Textbook Problem

Comprehensive The following are three independent situations:

1. 1. K. Herrmann has decided to set up a scholarship fund for students. She is willing to deposit $5,000 in a trust fund at the end of each year for 10 years. She wants the trust fund to then pay annual scholarships at the end of each year for 30 years.
2. 2. Charles Jordy is planning to save for his retirement. He has decided that he can save $3,000 at the end of each year for the next 10 years, $5,000 at the end of each year for Years 11 through 20, and $10,000 at the end of each year for Years 21 through 30.
3. 3. Patricia Karpas has $200,000 in savings on the day she retires. She intends to spend $2,000 per month traveling around the world for the next 2 years, during which time her savings will earn 18%, compounded monthly. For the next 5 years, she intends to spend $6,000 every 6 months, during which time her savings will earn 12%, compounded semiannually. For the rest of her life expectancy of 15 years, she wants an annuity to cover her living costs. During this period, her savings will earn 10% compounded annually. Assume that all payments occur at the end of each period.

Required:

1. 1. In Situation 1, how much will the annual scholarships be if the fund can earn 6%? How much at 10%?
2. 2. In Situation 2,
   1. (a) How much will Charles have at the end of 30 years if his savings can earn 10%? How much at 6%?
   2. (b) If Charles expects to live for 20 years in retirement, how much can he withdraw from his savings at the end of each year if his savings earn 10%? How much at 6%?
   3. (c) How much would Charles need to invest today to have the same amount available at the time he retires as calculated in Situation 2(a) at 10%? How much at 6%?
3. 3. In Situation 3, how much will Patricia’s annuity be?