Question

recently, a suburban chicago won powerball, a multistate lottery game. the game had rolled over for several weeks, so a hige jackpot was at stake. ticket buyers had the choice between a single ump sum of $104 million or a total of $198 million paid out over 25 years (or $7.92 million per year and the payment is made immediately) should they win the game. the winning couple opted for the lump sum. at what interest rate will those two payment options be equivalent?

Answer 1

Let the required interest rate be i%

So, the present value of both the options (the lumpsum and the annuity) must be the same if discounted to time 0 at i%

So,

PV of lumpsum = PV of annuity of 7.92 paid for 25 years.

Thus,

note: we have used the interpolation formula to calculate the interest rate as it is assumed that the rates are linear.

the formula is