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.
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You mean $3030$ or $30$ equal payments ? – callculus42 Jul 25 '17 at 00:19
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It seems that you´re not really interested in this questions. Therefore I´ve voted to close. – callculus42 Jul 25 '17 at 00:31
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30 equal payments – Eric Brown Jul 25 '17 at 00:50
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Hint:
So the present value of the loan was $170$ million, the individual payout being: $\frac{314.9}{30}$
Thus we have (in millions):
$170 = \sum_{i=0}^{29} \frac{314.9/30}{(1+r)^i}=314.9/30 \cdot \frac{1-(1+r)^{30}}{1-(1+r)}\cdot \frac1{(1+r)^{29}}$
Tony
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I think you know that there exists a closed form for the RHS. You can include that to your answer. – callculus42 Jul 25 '17 at 01:10
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1More or less it is $314.9/30 \cdot \frac{1-q^{30}}{1-q}\cdot \frac1{q^{29}}$ where $q=1+i$ The main flaw is, that you have forgot to discount (latter term). $314.9/30 \cdot q\cdot \frac{1-q^{30}}{1-q}$ is the future value. Then you have to discount 30 times. – callculus42 Jul 25 '17 at 01:20