Question

Your friend just won the lottery. He has a choice of receiving $50,000 a year for the next 20 years or a lump sum today. The lottery uses a 15% discount rate. What would be the lump sum your friend would receive? I know the answer is 312,966.57, however, I don't know why my calculator cannot get this number.

Answer 1

Here annuity amount = $50,000, n = 20 years and r = 15%

Thus lump sum today = present value of annuity

Year	Amount	1+r	PVIF	PV
1	50,000	1.15	0.8696	43,478.26
2	50,000		0.7561	37,807.18
3	50,000		0.6575	32,875.81
4	50,000		0.5718	28,587.66
5	50,000		0.4972	24,858.84
6	50,000		0.4323	21,616.38
7	50,000		0.3759	18,796.85
8	50,000		0.3269	16,345.09
9	50,000		0.2843	14,213.12
10	50,000		0.2472	12,359.24
11	50,000		0.2149	10,747.16
12	50,000		0.1869	9,345.36
13	50,000		0.1625	8,126.40
14	50,000		0.1413	7,066.43
15	50,000		0.1229	6,144.72
16	50,000		0.1069	5,343.24
17	50,000		0.0929	4,646.29
18	50,000		0.0808	4,040.26
19	50,000		0.0703	3,513.27
20	50,000		0.0611	3,055.01
			Total	312,966.57

Thus the answer is $312,966.57

You can also solve the question using PVIFA (present value interest factor of Annuity). From PVIFA table that is available on all financial books and on the net as well you will get PVIFA for 20 years and 15% to be 6.259331. Thus lump sum = 50,000*6.259331 = $312,966.57