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. Smiths ideas and questions are the following:

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

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?

Years. (10 points).

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?

%. (10 points).

(B) As another option, Mrs. Smith is considering letting her heirs fend for themselves and using her $420,000 to generate $3,300 per month for the rest of her life.

1. If Mrs. Smith manages to deposit the $420,000 at a an APR of 8% per year (8% APR =

8% / 12 per month) and receives $3,300 per month, what age will she be when her funds run out?

Years old. (10 points).

2. If Mrs. Smith plans to live to age 93, at what monthly interest rate must she deposit the $420,000 to be able to receive $3,300 per month with no balance left in the account at her death?

%. (10 points).

(C) As her last option, Mrs. Smith is considering leaving an endowment to her Alma Mater that will produce $10,000 a year forever.

1. If the current rate for such investment is 4%, how much money must Mrs. Smith deposit to generate $10,000 per year forever?

$ . (10 points).

2. If the current rate for such an investment is 6% and inflation is expected to be 1.5% per year, how much money must Mrs. Smith deposit to generate the equivalent of $10,000 per year, after inflation, forever? (i.e. the $10,000 would need to grow by 1.5% every single year).

$ . (10 points).