Case # 1

Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Moran. Ms. Moran by contract will retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an annual end-of-year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20-year period, the annual payments will pass to her heirs. During the 12-year accumulation period Sunrise wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 9% interest. Once the 20-year distribution period begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 12% per year. At the end of the distribution period, the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and that the first distribution payment will be received at the end of year 13.

Required

a. Draw a time line depicting all of the cash flows associated with Sunrises view of the retirement annuity.

b. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?

c. How large must Sunrises equal annual end-of-year deposits into the account be over the 12-year accumulation period to fund fully Ms. Morans retirement annuity?

d. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period?

e. How much would Sunrise have to deposit annually during the accumulation period if Ms. Morans retirement annuity were a perpetuity and all other terms were the same as initially described?

Case # 2

A client, 35 years old, who would like to retire at age 65 (30 years from today). Her goal is to have enough in her retirement account to provide an income of $75,000 a year, starting a year after retirement or year 31, for 25 years thereafter. She had a late start on saving for retirement, with a current balance of $10,000. To catch up, she is now committed to saving $5,000 a year, with the first contribution a year from now. A single parent with two children, both of which will be attending college starting in five years, she won't be able to increase the annual $5,000 commitment until after the kids have graduated. Once the children are finished with college, she will have extra disposable income, but is worried about just how much of an increase it will take to meet her ultimate retirement goals. To help her meet this goal, estimate how much she will need to save every year, starting 10 years from now, when the kids are out of college. Assume an average annual 8% return in the retirement account.

Case # 3

You plan to retire 33 years from now. You expect that you will live 27 years after retiring. You want to have enough money upon reaching retirement age to withdraw $180,000 from the account at the beginning of each year you expect to live, and yet still have $2,500,000 left in the account at the time of your expected death (60 years from now). You plan to accumulate the retirement fund by making equal annual deposits at the end of each year for the next 33 years. You expect that you will be able to earn 12% per year on your deposits. However, you only expect to earn 6% per year on your investment after you retire since you will choose to place the money in less risky investments. What equal annual deposits must you make each year to reach your retirement goal?

Case # 4

Debbie recently graduated from NC State University with a BS degree in Electrical Engineering. She is gainfully employed by GoPack Computing located in Research Triangle Park. Debbie is 25 and plans to retire at 65 or 40 years from now. She wants to travel during her retirement and has decided to start saving now. She can save $200 per month for the next ten years then she plans to increase her savings to $500 per month for the remaining 30 years. How much can Debbie withdraw each month during her retirement? Assume she will live for 20 years after retirement and withdraws all of the money in the account. She will earn 12% during the saving period and 6% during retirement. Assume monthly compounding during the savings and retirement periods.

Case # 5

Frank recently graduated from MIT with a Ph.D. in Physics. He has started an investment company applying his mathematical knowledge to valuing assets. Frank is 40 and plans to retire at 65 or 25 years from now. He wants to travel much like Debbie during his retirement and must start saving now. How much must he save per month for the next 25 years to be able to withdraw $24,368.98 per month? Assume he will live for 20 years after retirement and withdraws all of the money in the account. He will earn 12% during the saving period and 6%during retirement. Assume monthly compounding during the savings and retirement periods.