Exam 5: The Time Value of Money

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Which of the following investments has the highest effective annual return (EAR)? (Assume that all CDs are of equal risk.)

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Bill wants to buy a new boat in 7 years.He expects the new boat will cost $28,000.Bill has $18,000 in an investment account today.What rate of return must Bill earn on his investments to be able to buy the boat on time?

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An example of an annuity is the interest received from bonds.

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How much money must be put into a bank account yielding 6.42% (compounded annually)in order to have $1,671 at the end of 11 years (round to nearest $1)?

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In order to send your first child to Law School when the time comes,you want to accumulate $40,000 at the end of 18 years.Assuming that your savings account will pay 6% compounded annually,how much would you have to deposit if: a.you want to deposit an equal amount at the end of each year? b.you want to deposit one large lump sum today?

(Short Answer)
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A bond matures in 20 years,at which time it pays the owner $1,000.It also pays $70 at the end of each of the next 20 years.If similar bonds are currently yielding 7%,what is the market value of the bond?

(Multiple Choice)
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Your grandparents deposit $2,000 each year on your birthday,starting the day you are born,in an account that pays 7% interest compounded annually.How much will you have in the account on your 21st birthday,just after your grandparents make their deposit?

(Multiple Choice)
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You are going to pay $800 into an account at the beginning of each of 20 years.The account will then be left to compound for an additional 20 years until the end of year 40,when it will turn into a perpetuity.You will receive the first payment from the perpetuity at the end of the 41st year.If the account pays 14%,how much will you receive from the perpetuity each year (rounded to nearest $1,000)?

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What is the present value of an annuity of $120 received at the end of each year for 11 years? Assume a discount rate of 7%.The first payment will be received one year from today (round to nearest $1).

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You charged $1,000 on your credit card for Christmas presents.Your credit card company charges you 26% annual interest,compounded monthly.If you make the minimum payments of $25 per month,how long will it take (to the nearest month)to pay off your balance?

(Multiple Choice)
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How much would you be willing to pay (rounded to the nearest dollar)for a 20-year annuity due if the payments are $4,500 per year and you want to earn a rate of return equal to 5.5% per year?

(Multiple Choice)
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You inherit $300,000 from your parents and want to use the money to supplement your retirement.You receive the money on your 65th birthday,the day you retire.You want to withdraw equal amounts at the end of each of the next 20 years.What constant amount can you withdraw each month and have nothing remaining at the end of 20 years if you are earning 7% interest compounded monthly?

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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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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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If you put $10 in a savings account at the beginning of each month for 15 years,how much money will be in the account at the end of the 10th year? Assume that the account earns 12% compounded monthly and round to the nearest $1.

(Multiple Choice)
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If you want to have $3,575 in 29 months,how much money must you put in a savings account today? Assume that the savings account pays 12% and it is compounded monthly; round to nearest $1.

(Multiple Choice)
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Leigh Delight Candy,Inc.is choosing between two bonds in which to invest their cash.One is being offered from Hershey's and will mature in 10 years and pay $30 each quarter.The other alternative is a Mars' bond that will mature in 20 years and pay $30 each quarter.What would be the present value of each bond if the discount rate is 10% compounded quarterly,and each bond pays $1,000 at maturity?

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You sell valuable artifacts from your household estate for $200,000 and want to use the money to supplement your retirement.You receive the money on your 60th birthday,the day you retire.You want to withdraw equal amounts at the end of each of the next 25 years.What constant amount can you withdraw each year and have nothing remaining at the end of 20 years if you are earning 7% interest per year?

(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?

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If the interest rate is positive,then the future value of an annuity due will be greater than the future value of an ordinary annuity.

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