Your best friend consults you for investment advice. You learn that his tax rate is $35 \%$, and he has the following current investments and debts:

• A car loan with an outstanding balance of $\$ 5000$ and a $4.86 \%$ APR (monthly compounding)

• Credit cards with an outstanding balance of $\$ 10,000$ and a $14.89 \%$ APR (monthly compounding)

• A regular savings account with a $\$ 30,000$ balance, paying a $5.51 \%$ EAR

• A money market savings account with a $\$ 100,000$ balance, paying a $5.18 \%$ APR (daily compounding)

• A tax-deductible home equity loan with an outstanding balance of $\$ 25,000$ and a $5.09 \%$ APR (monthly compounding)

a. Which savings account pays a higher after-tax interest rate?

b. Should your friend use his savings to pay off any of his outstanding debts? Explain.

Johnson and Johnson's five-year borrowing rate is $1.9 \%$ and Xerox's is $4.0 \%$. Which would you prefer? $\$ 500$ from Johnson and Johnson paid today or a promise that the firm will pay you $\$ 575$ in five years? Which would you choose if Xerox offered you the same alternative?

Suppose the current one-year interest rate is $5.7 \%$. One year from now, you believe the economy will start to slow and the one-year interest rate will fall to $4.7 \%$. In two years, you expect the economy to be in the midst of a recession, causing the Federal Reserve to cut interest rates drastically and the one-year interest rate to fall to $1.7 \%$. The one-year interest rate will then rise to $2.7 \%$ the following year, and continue to rise by $1 \%$ per year until it returns to $5.7 \%$, where it will remain from then on.

a. If you were certain regarding these future interest rate changes, what two-year interest rate would be consistent with these expectations?

b. What current term structure of interest rates, for terms of $1$ to $10$ years, would be consistent with these expectations?

c. Plot the yield curve in this case. How does the one-year interest rate compare to the $10$-year interest rate?

What is the shape of the yield curve given the term structure below? What expectations are investors likely to have about future interest rates?

$$\begin{array}{lccccccc} \text{Term} & \text{1 year} & \text{2 years} & \text{3 years} & \text{5 years} & \text{7 years} & \text{10 years} & \text{20 years} \\ \hline \text{Rate (EAR \\\%)} & 1.97 & 2.36 & 2.62 & 3.21 & 3.72 & 4.15 & 4.95 \\ \hline \end{array}$$

Using the term structure in Problem above, what is the present value of an investment that pays $\$ 110$ at the end of each of years $1,2$ , and $3$? If you wanted to value this investment correctly using the annuity formula, which discount rate should you use?

Many academic institutions offer a sabbatical policy. Every seven years a professor is given a year free of teaching and other administrative responsibilities at full pay. For a professor earning $\$ 100,000$ per year who works for a total of $42$ years, what is the present value of the amount she will earn while on sabbatical if the interest rate is $6 \%$ (EAR)?