# Hw Chapter4 Essay

1530 Words
Nov 7th, 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.

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.

*…show more content…*
c. Plot the yield curve in this case. How does the one-year interest rate compare to the 10-year interest rate?

Sol:

a. The one-year interest rate is 6%. If rates fall next year to 5%, then if you reinvest at this rate over two years you would earn (1.06)(1.05) = 1.113 per dollar invested. This amount corresponds to an EAR of (1.113)1/2 – 1 = 5.50% per year for two years. Thus, the two-year rate that is consistent with these expectations is 5.50%. b. Year | Future Interest Rate | FV from re-investing | EAR | 1 | 6% | 1.0600 | 6.00% | 2 | 5% | 1.1130 | 5.50% | 3 | 2% | 1.1353 | 4.32% | 4 | 3% | 1.1693 | 3.99% | 5 | 4% | 1.2161 | 3.99% | 6 | 5% | 1.2769 | 4.16% | 7 | 6% | 1.3535 | 4.42% | 8 | 6% | 1.4347 | 4.62% | 9 | 6% | 1.5208 | 4.77% | 10 | 6% | 1.6121 | 4.89% |

c. We can get the yield curve by considering all EARs above. It is an inverted curve.

5-36. You are enrolling in an MBA program. To pay your tuition, you can either take out a standard student loan (so the interest payments are not tax deductible) with an EAR of 5 ½% or you can use a tax-deductible home equity loan with an APR (monthly) of 6%. You anticipate being in a very low tax bracket, so your tax rate will be only 15%. Which loan should you use?

Sol:

APR is given, So we can get EAR by,

(1+0.06/12)12 = 1.06168.

So, EAR = 6.168%.

We have to convert the before tax rate to after tax rate.

6.168×(1- 0.15) = 5.243%

Since student loan is higher after

Sol:

a. The one-year interest rate is 6%. If rates fall next year to 5%, then if you reinvest at this rate over two years you would earn (1.06)(1.05) = 1.113 per dollar invested. This amount corresponds to an EAR of (1.113)1/2 – 1 = 5.50% per year for two years. Thus, the two-year rate that is consistent with these expectations is 5.50%. b. Year | Future Interest Rate | FV from re-investing | EAR | 1 | 6% | 1.0600 | 6.00% | 2 | 5% | 1.1130 | 5.50% | 3 | 2% | 1.1353 | 4.32% | 4 | 3% | 1.1693 | 3.99% | 5 | 4% | 1.2161 | 3.99% | 6 | 5% | 1.2769 | 4.16% | 7 | 6% | 1.3535 | 4.42% | 8 | 6% | 1.4347 | 4.62% | 9 | 6% | 1.5208 | 4.77% | 10 | 6% | 1.6121 | 4.89% |

c. We can get the yield curve by considering all EARs above. It is an inverted curve.

5-36. You are enrolling in an MBA program. To pay your tuition, you can either take out a standard student loan (so the interest payments are not tax deductible) with an EAR of 5 ½% or you can use a tax-deductible home equity loan with an APR (monthly) of 6%. You anticipate being in a very low tax bracket, so your tax rate will be only 15%. Which loan should you use?

Sol:

APR is given, So we can get EAR by,

(1+0.06/12)12 = 1.06168.

So, EAR = 6.168%.

We have to convert the before tax rate to after tax rate.

6.168×(1- 0.15) = 5.243%

Since student loan is higher after