Exam 4: Time Value of Money

Merchants Bank offers to lend you $30,000 at a nominal rate of 6.0%,simple interest,with interest paid quarterly.Gold Coast Bank offers to lend you the $30,000,but it will charge 7.0%,simple interest,with interest paid at the end of the year.What's the difference in the effective annual rates charged by the two banks?

Your uncle has $500,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $40,000 at the beginning of each year,beginning immediately.How many years will it take to exhaust his funds,i.e.,run the account down to zero?

Your friend just won the lottery.She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000,with the first payment coming 1 year from today.What rate of return is built into the annuity?

Which statement best describes annuities?

You are negotiating to make a 7-year loan of $25,000 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 Years 4 through 7.Breck is essentially riskless,so you are confident the payments will be made,and you regard 8% as an appropriate rate of return on low-risk 7-year loans.What cash flow must the investment provide at the end of each of the final four years; that is,what is X?

Ten years ago,Levin Inc.earned $0.50 per share.Its earnings this year were $2.20 per share.What was the growth rate in Levin's earnings per share (EPS) over the 10-year period?

You are considering investing in a developing-country bank account that pays a nominal annual rate of 18%,compounded monthly.If you invest $5,000 at the beginning of each month,how many months will it take for your account to grow to $250,000? Round fractional years up.

A homeowner just obtained a 30-year amortized mortgage loan for $150,000 at a nominal annual rate of 6.5%,with 360 end-of-month payments.What percentage of the total payments made during the first 3 months will go toward payment of interest?

Which statement best describes time lines?

Which of the following is true regarding the present value of a future sum?

Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year.What is the effective annual rate on the loan?

Last year Toto Corporation's sales were $225 million.If sales grow at 6% per year,how large (in millions) will they be 5 years later?

Suppose a Government of Canada bond promises to pay $1,000 five years from now.If the going interest rate on 5-year government bonds is 5.5%,how much is the bond worth today?

Your uncle has $300,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $35,000 at the beginning of each year,beginning immediately.He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account.For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

Your subscription to Investing Wisely Weekly is about to expire.You plan to subscribe to the magazine for the rest of your life,and you can renew it by paying $75 annually,beginning immediately,or you can get a lifetime subscription for $750,also payable immediately.Assuming you can earn 5.5% on your funds and the annual renewal rate will remain constant,how many years must you live to make the lifetime subscription the better buy? Round fractional years up.(Hint: Be sure to remember that you are solving for how many years you must live,not for how many payments must be made.)

Your sister turned 35 today,and she is planning to save $5,000 per year for retirement,with the first deposit to be made 1 year from today.She will invest in a mutual fund that will provide a return of 8% per year.She plans to retire 30 years from today,when she turns 65,and she expects to live for 25 years after retirement,to age 90.Under these assumptions,how much can she spend in each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

Your uncle has $375,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $35,000 at the end of each year,beginning at the end of this year.How many years will it take to exhaust his funds,i.e.,run the account down to zero?

Which of the following is true regarding the present value of a loan?

East Coast Bank offers to lend you $25,000 at a nominal rate of 7.5%,compounded monthly.The loan (principal plus interest) must be repaid at the end of the year.Midwest Bank also offers to lend you the $25,000,but it will charge an annual rate of 8.3%,with no interest due until the end of the year.What is the difference in the effective annual rates charged by the two banks?

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?