BusFin Ch 5
Suppose Capital One is advertising a 60-month, 6.25 % APR motorcycle loan. If you need to borrow $ 10 comma 000 to purchase your dream Harley-Davidson, what will be your monthly payment?
$194.49
You have just sold your house for $ 900,000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $ 800,000. The mortgage is currently exactly 18½ years old, and you have just made a payment. If the interest rate on the mortgage is 7.75 % (APR), how much cash will you have from the sale once you pay off the mortgage?
$377,589
Equivalent n-Period Discount Rate
(1 + r)^n - 1
If the rate of inflation is 6.2 %, what nominal interest rate is necessary for you to earn a 4.1 % real interest rate on your investment?
10.55%
If the rate of inflation is 4.1 %, what nominal interest rate is necessary for you to earn a 3.4 % real interest rate on your investment?
7.64%
Annual Percentage Rate (APR)
Indicates the amount of simple interest earned in one year, that is the amount of without the effect of compounding
You are considering two ways of financing a spring break vacation. You could put it on your credit card, at 14 % APR, compounded monthly, or borrow the money from your parents, who want an interest payment of 9 % every six months. Which is the lower rate?
The effective annual rate for your credit card is 14.93%. The effective annual rate for the loan from your parents is 18.81%. The option with the lower effective annual rate is your credit card .
You are considering two ways of financing a spring break vacation. You could put it on your credit card, at 17 % APR, compounded monthly, or borrow the money from your parents, who want an 9 % interest payment every six months. Which is the lower rate?
The effective annual rate for your credit card is 18.39 %. The effective annual rate for the loan from your parents is 18.81 %. Therefore, your credit card has the lower effective annual rate
Effective Annual rate
The total amount of interest that will be earned at the end of one year
Your firm is purchasing a new telephone system that will last for four years. You can purchase the system for an upfront cost of $150,000, or you can lease the system from the manufacturer for $4,000 paid at the end of each month. The lease price is offered for a 48-month lease with no early termination—you cannot end the lease early. Your firm can borrow at an interest rate of 6% APR with monthly compounding. Should you purchase the system outright or pay $4,000 per month?
Thus paying $4,000 per month for 48 months is equivalent to paying a present value of $170,321.27 today. This cost is $170,321.27 - $150,000 = $20,321.27 higher than the cost of purchasing the system, so it is better to pay $150,000 for the system rather than lease it.
Your firm is purchasing a new telephone system that will last for five years. You can purchase the system for an upfront cost of $300,000, or you can lease the system from the manufacturer for $6,000 paid at the end of each month. The lease price is offered for a 60-month lease with no early termination—you cannot end the lease early. Your firm can borrow at an interest rate of 7% APR with monthly compounding. Should you purchase the system outright or pay $6,000 per month?
Thus paying $6,000 per month for 60 months is equivalent to paying a present value of $303,014.85 today. This cost is $303,014.85 - $300,000 = $3,014.85 higher than the cost of purchasing the system, so it is better to pay $300,000 for the system rather than lease it.
Your firm is purchasing a new fleet of trucks that will last for six years. You can purchase the system for an upfront cost of $500,000, or you can lease the system from the manufacturer for $8,000 paid at the end of each month. The lease price is offered for a 72-month lease with no early termination—you cannot end the lease early. Your firm can borrow at an interest rate of 6% APR with monthly compounding. Should you purchase the system outright or pay $8,000 per month?
Thus paying $8,000 per month for 72 months is equivalent to paying a present value of $482,716.11 today. This cost is $500,000 - $482,716.11 = $17,283.89 lower than the cost of purchasing the fleet, so it is better to lease the fleet for $8,000 per month than to pay $500,000 for it.
You are thinking about investing $ 5,300 in your friend's landscaping business. Even though you know the investment is risky and you can't be sure, you expect your investment to be worth $ 5,850 next year. You notice that the rate for one-year Treasury bills is 1 %. However, you feel that other investments of equal risk to your friend's landscape business offer an expected return of 12 % for the year. What should you do?
You should invest if the present value of the benefit is greater than the amount you originally invested; in this case you should not invest in the business.
You have just taken out a $ 31 comma 000 car loan with a 9 % APR, compounded monthly. The loan is for five years. When you make your first payment in one month, a. how much of the payment will go toward the principal of the loan and b. how much will go toward interest?
a. $232.50 b. $411.01
You have just taken out a $ 24 comma 000 car loan with a 8 % APR, compounded monthly. The loan is for five years. When you make your first payment in one month, a. how much of the payment will go toward the principal of the loan and b. how much will go toward interest?
a. $326.64 b. $159.98
Suppose your bank account pays interest monthly with an effective annual rate of 5%. What amount of interest will you earn each month? If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $150,000 in 20 years?
a. (1.05)1/12 - 1 = 0.4074% b. $369.64
Suppose your bank account pays interest monthly with an effective annual rate of 6%. What amount of interest will you earn each month? If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $100,000 in 10 years?
a. (1.06)1/12 - 1 = 0.4868% b. $615.47
You have found three investment choices for a one-year deposit: a. 13 % APR compounded monthly b.13 % APR compounded annually c.11 % APR compounded daily Compute the EAR for each investment choice.
a. 13.803% b. 13.000% c. 11.626%
Your bank is offering you an account that will pay 16 % interest (an effective two-year rate) in total for a two-year deposit. Determine the equivalent discount rate for the following periods: a. Six months b. One year c. One month
a. 3.78% b. 7.70% c. 0.620%
Your bank is offering you an account that will pay 22 % interest in total for a two-year deposit. Determine the equivalent discount rate for a period length of: a. Six months b. One year c. One month
a. 5.10 % b. 10.45% c. 0.8320%
You have found three investment choices for a one-year deposit: a. 9.4 % APR compounded monthly, b. 9.4 % APR compounded annually, and c. 8.7 % APR compounded daily Compute the EAR for each investment choice.
a. 9.816% b. 9.400% c. 9.089%
Suppose Capital One is advertising a 60-month, 5.03 % APR motorcycle loan. If you need to borrow $ 8 comma 800 to purchase your dream Harley-Davidson, what will be your monthly payment?
$166.19
You have just sold your house for $ 1,050,000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $ 850,000. The mortgage is currently exactly 18.50 years old, and you have just made a payment. If the interest rate on the mortgage is 6.50 % (APR), how much cash will you have from the sale once you pay off the mortgage?
$528,781