Exam 5: The Time Value of Money

Tim invested $1,000 in a mutual fund paying 8% per year.John invested $500 in the same fund.If both Tim and John keep their money invested for the same period of time,Tim will end up with twice as much money as John.

You are thinking of buying a craft emporium.It is expected to generate cash flows of $30,000 per year in years 1 through 5,and $40,000 per year in years 6 through 10.If the appropriate discount rate is 8%,what amount are you willing to pay for the emporium?

Tim has $100 in a bank account paying 2% interest per year.At the end of 5 years,Tim's bank account balance will be $110 if interest is not compounded,but will be greater than $110 if interest is compounded.

A 65 year-old man is retiring and can take either $500,000 in cash or an ordinary annuity that promises to pay him $50,000 per year for as long as he lives.Which of the following statements is MOST correct?

How much money do I need to place into a bank account that pays a 1.08% rate in order to have $500 at the end of 7 years?

You have been depositing money at the end of each year into an account drawing 8% interest.What is the balance in the account at the end of year four if you deposited the following amounts?

You have been accepted to study international economy at the European Central Bank (ECB)in Frankfurt.You will need $10,500 every 6 months (beginning today)for the next three years to cover tuition and living expenses.Mom and Dad have agreed to pay for your education,and want to make one deposit today in a bank account earning 6% interest,compounded semiannually.How much must they deposit now so that you can withdraw $10,500 at the beginning of each semester over the next 3 years?

How does compound interest differ from simple interest?

You own an annuity due contract that will pay you $3,000 per year for 12 years.You need money to pay back a loan in 5 years,and you are afraid if you get the annuity payments annually you will spend the money and not be able to pay back your loan.You decide to sell your annuity for a lump sum of cash to be paid to you five years from today.If the interest rate is 8%,what is the equivalent value of your 12-year annuity if paid in one lump sum five years from today?

Assume you are to receive a 10-year annuity with annual payments of $1000.The first payment will be received at the end of Year 1,and the last payment will be received at the end of Year 10.You will invest each payment in an account that pays 9 percent compounded annually.Although the annuity payments stop at the end of year 10,you will not withdraw any money from the account until 25 years from today,and the account will continue to earn 9% for the entire 25-year period.What will be the value in your account at the end of Year 25 (rounded to the nearest dollar)?

An investment earning simple interest is preferred over an investment earning compound interest because the simplicity adds value.

Why does the future value of a given amount increase when interest is compounded nonannually as opposed to annually?

The present value of a $100 perpetuity discounted at 5% is $5,000.

You can buy a $50 savings bond today for $25 and redeem the bond in 10 years for its full face value of $50.You could also put your money in a money-market account that pays 7% interest per year.Which option is better,assuming they are of equal risk?

The future value of an annuity due is greater than the future value of an otherwise identical ordinary annuity.

An investment will pay $500 in three years,$700 in five years and $1000 in nine years.If your opportunity rate is 6%,what is the present value of this investment?

If the interest rate is positive,then the present value of an annuity due will be less than the present value of an ordinary annuity.

Bill starts a retirement fund at age 21 and plans on depositing equal annual amounts on each birthday,starting at age 21,and ending at age 60.He wants to have $2 million at age 60.John starts his fund on his 30th birthday.He wants to deposit equal annual amounts on each birthday starting on his 30th birthday and ending on his 60th birthday.John wants to have $2 million at age 60.If the investment funds earn 10% per year,calculate the amounts the Bill and John respectively will have to save each year (rounded to the nearest dollar)to meet their goals.Comment on the difference.

Today is your 21st birthday and your bank account balance is $25,000.Your account is earning 6.5% interest compounded monthly.How much will be in the account on your 50th birthday?

You just graduated and landed your first job in your new career.You remember that your favorite finance professor told you to begin the painless job of saving for retirement as soon as possible,so you decided to put away $2,000 at the end of each year in a Roth IRA.Your expected annual rate of return on the IRA is 7.5%.How much will you accumulate at retirement after 40 years of investing? (Note: this may assume that you are even retiring early.)