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

The cash value of the Powerball jackpot is $185,870,742 (rounded to the nearest dollar).

Step-by-step explanation:

To find the cash value of the lottery jackpot, we need to calculate the present value of the yearly payments. For Mega Millions, the yearly payments are $26 million, and for Powerball, the yearly payments are $30 million. We need to use the compound interest formula to calculate the present value of these payments.

For Powerball, using an interest rate of 5.4%, the cash value of the jackpot is:

$360 million / (1 + 0.054)^{30} = $185,870,742

Therefore, the cash value of the Powerball jackpot is $185,870,742 (rounded to the nearest dollar).

Answer 2

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 = (360000000)/(30)`

`=12000000` ($)

Now,

The present value will be:

=
`R+R((1-(1+r)^(-n+1))/(r) )`

By substituting the values, we get

=
`12000000+12000000((1-(1+0.054)^(-30 + 1))/(0.054) )`

=
`12000000+12000000* 14.4892`

=
`185,870,742` ($)