Exercises on Time Value of Money

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Exercises on Time Value of Money
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1. Calculating Future Value

• Your wealthy uncle established a 1,000 bank
  account for you when you were born. For the first
  8 years of your life, the interest rate earned on
  the account was 8 percent. Since then, rates have
  only been 6 percent. Now you are 21 years old and
  ready to cash in. How much is in your account?

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2. Calculating Annuity Values

• You have just won the 28,000,000 superbowl
  lotto. The winnings are paid in 20 equal annual
  installments. The first payment is tomorrow. You
  have been contacted by a financial service
  company that is willing to trade an immediate
  single lump sum for your payments. What lump sum
  would be acceptable to you if the average
  interest rate is 8?

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3. Calculating Loan Payments

• You want to buy a state-of the-art laptop
  computer that sells for 1,850. The computer
  company is offering a 36-month loan at a quoted
  interest rate of 5.9 with no money down. What
  will your monthly payments be? What is the
  effective annual rate on this loan?

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4. Calculating Number of Periods

• One of your customers is delinquent on his
  accounts payable balance. Youve mutually agreed
  to a repayment schedule of 300 per month. You
  will charge 1.5 percent per month interest on the
  overdue balance. If the current balance is
  11,814.08, how long will it take for the account
  to be paid off?

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5. Calculating Annuity Values

• You want to have 25,000 in your savings account
  five years from now, and you are prepared to make
  equal annual deposits into the account at the end
  of each year. If the account pays 9.5 percent
  interest, what amount must you deposit each year?

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6. Calculating Annuity Values

• You are interested in saving money for your first
  house. Your plan is to make regular deposits
  into a brokerage account which will earn 14.
  Your first deposit of 5,000 will be made today.
  You also plan to make four additional deposits at
  the beginning of each of the next four years.
  You plan is to increase deposits by 10 a year
  (e.g., your second deposit 5,500, etc.). How
  much money will be in your account after five
  years?

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7. Calculating Annuity Values

• You believe that you will spend 40,000 a year
  for 20 years once you retire in 40 years. If the
  interest rate is 4 percent per year, how much
  must you save each year until retirement to meet
  your goal?
• How much would you need to save if you believe
  that you will inherit 100,000 in 10 years?

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8. Present Value with Multiple Cash Flows

• In January 1984, Richard Goose Gossage signed a
  contract to play for the San Diego Padres that
  guaranteed him a minimum of 9,950,000. The
  guaranteed payments were 875,000 for 1984,
  650,000 for 1985, 800,000 for 1986, 1 million
  for 1987, 1 million for 1988, and 300,000 for
  1989. In addition, the contract called for
  5,330,000 in deferred money payable at the rate
  of 240,000 per year from 1990 through 2006 and
  then 125,000 a year from 2007 through 2016. If
  the interest rate was 9 percent and the payments
  were to be made on July 1 of each year, what
  would be the present value of these payments on
  January 1, 1984?

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Present Value with Multiple Cash Flows

• If Gossage were to receive an equal salary at the
  end of each of the five years from 1984 to 1988,
  what would his equivalent annual salary be?

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9. Perpetual Cash Flows

• What is the value of an investment that pays
  7,500 every other year forever, if the first
  payment occurs one year from today and the
  discount rate is 15 percent per year compounded
  monthly? What is the value today if the first
  payment occurs four years from today?

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10. Calculating Annuities Due

• A ten-year annual annuity due with the first
  payment occurring at date N5 has a current value
  of 25,000. If the discount rate is 16 percent
  per year, what is the annuity payment amount?

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11. Deferred Annuities

• A 7-year annuity of 14 8,000 payments will begin
  6 years from now, with the first payment coming
  6.5 years from now. If the discount rate is 18
  percent compounded monthly, what is the value of
  this annuity 4 years from now?

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12. Deferred Perpetuity

• Given an interest rate of 14 percent compounded
  semiannually, what is the value a t5 of a
  perpetual stream of 5,000 payments made annually
  that begin at date t12?