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11 June, 15:11

# The Powerball winner has the option of taking a single payment immediately, or 30 annual payments, the first of which is immediate and the rest increase by 4% each year. If the total of the Powerball payout is to be \$365,000,000 and the winner chooses the annual payments, how much is the first payment

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1. 11 June, 15:53
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it will pay an amount of \$21107986.18

Explanation:

firstly we will be using the present value annuity formula to calculate how much will the first payment be for the annuity as there will be 30 annual payments of the lotto amount so:

Given \$365000000 which is the present value of the annuity Pv.

Interest that will be gained from saving the money which is 4% per annual (i)

now we also have 30 annual payments which is our n

we are looking to find C the monthly payments.

we will now substitute these values to the formula which follows and solve for C:

Pv = C[ (1 - (1+i) ^-n) / i]

365000000 = C[ (1 - (1+4%) ^-30) / 4%] then we divide both sides with what multiplies C

\$365000000 / [ (1 - (1+4%) ^-30) / 4%] = C

\$21107986.18 = C

This is the first payment that the power ball winner will get.