Exam 5: The Time Value of Money

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If we invest money for 10 years at 8 percent interest,compounded semi-annually,we are really investing money for 20 six-month periods,and receiving 4 percent interest each period.

(True/False)
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You want to travel to Europe to visit relatives when you graduate from college three years from now.The trip is expected to cost a total of $10,000 at that time.Your parents have deposited $5,000 for you in a CD paying 6% interest annually,maturing three years from now.Aunt Hilda has agreed to finance the balance.If you are going to put Aunt Hilda's gift in an investment earning 10% over the next three years,how much must she deposit now,so you can visit your relatives at the end of three years?

(Multiple Choice)
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You believe in the power of compounding and decide to save $1 per day by avoiding the purchase of a soda.You deposit the $1 at the end of each day in a bank account that pays 8% interest compounded daily.You are going to take a trip in 20 years with the money you have accumulated.How much money will you have in 20 years,assuming 365 days per year?

(Multiple Choice)
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You are ready to retire.A glance at your 401(k)statement indicates that you have $750,000.If the funds remain in an account earning 9.0%,how much could you withdraw at the beginning of each year for the next 25 years?

(Multiple Choice)
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A retirement home in Florida costs $200,000 today.Housing prices in Florida are increasing at a rate of 4% per year.Joe wants to buy the home in 8 years when he retires.Joe has $25,000 right now in a savings account paying 8% interest per year.Joe wants to make eight equal annual deposits into the savings account starting today.How much must each deposit be so Joe will have enough money in his savings account to buy the retirement home when he retires?

(Essay)
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If you put $200 in a savings account at the beginning of each year for 10 years and then allow the account to compound for an additional 10 years,how much will be in the account at the end of the 20th year? Assume that the account earns 10% and round to the nearest $100.

(Multiple Choice)
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If Cathy deposits $12,000 into a bank account that pays 6% interest compounded quarterly,what will the account balance be in seven years?

(Multiple Choice)
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It is never appropriate to compare nominal rates unless they include the same number of compounding periods per year.

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You decide you want your child to be a millionaire.You have a son today and you deposit $15,000 in an investment account that earns 9% per year.The money in the account will be distributed to your son whenever the total reaches $1,000,000.How old will your son be when he gets the money (rounded to the nearest year)?

(Multiple Choice)
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Cary's wonderful parents established a college savings plan for him when he was born.They deposited $50 into the account on the last day of each month.The account has earned 10% compounded monthly,tax-free.How much can they withdraw on his 18th birthday to spend on his education?

(Multiple Choice)
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The present value of a $100 perpetuity discounted at 5% is $5,000.

(True/False)
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When solving time value of money problems using Excel,the type = 0 variable means payments are made at the end of each period,and the type = 1 variable means payments are made at the beginning of each period.

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If you only earned interest on your initial investment,and not on previously earned interest,it would be called simple interest.

(True/False)
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Bill saves $3,000 per year in his IRA starting at age 25 and continuing to age 65,when he retires.The amount Bill has in his IRA at age 65 can be characterized as the future value of an annuity.

(True/False)
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Cary's wonderful parents established a college savings plan for him when he was born.They deposited $50 into the account on the last day of each month.The account has earned 10% compounded monthly,tax-free.Now he's off to State U.What equal amount can they withdraw beginning today (his 18th birthday)and each year for three additional years to spend on his education,assuming that the account now earns 7% annually.

(Multiple Choice)
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What is the value on 1/1/10 of the following cash flows: Date Cash Received Amount of Cash What is the value on 1/1/10 of the following cash flows: Date Cash Received Amount of Cash   Use a 7% discount rate,and round your answer to the nearest $10. Use a 7% discount rate,and round your answer to the nearest $10.

(Multiple Choice)
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One bank offers you 4% interest compounded semiannually.What is the equivalent rate if interest is compounded quarterly?

(Multiple Choice)
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You have just purchased a share of preferred stock for $50.00.The preferred stock pays an annual dividend of $5.50 per share forever.What is the rate of return on your investment?

(Multiple Choice)
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Your daughter is born today and you want her to be a millionaire by the time she is 35 years old.You open an investment account that promises to pay 12% per year.How much money must you deposit each year,starting on her 1st birthday and ending on her 35th birthday,so your daughter will have $1,000,000 by her 35th birthday?

(Multiple Choice)
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You borrow $30,000 and agree to pay it off with one lump sum payment of $40,000 in 6 years.What annual rate of interest will you be charged?

(Short Answer)
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