Powerball Lottery Amounts

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hardddddddd engineering economy question?

The multistate Powerball Lottery prize was won by a single individual who had purchased five tickets at 1 dollar each. The individual was given two choices: Receive 13 payments of 690 dollars each,
with the first payment to be made now and the rest to be made at the end of each of the next 13-1 years; or receive a single lump-sum payment now that would be equivalent to the 13 payments of 690 dollars each. If the state uses an interest rate of 17.89% per year, what is the amount of the lump-sum payment?

Use the “P=” formula from here: http://en.wikipedia.org/wiki/Annuity_(finance_theory)#Ordinary_annuity

or compute it directly, e.g. in Excel:
690 * [ 1 + 1/1.1789 + 1/1.1789^2 + ... + 1/1.1789^12 ]