Hw Chapter4
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.
b. 1 year.
c. 1 1/2 years.
Sol:
Since we can earn $50 interest on a $1000 deposit,
Rate of interest is 5%
Therefore, EAR = (1.05)12/8 -1 =7.593% a) 1000(1.075936/12 – 1) = 37.27 b) 1000(1.07593−1) = 75.93 c) 1000(1.075933/2 −1) = 116.03
5-12. Capital One is advertising a 60-month, 5.99% APR motorcycle loan. If you need to borrow $8000 to purchase your dream Harley Davidson, what will your monthly payment be?
Sol:
Discount rate for 12 months is,
5.99/12 = 0.499167%
C= 8000/[1/0.004991(1-1/(1+0.004991)60)] = $154.63
5-16. You have just purchased a home and taken out a $500,000 mortgage. The mortgage has a 30-year term with monthly payments and an APR of 6%.
a. How much will you pay in interest, and how much will you pay in principal, during the first year?
b. How much will you pay in interest, and how much will you pay in principal, during the 20th year (i.e., between 19 and 20 years from now)? Sol: a. APR of 6%/12 = 0.5% per month.
Payment = 500,000/[(1/.005)(1- 1/1.005360)]= $2997.75
Total annual payments = 2997.75 × 12 = $35,973.
Loan Balance after 1 year is 2997.75[1/0.005(1- 1/1.005348)] = $493,860.
Therefore,
500,000 – 493,860 = $6140 is principal repaid in first year.
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.
b. 1 year.
c. 1 1/2 years.
Sol:
Since we can earn $50 interest on a $1000 deposit,
Rate of interest is 5%
Therefore, EAR = (1.05)12/8 -1 =7.593% a) 1000(1.075936/12 – 1) = 37.27 b) 1000(1.07593−1) = 75.93 c) 1000(1.075933/2 −1) = 116.03
5-12. Capital One is advertising a 60-month, 5.99% APR motorcycle loan. If you need to borrow $8000 to purchase your dream Harley Davidson, what will your monthly payment be?
Sol:
Discount rate for 12 months is,
5.99/12 = 0.499167%
C= 8000/[1/0.004991(1-1/(1+0.004991)60)] = $154.63
5-16. You have just purchased a home and taken out a $500,000 mortgage. The mortgage has a 30-year term with monthly payments and an APR of 6%.
a. How much will you pay in interest, and how much will you pay in principal, during the first year?
b. How much will you pay in interest, and how much will you pay in principal, during the 20th year (i.e., between 19 and 20 years from now)? Sol: a. APR of 6%/12 = 0.5% per month.
Payment = 500,000/[(1/.005)(1- 1/1.005360)]= $2997.75
Total annual payments = 2997.75 × 12 = $35,973.
Loan Balance after 1 year is 2997.75[1/0.005(1- 1/1.005348)] = $493,860.
Therefore,
500,000 – 493,860 = $6140 is principal repaid in first year.