Inflation and Loan
Chapter 5 Interest Rates
Problem 3
Which do you prefer: a bank account that pays 5% per year (EAR) for three years or
a. An account that pays 2 every six months for three years?
b. An account that pays 7 every 18 months for three years?
c. An account that pays per month for three years?
If you deposit $1 into a bank account that pays 5% per year for 3 years you will have after 3 years.
a. If the account pays per 6 months then you will have after 3 years, so you prefer every 6 months.
b. If the account pays per 18 months then you will have after 3 years, so you prefer 5% per year.
c. If the account pays per month then you will have after 3 years, so you prefer every month.
Problem 6 Your bank account pays interest with an EAR of 5%. What is the APR quote for this account based on semiannual compounding? What is the APR with monthly compounding?
Using the formula for converting from an EAR to an APR quote
With annual payments k = 1, so APR = 5% With semiannual payments k = 2, so APR = 4.939% With monthly payments k = 12, so APR = 4.889% Problem 16
You have just purchased a car and taken out a $50,000 loan. The loan has a five-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 month, second month, and first year? (Hint: Compute the loan balance after one month, two months and one year.) b. How much will you pay in interest, and how much will you pay in principal, during the fourth year (i.e., between there and four years from now)?
Timeline: 0 | 1 | 2 | 3 | | | | 60 | | | | | | | | | | | | | | | | | | | | | | | | | | | 50,000 | –C | –C | –C | | | | –C | a. First, solve for the monthly mortgage payment at 6% APR. The 6% APR implies a monthly rate of
Each monthly payment is $966.64. After one month, the balance (principal) of the
Problem 3
Which do you prefer: a bank account that pays 5% per year (EAR) for three years or
a. An account that pays 2 every six months for three years?
b. An account that pays 7 every 18 months for three years?
c. An account that pays per month for three years?
If you deposit $1 into a bank account that pays 5% per year for 3 years you will have after 3 years.
a. If the account pays per 6 months then you will have after 3 years, so you prefer every 6 months.
b. If the account pays per 18 months then you will have after 3 years, so you prefer 5% per year.
c. If the account pays per month then you will have after 3 years, so you prefer every month.
Problem 6 Your bank account pays interest with an EAR of 5%. What is the APR quote for this account based on semiannual compounding? What is the APR with monthly compounding?
Using the formula for converting from an EAR to an APR quote
With annual payments k = 1, so APR = 5% With semiannual payments k = 2, so APR = 4.939% With monthly payments k = 12, so APR = 4.889% Problem 16
You have just purchased a car and taken out a $50,000 loan. The loan has a five-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 month, second month, and first year? (Hint: Compute the loan balance after one month, two months and one year.) b. How much will you pay in interest, and how much will you pay in principal, during the fourth year (i.e., between there and four years from now)?
Timeline: 0 | 1 | 2 | 3 | | | | 60 | | | | | | | | | | | | | | | | | | | | | | | | | | | 50,000 | –C | –C | –C | | | | –C | a. First, solve for the monthly mortgage payment at 6% APR. The 6% APR implies a monthly rate of
Each monthly payment is $966.64. After one month, the balance (principal) of the