# Hw Chapter4 Essay

1543 Words Nov 30th, 2012 7 Pages
5.4. You have found three investment choices for a one-year deposit: 10% APR
Compounded monthly, 10% APR compounded annually, and 9% APR compounded daily. Compute the EAR for each investment choice. (Assume that there are 365 days in the year.)
Sol:
1+EAR= (1+r/k)k
So, for 10% APR compounded monthly, the EAR is 1+EAR= (1+0.1/12)12 = 1.10471
=> EAR= 10.47%
For 10% compounded annually, the EAR is
1+EAR= (1+0.1)=1.1 * EAR= 10% (remains the same).
For 9% compounded daily
1+EAR= (1+0.09/365)365 = 1.09416 * EAR= 9.4%

5-8. You can earn \$50 in interest on a \$1000 deposit for eight months. If the EAR is the same regardless of the length of the investment, how much interest will you earn on a \$1000 deposit for
a. 6 months.
So by switching credit cards we are able to spend an extra 31, 250 − 25, 000 = \$6, 250.
We do not have to pay taxes on this amount of new borrowing, so this is our after-tax benefit of switching cards.

5-28. Consider a project that requires an initial investment of \$100,000 and will produce a single cash flow of \$150,000 in five years.
a. What is the NPV of this project if the five-year interest rate is 5% (EAR)?
b. What is the NPV of this project if the five-year interest rate is 10% (EAR)?
c. What is the highest five-year interest rate such that this project is still profitable?
Sol:
a. NPV = –100,000 + 150,000 / 1.055 = \$17,529.
b. NPV = –100,000 + 150,000 / 1.105 = –\$6862.
Here we need to calculate the IRR.
Therefore,
IRR = (150,000 / 100,000)1/5 – 1 = 8.45%.

5-32. Suppose the current one-year interest rate is 6%. One year from now, you believe the economy will start to slow and the one-year interest rate will fall to 5%. 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 2%. The one-year interest rate will then rise to 3% the following year, and continue to rise by 1% per year until it returns to 6%, 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