Please use the data to answer question 2
2. HWAP2 Insert Draw Page Layout Formulas Data Tell me Comments Hometown Insurance 2. Hometown Insurance sells 10 -year annuities to retirees who are looking for stable sources of investment income. Hometown invests the annuity funds it receives in an equity index fund with annual returns that are normally distributed with a mean of 9% and standard deviation of 3%. It guarantees investors a minimum annual return of 6.5% and a maximum return (or rate cap) of 8.75%. This limits both the retirees' down-side risk and up-side return potential. Of course, Hometown makes its money on these contracts when the actual return exceeds the rate cap. Suppose a retiree invests $50,000 in such an annuity contract. Assume investment earnings are credited at the end of the year and are reinvested. a. How much money can Hometown expect to make on average on the contract? [10] b. What is the probability that Hometown would lose money on the contract? [10] c. Suppose that Hometown wants to identify the minimum guaranteed annual rate of return that provides a 2% chance of the company losing money on the contract. What should the minimum guaranteed annual rate of return be? [15] 3. Each year, the Schriber Corporation must determine how much to contribute to the company's pension plan. The company uses a ten-year planning horizon to determine the contribution which, if made annually in each of the next ten years, would allow for only a 10% chance of the fund 2. HWAP2 Insert Draw Page Layout Formulas Data Tell me Comments Hometown Insurance 2. Hometown Insurance sells 10 -year annuities to retirees who are looking for stable sources of investment income. Hometown invests the annuity funds it receives in an equity index fund with annual returns that are normally distributed with a mean of 9% and standard deviation of 3%. It guarantees investors a minimum annual return of 6.5% and a maximum return (or rate cap) of 8.75%. This limits both the retirees' down-side risk and up-side return potential. Of course, Hometown makes its money on these contracts when the actual return exceeds the rate cap. Suppose a retiree invests $50,000 in such an annuity contract. Assume investment earnings are credited at the end of the year and are reinvested. a. How much money can Hometown expect to make on average on the contract? [10] b. What is the probability that Hometown would lose money on the contract? [10] c. Suppose that Hometown wants to identify the minimum guaranteed annual rate of return that provides a 2% chance of the company losing money on the contract. What should the minimum guaranteed annual rate of return be? [15] 3. Each year, the Schriber Corporation must determine how much to contribute to the company's pension plan. The company uses a ten-year planning horizon to determine the contribution which, if made annually in each of the next ten years, would allow for only a 10% chance of the fund
