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Future Value What is the future value in seven years of \(\$ 1,000\) invested in an account with a stated annual interest rate of 8 percent, 1\. Compounded annually? 2\. Compounded semiannually? 3\. Compounded monthly? 4\. Compounded continuously? 5\. Why does the future value increase as the compounding period shortens?

Calculating Annuities You are planning to save for retirement over the next \(\mathbf{3 0}\) years. To do this, you will invest \(\$ 700\) a month in a stock account and \(\$ \mathbf{\$ 0 0}\) a month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with an 8 percent return. How much can you withdraw each month from your account assuming a 25-year withdrawal period?

Calculating Rates of Return Suppose an investment offers to quadruple your money in 12 months (don't believe it). What rate of return per quarter are you being offered?

Calculating Rates of Return You're trying to choose between two different investments, both of which have up-front costs of \(\$ 75,000\). Investment \(\mathrm{G}\) returns \(\$ 135,000\) in six years. Investment \(H\) returns \(\$ 195,000\) in 10 years. Which of these investments has the higher return?

Growing Perpetuities Mark Weinstein has been working on an advanced technology in laser eye surgery. His technology will be available in the near term. He anticipates his first annual cash flow from the technology to be \(\$ 215,000\), received two years from today. Subsequent annual cash flows will grow at 4 percent in perpetuity. What is the present value of the technology if the discount rate is 10 percent?

Perpetuities A prestigious investment bank designed a new security that pays a quarterly dividend of \(\$ 5\) in perpetuity. The first dividend occurs one quarter from today. What is the price of the security if the stated annual interest rate is 7 percent, compounded quarterly?

Annuity Present Values What is the present value of an annuity of \(\$ 5,000\) per year, with the first cash flow received three years from today and the last one received 25 years from today? Use a discount rate of 8 percent.

Annuity Present Values What is the value today of a 15 -year annuity that pays \(\$ 750\) a year? The annuity's first payment occurs six years from today. The annual interest rate is 12 percent for years 1 through 5 , and 15 percent thereafter.

Growing Annuity Southern California Publishing Company is trying to decide whether to revise its popular textbook, Financial Psychoanalysis Made Simple. The company has estimated that the revision will cost \(\$ 65,000\). Cash flows from increased sales will be \(\$ 18,000\) the first year. These cash flows will increase by 4 percent per year. The book will go out of print five years from now. Assume that the initial cost is paid now and revenues are received at the end of each year. If the company requires an 11 percent return for such an investment, should it undertake the revision?

Growing Annuity Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31 , you just received your salary of \(\$ 60,000\), and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 5 percent of your annual salary in an account that will earn 9 percent per year. Your salary will increase at 4 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today?