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Determining the future value of an annuity

Problem 1. Determine the future value of an annuity that pays $5,000 at the end of the next 11 years. Similar securities pay an interest rate of 7%.

Problem 2. How much money would you be willing to pay in order to receive $800,000 40 years from today? Assume that your required rate of return on investments is 8% compounded semiannually.

Problem 3. You are currently making $300 monthly payments on a $12,000 7% fixed interest loan that compounds interest monthly. At this rate how long will it take you to repay your loan?

Problem 4. You buy a home for $295,000 with a 15 year fixed mortgage that has an 8.75% interest rate compounded monthly. Determine (1) the monthly payment, and (2) the total interest, principle, and total cash outflow at the end of 1 year.

Problem 5. Your friend Jack hires ABC Lawn Service to trim the hedges in his garden. There are three payment options with the company. Which of the following three options should Jack choose if he can earn 8% interest compounded quarterly on his money?

a. Option 1 Pay $5650 cash immediately

b. Option 2 Pay $6750 in one lump sum two years from now

c. Option 3 Pay $800 at the end of each quarter for two years

Problem 6. Your boss wants to know which project had a better return. She says that Project Y returned $7,560 today on a $2,200 investment three years ago (use annual compounding for Project Y). She also says that Project Z returned $9,887 today and required investments of $367 each quarter for the last three years. Which project has a higher return?

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## Q : Pretax annual operating costs

System A costs $456,000, has a 3-year life, and requires $150,000 in pretax annual operating costs.