You are considering whether to buy or lease a machine whose purchase price is $\$ 12,000$. Taxes on the machine will be $\$ 580$ due in one year, $\$ 464$ due in two years, and $\$ 290$ due in three years. If you buy the machine, you expect to be able to sell it after three years for $\$ 5,000$. If you lease the machine for three years, you make an initial payment of $\$ 2650$ and then three payments of $\$ 2650$ at the end of each of the next three years. The leasing company will pay the taxes. The interest rate is $7.75 \%$ per year, compounded annually. Should you buy or lease the machine? Explain.

Interest is compounded annually. Consider the following choices of payments to you: Choice 1: $1500 now and$3000 one year from now
Choice 2: $1900 now and$2500 one year from now If the interest rate on savings were $5\%$ per year, which would you prefer ?

Interest is compounded annually. Consider the following choices of payments to you: Choice 1: $1500 now and$3000 one year from now
Choice 2: $1900 now and$2500 one year from now Is there an interest rate that would lead you to make a different choice? Explain.

In Exercises $28$ through $31$, use the formula in Exercise $26$ to answer the given question.

MORTGAGE PAYMENTS A homeowner puts $\$ 35,000$ down on a $\$ 350,000$ home and takes out a $30$-year mortgage for the balance. If the interest rate is $6 \%$ per year, compounded monthly, what are the monthly mortgage payments?

Oppenheimer Bank is offering a $30$-year mortgage with an APR of $5.25 \%$ based on monthly compounding. With this mortgage your monthly payments would be $\$ 2,000$ per month. In addition, Oppenheimer Bank offers you the following deal: Instead of making the monthly payment of $\$ 2,000$ every month, you can make half the payment every two weeks (so that you will make $52 / 2=26$ payments per year). With this plan, how long will it take to pay off the mortgage if the EAR of the loan is unchanged?

Use a spreadsheet to generate the last year of payments in a loan amortization table for a $600,000, 15-year mortgage with an APR of 5.5%

Use a spreadsheet or financial program on a calculator or computer to complete the problems.

Develop an amortization schedule for a $10$-year mortgage loan of $\$ 80,000$ at $7.2 \%$ compounded monthly.

The $40 million lottery prize that you have just won actually pays out$2 million a year for 20 years. The interest rate is 8%.
b. What is the present value if the first payment comes immediately?

The $40 million lottery prize that you have just won actually pays out$2 million a year for 20 years. The interest rate is 8%.
a. If the first payment comes after 1 year, what is the present value of your winnings?

A firm decides to increase output at a constant relative rate from its current level of 20,000 to 30,000 units during the next five years. Calculate the annual percent rate of increase required to achieve this growth .

You have purchased one lottery ticket each week for many months and have not won more than $5.00. You decide, based on your past experience, that you are not going to win the grand prize and so you stop playing the lottery. What type of reasoning did you use? Explain.

Determine the size of your investment account 30 years from now (when you plan to retire) if you deposit $12,000 each year, beginning 1 year from now, and the account earns interest at a rate of 10% per year.

You want to buy a new car, but you can make an initial payment for only $2,000 and can afford monthly payments of at most$400. a. If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the maximum price you can pay for the car? b. How much can you afford if you finance the purchase over the 60 months?

Buying and selling stock over the Internet has become a common way of playing the stock market. Why can this be risky for small investors?