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Exam 4: Time Value of Money

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Question 21

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You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?

A) Bank 1; 6.0% with monthly compounding
B) Bank 2; 6.0% with annual compounding
C) Bank 3; 6.0% with quarterly compounding
D) Bank 4; 6.0% with daily (365-day) compounding

E) C) and D)
F) A) and B)

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Question 22

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You just deposited $2,500 in a bank account that pays a 12% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (12 months) from now and another $7,500 to the account 2 years from now, how much will be in the account 3 years (12 quarters) from now?

A) $17,422.59
B) $18,339.57
C) $19,256.55
D) $20,219.37

E) All of the above
F) B) and C)

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Question 23

Multiple Choice

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You have a chance to buy an annuity that pays $1,200 at the end of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

You plan to make annual deposits into a bank account that pays a 5.00% nominal annual rate. You think inflation will amount to 2.50% per year. What is the expected annual real rate at which your money will grow?

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.

Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. Your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning 1 year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the third deposit, 3 years from now?

Which of the following statements is correct, assuming positive interest rates and other things held constant?

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded monthly?

Steve and Ed are cousins who were both born on the same day. Both turned 25 today. Their grandfather began putting $2,500 per year into a trust fund for Steve on his 20th birthday, and he just made a sixth payment into the fund. The grandfather (or his estate's trustee) will continue with these $2,500 payments until a 46th and final payment is made on Steve's 65th birthday. The grandfather set things up this way because he wants Steve to work, not to be a "trust fund baby," but he also wants to ensure that Steve is provided for in his old age. Until now, the grandfather has been disappointed with Ed, hence has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Ed. He will make the first payment to a trust for Ed later today, and he has instructed his trustee to make additional equal annual payments each year until Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Ed's trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday?

What would the future value of $125 be after 8 years at 8.5% compound interest?

Which investment will have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same.

Your father now has $1,000,000 invested in an account that pays 9.00%. He expects inflation to average 3%, and he wants to make annual constant dollar (real) end-of-year withdrawals over each of the next 20 years and end up with a zero balance after the 20th year. How large will his initial withdrawal (and thus constant dollar [real] withdrawals) be?

You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is correct?

After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years and $15,000 annually for the following 6 years, with the first deposit being made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift, which you will deposit immediately. If the account earns 9%, compounded annually, how much will you have when you start your business 12 years from now?

You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning 1 year from today. You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year. Under these conditions, how much will you have just after you make the fifth deposit, 5 years from now?

Your company has just taken out a 1-year installment loan for $72,500. The nominal rate is 12.0%, but with equal end-of-month payments. What percentage of the second monthly payment will go toward the repayment of principal?

What is the present value of the following cash flow stream if the interest rate is 6.0% per year: 0 at Time 0; $1,000 at the end of Year 1; and $2,000 at the end of Years 2, 3, and 4?

You plan to borrow $75,000 at a 7% annual interest rate. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?

An investment costs $725 and is expected to produce cash flows of $75 at the end of Year 1, $100 at the end of Year 2, $85 at the end of Year 3, and $625 at the end of Year 4. What rate of return would you earn if you bought this investment?