Question

Find the cash value of the lottery jackpot (to the nearest dollar). Yearly jackpot payments begin immediately (26 for Mega Millions and 30 for Powerball). Assume the lottery can invest at the given interest rate. Powerball: $360 million; 5.4% interest
a. $188,347,953
b. $282,573,702
c. $185,870,742
d. $298,386,685

Answer 1

Answer:

The right response is Option c ($185,870,742).

Step-by-step explanation:

Given:

n = 30

r = 5.4%

or,

 = 0.054

Periodic payment will be:

$R = \frac{360000000}{30}$

   $=12000000$ ($)

Now,

The present value will be:

= $R+R(\frac{1-(1+r)^{-n+1}}{r} )$

By substituting the values, we get

= $12000000+12000000(\frac{1-(1+0.054)^{-30 + 1}}{0.054} )$

= $12000000+12000000\times 14.4892$

= $185,870,742$ ($)