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Exam 4: Time Value of Money

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Question 1

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Ellen now has $125.How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding?

A) $205.83
B) $216.67
C) $228.07
D) $240.08
E) $252.08

F) C) and D)
G) B) and D)

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Question 2

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Which of the following statements is CORRECT?

A) An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.
B) The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.
C) If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.
D) If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.
E) The proportion of the payment that goes toward interest on a fully amortized loan increases over time.

F) A) and D)
G) A) and C)

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Question 3

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The store where you bought new home furnishings offers you two alternative payment plans.The first plan requires a $4,000 immediate up-front payment.The second plan requires you to make monthly payments of $137.41,payable at the end of each month for 3 years.What nominal annual interest rate is built into the monthly payment plan?

You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1,$1,000 at the end of Year 2,$850 at the end of Year 3,and $6,250 at the end of Year 4.What rate of return would you earn if you bought this asset?

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

Billy Thornton borrowed $20,000 at a rate of 7.25%,simple interest,with interest paid at the end of each month.The bank uses a 360-day year.How much interest would Billy have to pay in a 30-day month?

You agree to make 24 deposits of $500 at the beginning of each month into a bank account.At the end of the 24^th month,you will have $13,000 in your account.If the bank compounds interest monthly,what nominal annual interest rate will you be earning?

You have just purchased a U.S.Treasury bond for $747.25.No payments will be made until the bond matures 5 years from now,at which time it will be redeemed for $1,000.What interest rate will you earn on this bond?

Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts.

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years.By how much would you reduce the amount you owe in the first year?

Starting to invest early for retirement increases the benefits of compound interest.

Your bank account pays an 8% nominal rate of interest.The interest is compounded quarterly.Which of the following statements is CORRECT?

The present value of a future sum increases as either the discount rate or the number of periods per year increases,other things held constant.

You plan to work for Strickland Corporation for 12 years after graduation and after that want to start your own business.You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12) .The first deposit will be made a year from today.In addition,your grandmother just gave you a $25,000 graduation gift that you will deposit immediately (t = 0) .If the account earns 9% compounded annually,how much will you have when you start your business 12 years from now?

The payment made each period on an amortized loan is constant,and it consists of some interest and some principal.The closer we are to the end of the loan's life,the greater the percentage of the payment that will be a repayment of principal.

Wildwoods,Inc.earned $1.50 per share five years ago.Its earnings this year were $3.20.What was the growth rate in earnings per share (EPS) over the 5-year period?

Which of the following statements is CORRECT?

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years.How much would you still owe at the end of the first year,after you have made the first payment?

Julian and Jonathan are twin brothers (and so were born on the same day) .Today,both turned 25.Their grandfather began putting $2,500 per year into a trust fund for Julian on his 20th birthday,and he just made a 6th payment into the fund.The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Julian's 65th birthday.The grandfather set things up this way because he wants Julian to work,not be a "trust fund baby," but he also wants to ensure that Julian is provided for in his old age. Until now,the grandfather has been disappointed with Jonathan and so has not given him anything.However,they recently reconciled,and the grandfather decided to make an equivalent provision for Jonathan.He will make the first payment to a trust for Jonathan today,and he has instructed his trustee to make 40 additional equal annual payments until Jonathan 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 Jonathan's trust today and each subsequent year to enable him to have the same retirement nest egg as Julian after the last payment is made on their 65th birthday?

Geraldine was injured in a car accident,and the insurance company has offered her the choice of $25,000 per year for 15 years,with the first payment being made today,or a lump sum.If a fair return is 7.5%,how large must the lump sum be to leave her as well off financially as with the annuity?