The state Set 4 Life Lottery offers the winner $500 000 now plus 19 annual payments...

The state Set 4 Life Lottery offers the winner $500 000 now plus 19 annual payments of $500 000. If the market interest rate on investments is 4%, what is the present value of these payments? What is the future value of these payments at the time the last payment is received?

Expert Solution

Solution:

Formula to calculate Present Value & Future Value is:

Present Value = Cash flow / (1+r)^n

Future Value = Cash flow (1+r)^n

		(1+r)^n	Present Value
initial	500000		500000
1	500000	1.040	480769
2	500000	1.082	462278
3	500000	1.125	444498
4	500000	1.170	427402
5	500000	1.217	410964
6	500000	1.265	395157
7	500000	1.316	379959
8	500000	1.369	365345
9	500000	1.423	351293
10	500000	1.480	337782
11	500000	1.539	324790
12	500000	1.601	312299
13	500000	1.665	300287
14	500000	1.732	288738
15	500000	1.801	277632
16	500000	1.873	266954
17	500000	1.948	256687
18	500000	2.026	246814
19	500000	2.107	237321
Total			7066970


Remaining installment		(1+r)^n	Future Value
19	500000	2.107	1053425
18	500000	2.026	1012908
17	500000	1.948	973950
16	500000	1.873	936491
15	500000	1.801	900472
14	500000	1.732	865838
13	500000	1.665	832537
12	500000	1.601	800516
11	500000	1.539	769727
10	500000	1.480	740122
9	500000	1.423	711656
8	500000	1.369	684285
7	500000	1.316	657966
6	500000	1.265	632660
5	500000	1.217	608326
4	500000	1.170	584929
3	500000	1.125	562432
2	500000	1.082	540800
1	500000	1.040	520000
Last payment	500000	1.000	500000
Total			14889039

Answer Present Value is $7066970 & the Future Value is $14889039.

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