Jessie won big in a recent raffle. Her prize entitles her to a 20-year annuity w

Question

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.

Explanation / Answer

Since the payments begin immediately , this is annuity due.

SInce the company is paying now this is present value scenario.

The annual payment would be : 10000000/20 = 50,000

(a) the present value of 50000 annual payment @5%

PV = 50000 x 1.05 x (1-1.05-20) / 0.05

PV = $654266.04

(b) If r=3% then PV would be greater. The smaller the interest rate the greater is the present value:

PV = $766189.95

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