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A lottery claims its grand prize is ​$5 ​million, payable over 5 years at ​$1 comma 000 comma 000 per year. If the first payment is made​ immediately, what is the grand prize really​ worth? Use an interest rate of 4​%.The real value of the grand prize is ​$nothing. ​(Round your response to the nearest​ dollar.)

Respuesta :

TomShelby

Answer:

present value of the prize: 4,451,822 dollars

Explanation:

we will calcualte the present value of an annuity-due of 5 payment of 1,000,000 discount at 4%

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

C 1,000,000

time 5

rate 0.04

[tex]1000000 \times \frac{1-(1+0.04)^{-5} }{0.04}(1+0.04) = PV\\[/tex]

PV $4,451,822.3310

This will be the present value of the prize today

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