Finance 300 Chapter Five

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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 $700,000. The mortgage is currently exactly​ 18½ years​ old, and you have just made a payment. If the interest rate on the mortgage is 6.25% ​(APR), how much cash will you have from the sale once you pay off the​ mortgage? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Cash that remains after payoff of mortgage is <$476531.95>

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?​ (Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The APR quote for the account with semiannual compounding is <4.939%> The APR quote for the account with monthly compounding is <4.887%>

You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $2,356 and you have made every payment on time. The original term of the mortgage was 30​ years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 7.500% ​(APR). How much do you owe on the mortgage​ today? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The amount you owe today is <$320244.25>

A payday loan is structured to obscure the true interest rate you are paying. For​ example, in​ Washington, you pay a $30 ​"fee" for a​ two-week $195 payday loan​ (when you repay the​ loan, you pay $225​). What is the effective annual interest rate for this​ loan? ​(Assume 26​ bi-weekly periods per​ year.)

The effective annual interest rate is <4029.01%>

You are considering two ways of financing a spring break vacation. You could put it on your credit​ card, at 18% ​APR, compounded​ monthly, or borrow the money from your​ parents, who want an interest payment of 8% every six months. Which is the lower​ rate? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The effective annual rate for your credit card is <19.56%> The effective annual rate for the loan from you parents is <16.64%> The option with the lower effective annual rate is <the loan from your parents>

You have invested in a business that proudly reports that it is profitable. Your investment of $4,900 has produced a profit of $296. The managers think that if you leave your $4,900 invested with​ them, they should be able to generate $296 per year in profits for you in perpetuity. Evaluating other investment​ opportunities, you note that other​ long-term investments of similar risk offer an expected return of 7.7%. Should you remain invested in this​ firm?

The expected return of your investment is <6.0%> If projects that are similar in horizon and risk are offering an expected return on 7.7%, the this business <is not> earning your opportunity cost of capital, and you should <invest elsewhere>

You are looking to buy a car and you have been offered a loan with an APR of 5.5%​, compounded monthly. a. What is the true monthly rate of​ interest? b. What is the​ EAR?

The monthly rate of interest is <0.4583%> The EAR is <5.6408%>

The mortgage on your house is five years old. It required monthly payments of $1,390​, had an original term of 30​ years, and had an interest rate of 10% ​(APR). In the intervening five​ years, interest rates have fallen and so you have decided to refinance—that ​is, you will roll over the outstanding balance into a new mortgage. The new mortgage has a​ 30-year term, requires monthly​ payments, and has an interest rate of 5.625% ​(APR). a. What monthly repayments will be required with the new​ loan? b. If you still want to pay off the mortgage in 25​ years, what monthly payment should you make after you​ refinance? c. Suppose you are willing to continue making monthly payments of $1,390. How long will it take you to pay off the mortgage after​ refinancing? d. Suppose you are willing to continue making monthly payments of $1,390​, and want to pay off the mortgage in 25 years. How much additional cash can you borrow today as part of the​ refinancing? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The monthly repayments with the new loan will be <$880.56> If you still want to pay off the mortgage in 23 years, the monthly repayments will be <$950.80> It will take approximately <155> months

If the rate of inflation is 5.1%​, what nominal interest rate is necessary for you to earn a 2.4% real interest rate on your​ investment? What is the nominal interest rate? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The nominal interest rate is <7.62%>

You have an outstanding student loan with required payments of $550 per month for the next four years. The interest rate on the loan is 8% APR​ (compounded monthly). Now that you realize your best investment is to prepay your student​ loan, you decide to prepay as much as you can each month. Looking at your​ budget, you can afford to pay an extra $150 a month in addition to your required monthly payments of $550​, or $700 in total each month. How long will it take you to pay off the​ loan? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The number of months to pay off the loan is <36.35>

You make monthly payments on your car loan. It has a quoted APR of 5.7% ​(monthly compounding). What percentage of the outstanding principal do you pay in interest each​ month? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The percentage of the outstanding principle you pay in interest each month is <0.47500%>

In​ 1975, interest rates were 7.85% and the rate of inflation was 12.3% in the United States. What was the real interest rate in​ 1975? How would the purchasing power of your savings have changed over the​ year? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The real interest rate is <-3.96%> The purchasing power over that year did the following: <declined by 3.96%>

You are pleased to see that you have been given a 6.73% raise this year.​ However, you read on the Wall Street Journal Web site that inflation over the past year has been 2.68%. How much better off are you in terms of real purchasing​ power? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The real purchasing power is <3.94%>

What is the shape of the yield curve given in the following term structure? what expectations are investors likely to have about future interest rates? Term---Rate(EAR%) 1---1.99 2---2.44 3---2.74 5---3.32 7---3.74 10---4.14 20---4.93

The yield curve is a normal yield curve (increasing) Interest rate might rise in the future

You have just taken out a $28,000 car loan with a 6% ​APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest?​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

When you make your first payment <$401.32> will go toward the principle of the loan and <$140> will go toward the interest

You are thinking about leasing a car. The purchase price of the car is $35,000. The residual value​ (the amount you could pay to keep the car at the end of the​ lease) is $15,000 at the end of 36 months. Assume the first lease payment is due one month after you get the car. The interest rate implicit in the lease is 5% ​APR, compounded monthly. What will be your lease payments for a 36​-month ​lease? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Your monthly lease payments will be <$661.92>

Suppose Oppenheimer Bank is offering a​ 30-year mortgage with an EAR of 5.375%. If you plan to borrow $220,000​, what will be your monthly​ payment? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Your monthly payment will be <$1214.41>

Suppose Capital One is advertising a 60​-month, 5.27% APR motorcycle loan. If you need to borrow $9,300 to purchase your dream​ Harley-Davidson, what will be your monthly​ payment?​ (Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Your monthly payment will be <$176.66>

You have found three investment choices for a​ one-year deposit 9.6% APR compounded​ monthly, 9.6% APR compounded​ annually, and 8.8% APR compounded daily. Compute the EAR for each investment choice.​ (Assume that there are 365 days in the​ year.) ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

the EAR for the first investment choice is <10.03%> the EAR for the second investment choice is <9.6%> the EAR for the third investment choice is <9.198%>

You are thinking about investing $4,872 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 $5,651 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 9% for the year. What should you​ do?

the PV of the return is <$5184.40> You should <invest in the business>


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