## The future value of this cash flow

Part A

Given the following cash inflow at the end of each year, what is the future value of this cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year?
Year 1 \$15,000
Year 2 \$20,000
Year 3 \$30,000
Years 4 through 6 \$0
Year 7 \$150,000

Part B

County Ranch Insurance Company wants to offer a guaranteed annuity in units of \$500, payable at the end of each year for 25 years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume that it is an ordinary annuity and the price is the same as present value.

Part C

A local government is about to run a lottery but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive \$150,000 a year for the next 25 years. The local government will give the trust \$2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement?

Part D

Your dream of becoming rich has just come true. You have won the State of Tranquility’s Lottery. The State offers you two payment plans for the \$5 million jackpot. You can take annual payments of \$250,000 for the next 20 years or \$2,867,480 today.

a. If your investment rate over the next 20 years is 8%, which payoff will you choose?
b. If your investment rate over the next 20 years is 5%, which payoff will you choose?
c. At what investment rate will the annuity stream of \$250,000 be the same as the lump sum payment of \$2,867,480?