You have just won the lottery and will receive $500,000 in one year. You will receive...

You have just won the lottery and will receive $500,000 in one year. You will receive payments for 25 years, and the payments will increase 4 percent per year. If the appropriate discount rate is 11 percent, what is the present value of your winnings?

5,511,586
$29,258,112
$36,804
$29,258,112
$5,741,235

Expert Solution

We are given,

Amount to be received next year = $500,000

Growth rate = 4%

Discount rate = 11%

We have to calculate present value. We can do this in excel,

Yr	Amount	Discount factor(1/(1+r)^t	Present value
1	500000	0.901	450450.5
2	520000	0.812	422043.7
3	540800	0.731	395428.3
4	562432	0.659	370491.4
5	584929.3	0.593	347127.1
6	608326.5	0.535	325236.2
7	632659.5	0.482	304725.8
8	657965.9	0.434	285508.8
9	684284.5	0.391	267503.8
10	711655.9	0.352	250634.2
11	740122.1	0.317	234828.4
12	769727	0.286	220019.4
13	800516.1	0.258	206144.3
14	832536.8	0.232	193144.2
15	865838.2	0.209	180964.0
16	900471.8	0.188	169551.8
17	936490.6	0.170	158859.4
18	973950.2	0.153	148841.2
19	1012908	0.138	139454.8
20	1053425	0.124	130660.4
21	1095562	0.112	122420.5
22	1139384	0.101	114700.3
23	1184959	0.091	107467.0
24	1232358	0.082	100689.8
25	1281652	0.074	94340.0
		Total	5,741,235

Hence the present value is 5,741,235. The answer is option v).

If you have any doubts please let me know in the comments. Please give a positive rating if the answer is helpful to you. Thanks.

jeff jeffy answered 3 years ago

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