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