Titus Tribble wins the big Powerball lottery which pays $17 million at the beginning of each of the next 30 years. The reported prize is $510 million which is just the total of these 30 annuity payments. What is the present value of this prize today at a 5% annual rate? Express your answer in terms of millions of dollars and round the answer to the nearest tenth of a million, for example 17.0 for 17 million.

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TomShelby TomShelby · Answer 1 · 2019-09-14T03:18:36+02:00

Answer:

Present value of the prize today rounded to the nearest tenth of a million:

274.4 millions

Explanation:

We will calculate the present value of the 30 years annuity-due of 17 millions at 5% discount rate

[tex]C \times \frac{1-(1+r)^{-time} }{rate} \times (1+r)= PV\\[/tex]

C 17,000,000

time 30 years

rate 5% = 5/100 = 0.05

[tex]17000000 \times \frac{1-(1+0.05)^{-30} }{0.05} times (1+0.05)= PV\\[/tex]

PV $274,398,250.83

Rounding: 274.4 millions

The additional term (1+ r) is added because the cash received capitalize for an additional period, so it generates a higher present value.