The following two questions are based on this scenario: You want to start a savings program for
Question:
The following two questions are based on this scenario:
You want to start a savings program for a college fund for your daughter. She is currently two years old (t=0) and will start college when she is 18 (t=16). Assume you are currently 30 years old.
- College education currently costs $90,000 per year at a private university like Northwestern, including room and board.
- You expect your daughter will attend college for four years.
- Assume the costs of a college education grow at a 10% rate per year.
- You want to save the same amount each year starting next year, and your savings program will end when you daughter is 17, at t=15.
- Assume that the market interest rate is 2%. You earn this interest on your savings.
Hint: I recommend drawing the cash flow stream on paper or tracing out all cash flows in Excel.
Problem 1, Question 1a.
Based on the above, what are the expected costs of college education in year t=16?
Problem 1, Question 1b.
Based on the above, what are the expected costs of college education in year t=17?
Problem 1, Question 1c.
Based on the above, what are the expected costs of college education in year t=18?
Problem 1, Question 1d.
Based on the above, what are the expected costs of college education in year t=19?
Problem 1, Question 2.
How much cash must you have in the bank when your daughter is 17 to fund her four years of college; i.e., what is the present value at t=15 of the costs calculated in question 1?
Problem 1, Question 3.
What is the PV of the costs today, at t=0?
Problem 1, Question 4.
How much must you save each year (the same amount each year), starting next year, such that you will have enough saved for your daughter’s education?
Problem 2: Retirement Planning
In the next two questions we will examine a realistic retirement planning situation.
- Assume you are 30 years old (t=0) and you will retire when you are 65 (t=35).
- You will save the maximum amount allowed into your 401-k plan every year, starting next year, when you are 31 (t=1).
- Assume the maximum amount you can save next year is $17,500 and that this amount will grow by 1% per year until you retire. Hint: This is a growing annuity.
- Assume that in retirement, you will spend the same amount each year.
- Assume you will live until you are 90 years old.
- Assume the market interest rate for this question is 2%.
Problem 2, Question 1.
Based on the above, if you follow this retirement savings plan, saving the maximum allowed, how much cash would you have in the bank when you retire; i.e., what is the future value at t=35 (age 65) of the cash flows?
Problem 2, Question 2.
Given your answer to the last question, assume you take all of the money from your 401-k account and use it to buy an annuity when you are 65. The annuity will pay you a constant cash amount each year from the age 66 to 90 (t=36 to 60); i.e., this is a simple (non-growing) annuity.
How much will the annuity pay you each year through your retirement?
Problem 3: Rates of Return
The next four questions are based on the following: You invested a lump sum of $50,000 in a new company ten years ago and left it there without any further investments and now, today, the company listed on the stock exchange (an initial public offering, IPO) and your investment is worth $575,000.
Hint: The (rate of) return from today up to a period t (also called holding period return) is defined as
Problem 3, Question 1.
Given the above, what total return (i.e., cumulative,notannualized) did you earn on your investment across the ten years?
Problem 3, Question 2.
Given the above, what was the effective annual return on your investment?
Problem 3, Question 3.
Given the above, what was the effective monthly return on your investment?
Problem 3, Question 4.
For this question, assume the Banker’s rule, which is to assume every month has 30 days, and there are 360 days in the year. Based on the above, what was the effective daily return on your investment?
Principles of Risk Management and Insurance
ISBN: 978-0132992916
12th edition
Authors: George E. Rejda, Michael McNamara