Lottery, Annuity, Interest rate

Question

The largest amount won by an individual in a U.S. lottery was $314.9$ million. Instead of receiving $314.9$ million in 30 equal annual payments, including one immediately, the winner chose a lump sum, which came to $170$ million. What was the corresponding interest rate of the annuity the lottery administrator would have used to payout the winnings in installments? We are using the present value of an ordinary annuity formula to solve for the interest rate $r$ and we want to know if this is correct math. The problem we have is determining what are the annual installment payments, which is the d(for deposit) or PMT (for periodic payment) of the present value of an ordinary annuity formula.

Answer 1

Hint:

So the present value of the loan was $170$ million, the individual payout being: $\frac{314.9}{30}$

Thus we have (in millions):

$170 = \sum_{i=0}^{29} \frac{314.9/30}{(1+r)^i}=314.9/30 \cdot \frac{1-(1+r)^{30}}{1-(1+r)}\cdot \frac1{(1+r)^{29}}$