Exam 5: Time Value of Money

You are considering investing in a bank account that pays a nominal annual rate of 7%,compounded monthly.If you invest $3,000 at the end of each month,how many months will it take for your account to grow to $310,000?

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

Suppose a U.S.treasury bond will pay $1,050 five years from now.If the going interest rate on 5-year treasury bonds is 4.25%,how much is the bond worth today?

What's the future value of $1,300 after 5 years if the appropriate interest rate is 6%,compounded monthly?

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

When a loan is amortized,a relatively low percentage of the payment goes to reduce the outstanding principal in the early years,and the principal repayment's percentage increases in the loan's later years.

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

Janice has $5,000 invested in a bank that pays 6.2% annually.How long will it take for her funds to triple?

Steve and Ed are cousins who were both born on the same day,and both turned 25 today.Their grandfather began putting $2,100 per year into a trust fund for Steve 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 $2,100 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 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 today,and he has instructed his trustee to make 40 additional equal annual payments 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? Assume that all payments are made at the end of the year.

You are negotiating to make a 7-year loan of $37,500 to Breck Inc.To repay you,Breck will pay $2,500 at the end of Year 1,$5,000 at the end of Year 2,and $7,500 at the end of Year 3,plus a fixed but currently unspecified cash flow,X,at the end of each year from Year 4 through Year 7.Breck is essentially riskless,so you are confident the payments will be made.You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan.What cash flow must the investment provide at the end of each of the final 4 years,that is,what is X?

Your Aunt Ruth has $540,000 invested at 6.5%,and she plans to retire.She wants to withdraw $40,000 at the beginning of each year,starting immediately.How many years will it take to exhaust her funds,i.e. ,run the account down to zero?

You plan to borrow $47,400 at a 7.5% annual interest rate.The terms require you to amortize the loan with 7 equal end-of-year payments.How much interest would you be paying in Year 2?

Your brother's business obtained a 30-year amortized mortgage loan for $300,000 at a nominal annual rate of 7.0%,with 360 end-of-month payments.The firm can deduct the interest paid for tax purposes.What will the interest tax deduction be for Year 1?

You are offered a chance to buy an asset for $4,500 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?

Your uncle is about to retire,and he wants to buy an annuity that will provide him with $80,000 of income a year for 20 years,with the first payment coming immediately.The going rate on such annuities is 5.25%.How much would it cost him to buy the annuity today?

Your father's employer was just acquired,and he was given a severance payment of $365,000,which he invested at a 7.5% annual rate.He now plans to retire,and he wants to withdraw $35,000 at the end of each year,starting at the end of this year.How many years will it take to exhaust his funds,i.e. ,run the account down to zero?

Midway through the life of an amortized loan,the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal.This is true regardless of the original life of the loan or the interest rate on the loan.

Five years ago,Weed Go Inc.earned $2.70 per share.Its earnings this year were $3.20.What was the growth rate in earnings per share (EPS)over the 5-year period?

Your uncle will sell you his bicycle shop for $170,000,with "seller financing," at a 6.0% nominal annual rate.The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years,and then make an additional final (balloon)payment of $50,000 at the end of the last month.What would your equal monthly payments be?

Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.