The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

Exercises 4.1 145

13. Wyatt just attended a sales presentation held by the investment company that administers his employer’s 401(k)
    savings plan. According to the sales representative, if he puts just $125 into the plan with each paycheck he could be
    a millionaire when he hits retirement age. Is the $1,000,000 projection a present or future value?


14. Otisco County won a judgment against a former contractor that will require the contractor to pay the county $52,000
    per year for the next 20 years. Instead of having to make payments for the next 20 years, the contractor offers to pay
    the county $835,000 in one lump sum today. Would this be a present value or future value?


15. Fifteen years ago, Ken quit smoking, and instead of spending $30 a week on cigarettes he put that money in a special
    savings account each week. Is the value of his account today a present or future value?


16. Three years ago, Len bought a new car and borrowed the entire cost. Is the cost of the car the present value of his
    monthly payments or the future value?


17. During his college years, Teddy took out student loans to pay his tuition and living expenses. Now he is making equal
    payments each month on those loans. Is the amount he borrowed the present value or the future value of his loans?


18. Tessa was laid off from her job and was out of work for 6 months. Every month, she borrowed $1,000 from her father
    to help cover her living expenses. Was the total she owed him at the end of the 6 months the present value or the future
    value of the amounts she borrowed?

C. Ordinary Annuities and Annuities Due

Each of the following problems describes an annuity. Determine whether it is an ordinary annuity or an annuity due. Justify

your answer.

19. John won a lottery jackpot, which will pay him $100,000 every year for 20 years, starting right away.


20. At the end of each quarter, the TiJiBi Acoustic Electric Corporation pays each of its shareholders a dividend of 25 cents
    for each share owned.


21. Because he is self-employed, Dylan does not have income taxes withheld from paychecks. Instead, he is required to
    make estimated tax payments to the IRS. This year, he has to pay $1,845 each quarter.


22. Every month I pay my insurance company $78.59 for my car insurance premium.


23. The rent for Lourdes’ apartment is $845 a month and is due at the beginning of each month.


24. A customer of the Mendon Falls Gas and Electric Company pays his utility bills on a budget plan. Instead of having his
    bill fl uctuate from month to month, he pays the utility $165 at the end of each month.


25. Jenny and Rob’s monthly mortgage payment is $1,257.09.