Finance 300 Chapter Five
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>
