Please do question 1. a b c d ef

1. Lynn Price recently completed her MBA and accepted a job with an electronics manufacturing company. Although she likes her job, she is also looking forward to retiring one day. To ensure that her retirement is comfortable, Lynn intends to invest $4,000 of her salary into a tax-sheltered retirement fund at the end of each year. Lynn is not certain what rate of return this investment will earn each year, but she expects each year's rate of return could be modeled appropriately as a normally distributed random variable with a mean of 10.5% and standard deviation of 2%. a. If Lynn is 30 years old, how much money should she expect to have (on average) in her retirement fund at age 60 ? [5] b. What is the probability that Lynn will have more than $1 million in her retirement fund when she reaches age 60 ? [5] c. How much should Lynn invest each year if she wants there to be a 90% chance of having at least $1 million in her retirement fund at age 60? [6] d. Suppose that Lynn contributes $4,000 annually to her retirement fund for eight years and then terminates these annual contributions. How much of her salary would she have contributed to this retirement plan and how much money could she expect to have accumulated at age 60 [ [7] e. Now suppose that Lynn contributes nothing to her retirement fund for eight years and then begins contributing $4,000 annually until age 60 . How much of her salary would she have contributed to this retirement plan and how much money could she expect to have accumulated at age 60?[7] f. What should Lynn (and you) learn from the answers to questions d and e ? [S] 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 eamings are credited at the end of the year and are reinvested. 1. Lynn Price recently completed her MBA and accepted a job with an electronics manufacturing company. Although she likes her job, she is also looking forward to retiring one day. To ensure that her retirement is comfortable, Lynn intends to invest $4,000 of her salary into a tax-sheltered retirement fund at the end of each year. Lynn is not certain what rate of return this investment will earn each year, but she expects each year's rate of return could be modeled appropriately as a normally distributed random variable with a mean of 10.5% and standard deviation of 2%. a. If Lynn is 30 years old, how much money should she expect to have (on average) in her retirement fund at age 60 ? [5] b. What is the probability that Lynn will have more than $1 million in her retirement fund when she reaches age 60 ? [5] c. How much should Lynn invest each year if she wants there to be a 90% chance of having at least $1 million in her retirement fund at age 60? [6] d. Suppose that Lynn contributes $4,000 annually to her retirement fund for eight years and then terminates these annual contributions. How much of her salary would she have contributed to this retirement plan and how much money could she expect to have accumulated at age 60 [ [7] e. Now suppose that Lynn contributes nothing to her retirement fund for eight years and then begins contributing $4,000 annually until age 60 . How much of her salary would she have contributed to this retirement plan and how much money could she expect to have accumulated at age 60?[7] f. What should Lynn (and you) learn from the answers to questions d and e ? [S] 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 eamings are credited at the end of the year and are reinvested