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Calculating Future Values Compute the future value of \(\$ 1,000\) compounded annually for 1\. 10 years at 6 percent. 2\. 10 years at 9 percent.

Calculating the Number of Periods At 9 percent interest, how long does it take to double your money? To quadruple it?

Calculating Present Values Imprudential, Inc., has an unfunded pension liability of \(\$ 750\) million that must be paid in 20 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 8.2 percent, what is the present value of this liability?

Continuous Compounding Compute the future value of \(\$ 1,900\) continuously compounded for 1\. 5 years at a stated annual interest rate of \(\mathbf{1 2}\) percent. 2\. 3 years at a stated annual interest rate of \(\mathbf{1 0}\) percent. 3\. 10 years at a stated annual interest rate of 5 percent. 4\. 8 years at a stated annual interest rate of 7 percent.

Present Value and Multiple Cash Flows Conoly Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 18 percent? At 24 percent?

Present Value and Multiple Cash Flows Investment \(X\) offers to pay you \(\$ 5,500\) per year for nine years, whereas Investment \(Y\) offers to pay you \(\$ 8,000\) per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 22 percent?

Calculating Annuity Present Value An investment offers \(\$ 4,300\) per year for 15 years, with the first payment occurring one year from now. If the required return is 9 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For \(\mathbf{7 5}\) years? Forever?

Calculating Perpetuity Values The Perpetual Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs \(\$ 20,000\) per year forever. If the required return on this investment is 6.5 percent, how much will you pay for the policy? Suppose the Perpetual Life Insurance Co. told you the policy costs \(\$ 340,000\). At what interest rate would this be a fair deal?

Interest Rates Well-known financial writer Andrew Tobias argues that he can earn 177 percent per year buying wine by the case. Specifically, he assumes that he will consume one \(\$ 10\) bottle of fine Bordeaux per week for the next 12 weeks. He can either pay \(\$ 10\) per week or buy a case of 12 bottles today. If he buys the case, he receives a 10 percent discount and, by doing so, earns the 177 percent. Assume he buys the wine and consumes the first bottle today. Do you agree with his analysis? Do you see a problem with his numbers?

Calculating EAR Friendly's Quick Loans, Inc., offers you "three for four or I knock on your door." This means you get \(\$ 3\) today and repay \(\$ 4\) when you get your paycheck in one week (or else). What's the effective annual return Friendly's earns on this lending business? If you were brave enough to ask, what APR would Friendly's say you were paying?