Directions: Be sure to save an electronic copy of your answer before submitting it to Ashworth College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English, spelling, and grammar.
Respond to the items below.
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 that 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 dreams of becoming rich have just come true. You have won the State of Tranquility’s Lottery. The State offers you two payment plans for the $5,000,000 advertised jackpot. You can take annual payments of $250,000 for the next 20 years or $2,867,480 today.
- If your investment rate over the next 20 years is 8%, which payoff will you choose?
- If your investment rate over the next 20 years is 5%, which payoff will you choose?
- At what investment rate will the annuity stream of $250,000 be the same as the lump sum payment of $2,867,480?