$370,370
		2	$400,000	$342,936
		3	$400,000	$317,533
		4	$400,000	$294,012
		5	$400,000	$272,233
			SUM	$1,597,084
	Present Value of the Prize	$1,597,084