Question

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re 6, Video e Z e7 Video 8 Video Materials al videos ts and due Remaining Time: 58 minutes, 21 seconds. Question Completion Status: Question 1 of 10 1 points Save Answer You have just won a lottery, which offers a choice in how you may receive compounded annually, whic your prize. If the interest rate is 10% per annum h of the following prizes has the highest present value? $2 000 000 immediately O An ordinary annuity of $300 000 per year for each of the next 10 years (starting one year from now) O $3 000 000 at the end of five years perpetuity of $250 000 per year starting one year from now to the next question prevents changes to this answer Question 1 of 10

Answer 1

A	B	C	D	E	F	G
2
3		Interest rate	10%
4
5		$2000,000 paid immediately will have present value of $2,000,000.
6
7		Present value annuity of $300,000 per year for next 10 year.	=300,000*(P/A,10%,10)
8			$1,843,370.13	=300000*PV(D3,10,-1,0)
9
10		Present value of $3,000,000 received at the end of 5 years	=3,000,000*(P/F,10%,5)
11			$1,862,763.97	=3000000*(1/((1+D3)^5))
12
13		Present value of perpetuity of $250,000 per year	=$250,000 / 10%
14			$2,500,000.00	=250000/D3
15
16		Thus the present value of perpetuity of $250,000 is the highest,
17		therefore the fourth option is correct.
18

Formula sheet

A	B	C	D	E	F	G
2
3		Interest rate	0.1
4
5		$2000,000 paid immediately will have present value of $2,000,000.
6
7		Present value annuity of $300,000 per year for next 10 year.	=300,000*(P/A,10%,10)
8			=300000*PV(D3,10,-1,0)	=300000*PV(D3,10,-1,0)
9
10		Present value of $3,000,000 received at the end of 5 years	=3,000,000*(P/F,10%,5)
11			=3000000*(1/((1+D3)^5))	=3000000*(1/((1+D3)^5))
12
13		Present value of perpetuity of $250,000 per year	=$250,000 / 10%
14			=250000/D3	=250000/D3
15
16		Thus the present value of a perpetuity of $250,000 is the highest,
17		therefore the fourth option is correct.
18