Jessie won big in a recent raffle. Her prize entitles her to a 20-year annuity with equal annual payments beginning immediately and totaling $10,000,000. Jessie has agreed to strike a deal with Liberty Settlement Funding, a financial services company located in Fort Lauderdale, Florida. The company offers to purchase this annuity by paying her a lump sum immediately.
(a) If the interest rate is 5%, how much would the company pay Jessie? Please show all work. Hint: If they are paying her now, is this a future value or a present value scenario? Is this an annuity due or ordinary annuity?
(b) If Liberty Settlement Funding were to use an interest rate less than 3% in the calculation, would the lump sum be larger or smaller than your answer in part (a) above. Explain in 1 or 2 sentences only.