Question

You have just won a lottery entitling you to receive, starting today, a series of 21 quarterly payments of $25,000 each, followed, one year after this series of payments ends, by a second series of annual payments of $30,000 each forever! (The first $30,000 payment is to be received exactly one year after the last $25,000 payment is received.) If the appropriate discount rate is r = 10 percent compounded continuously, what is the present value of all these future lottery payments?

No excel

Answer 1

Answer :

The process of converting comuting the Present value of a future sum is called discounting. in this case we have to find the present value of all the future lottery payments considering discount rate as 10% compounded continuously.

As the lottery payment is received quaterly thus we have to convert the annual discount rate into qtrly rate

ie 10% / no of qtrs = 2.5%

1. Present value of 1st Lottery will be calculated by

Qtry lottery amount X PVIF (using Present value interest factor table ) which is as follow in a table form

  

Qtr	lottery payment ($)	PVIF	PV ( $)
1	25000	0.976	24390.24
2	25000	0.952	23795.36
3	25000	0.929	23214.99
4	25000	0.906	22648.77
5	25000	0.884	22096.36
6	25000	0.862	21557.42
7	25000	0.841	21031.63
8	25000	0.821	20518.66
9	25000	0.801	20018.21
10	25000	0.781	19529.96
11	25000	0.762	19053.62
12	25000	0.744	18588.90
13	25000	0.725	18135.51
14	25000	0.708	17693.18
15	25000	0.690	17261.64
16	25000	0.674	16840.62
17	25000	0.657	16429.88
18	25000	0.641	16029.15
19	25000	0.626	15638.19
20	25000	0.610	15256.77
21	25000	0.595	14884.66
			404613.71

2. in second lottery the payment of $ 30,000 /- will start after the end of 1st year and it will be continues forever thus it is call prepetuity . which will be calculated by using following formula

PV0= PMT / r were

PV0 = Present value

PMT = periodical payment

r = discount rate

thus by using the above formula

pv0 = $30,000/ .025 = $ 12,00,000

present value of total lottery amount = ( 404613.71+12,00,000) = $ 1604613.71