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Exam 22: Continuous Compounding and Discounting

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Question 1

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For a 10-year deposit,what annual rate payable semiannually will produce the same effective rate as 4% compounded continuously?

A) 3.46%
B) 3.65%
C) 3.84%
D) 4.04%
E) 4.24%

F) A) and C)
G) B) and C)

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Question 2

Multiple Choice

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How much should you be willing to pay for an account today that will have a value of $1,000 in 10 years under continuous compounding if the nominal rate is 10%?

A) $349.49
B) $367.88
C) $386.27
D) $405.59
E) $425.87

F) C) and E)
G) None of the above

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B

Question 3

Multiple Choice

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In six years' time,you are scheduled to receive money from a trust established by your grandparents.When the trust matures there will be $100,000 in the account.If the account earns 9% compounded continuously,how much is in the account today?

You need a down payment of $19,000 in order to purchase your first home 4 years from today.You currently have $14,014 to invest.In order to achieve your goal,what nominal interest rate,compounded continuously,must you earn on this investment?

Assume one bank offers you a nominal annual interest rate of 6% compounded daily while another bank offers you continuous compounding at a 5.9% nominal annual rate.You decide to deposit $1,000 with each bank.Exactly two years later you withdraw your funds from both banks.What is the difference in your withdrawal amounts between the two banks?

You have $5,436.60 in an account that pays 10% interest,compounded continuously.If you deposited some funds 10 years ago,how much was your original deposit?

You place $1,000 in an account that pays 7% interest compounded continuously.You plan to hold the account exactly 3 years.Simultaneously,in another account you deposit money that earns 8% compounded semiannually.If the accounts are to have the same amount at the end of the 3 years,how much of an initial deposit do you need to make now in the account that pays 8% interest compounded semiannually?

If you receive $15,000 today and can invest it at a 5% annual rate compounded continuously,what will be your ending value after 20 years?