Reference no: EM132996097

This morning, you arrived at your job as Head of Client Advisory Services for a major investment firm and saw only two items of your calendar. At 10:00 am you have an appointment with a major client, Mrs. Smith, and at 2:00pm you have a tee time to play Golf with several colleagues. While at first you were happy, you then read the details of your first appointment. Mrs. Smith today is turning 65, it is the first day of her retirement and she wants to discuss multiple options regarding her investments. You may have to skip golf today.

Before Mrs. Smith arrives, you study her account file and notice she has six different investments:

1. A promissory note entitling her to receive a lump sum of $100,000 5 years from today. Similar notes today yield 5% per year.

2. A 10 year CD paying 8% interest per year that she opened exactly 10 years ago with a $35,000 deposit.

3. An insurance settlement that will pay her $1,200 per month for the next 40 months. A finance company, GJ Worthless, is willing to buy this settlement from her today as long it can obtain a yield of 0.85% per month on its investment.

4. A retirement account that has always paid an APR of 6% per year (0.5% per month) compounded monthly, into which she has deposited $310 at the end of every month for the last 10 years.

5. 50 shares of a stock that will pay a $25 quarterly dividend (per share) three months from today and is expected to continue paying the same $25 per quarter forever. Similar investments today are priced to yield 1.25% per quarter.

6. 250 shares of a stock that will pay a $15 annual dividend (per share) a year from today and has increased its dividend payout by 2% every single year. This sock is expected to continue increasing its dividend payout at the same rate forever. Similar investments today are priced to yield 5% per year.

When Mrs. Smith arrives, after wishing her a happy 65th birthday and congratulating her on the first day of her retirement, you ask her what she has in mind for her investments. Mrs. Smith has several ideas and wants you to help her figure out some numbers she is not very clear on. For starters, Mrs. Smith plans to buy a luxury car. After this, she expects to have $420,000 left over in her account.

Mrs. Smith's ideas and questions are the following:

As one option, Mrs. Smith would like to leave her heirs $1,000,000 upon her death.

Problem 1. If she starts with $420,000 today and deposits the proceeds in an account paying 6% annual interest, how many years must he/she live for the balance to grow to $1million?

Problem 2. If she lives to age 88, what annual APR will result in the $420,000 reaching a balance of $1,000,000 upon her death, if she deposits them in an account that offers monthly compounding?