Exam 5: The Time Value of Money

Two sisters each open IRAs in 2011 and plan to invest $3,000 per year for the next 30 years.Mary makes her first deposit on January 1,2011,and will make all future deposits on the first day of the year.Jane makes her first deposit on December 31,2011,and will continue to make her annual deposits on the last day of each year.At the end of 30 years,the difference in the value of the IRAs (rounded to the nearest dollar),assuming an interest rate of 7% per year,will be

Your grandparents deposit $2,000 each year on your birthday,starting the day you are born,in an account that pays 7% interest compounded annually.How much will you have in the account on your 21st birthday,just after your grandparents make their deposit?

You wish to accumulate $10,000 by depositing $481.46 per month into a savings account that earns 4.75% compounded monthly.How many monthly deposits must you make?

You have the choice of two equally risk annuities,each paying $5,000 per year for 8 years.One is an annuity due and the other is an ordinary annuity.If you are going to be receiving the annuity payments,which annuity would you choose to maximize your wealth?

How much money must you pay into an account at the end of each of 20 years in order to have $100,000 at the end of the 20th year? Assume that the account pays 6% per year,and round to the nearest $1.

Your daughter is born today and you want her to be a millionaire by the time she is 35 years old.You open an investment account that promises to pay 12% per year.How much money must you deposit each year,starting on her 1st birthday and ending on her 35th birthday,so your daughter will have $1,000,000 by her 35th birthday?

Suppose a corporation can change its depreciation method so that its tax payments will decrease by $5,000 this year but increase by $5,000 next year.

You have $25,000 in an investment account today.How much will be in the account in 30 years if the account earns (a)8% per year,(b)8% compounded semiannually,(c)8% compounded quarterly,(d)8% compounded monthly,and (e)8% compounded daily? Comment on the effect of more frequent compounding.

How much money must you pay into an account at the beginning of each of 20 years in order to have $10,000 at the end of the 20th year? Assume that the account pays 12% per year,and round to the nearest $1.

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)?

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

Manny and Irene will be retiring in fifteen years and would like to buy a Mexican villa.The villa costs $500,000 today,and housing prices in Mexico are expected to increase by 6% per year.Manny and Irene want to make fifteen equal annual payments into an account,starting today,so there will be enough money to purchase the villa in fifteen years.If the account earns 10% per year,what is the amount of each deposit?

It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account).Darwin will put $1000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total).How much money will Darwin have in his account at the end of the 40^th year? Assume that the account pays 12% interest compounded annually and round to nearest $1000.

What is the present value of the following perpetuities? a.$200 per year discounted at 6% annually b.$500 per year discounted at 9% annually c.$1,000 per year discounted at 5% annually d.$550 per year discounted at 8% annually

If you invest $750 every six months at 8 percent compounded semiannually,how much would you accumulate at the end of 10 years?

For a given stated interest rate,an investor would receive a greater future value with daily compounding as opposed to monthly compounding.

If you put $2,000 in a savings account that yields 8% compounded semiannually,how much money will you have in the account in 20 years (round to nearest $10)?

The value of a bond investment,which provides fixed interest payments,will increase when discounted at a 8% rate rather than at a 11% rate.

Today is your 21^st 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 50^th birthday?

Betty borrows $60,000 at 12 percent compounded annually.The loan is to be repaid in five equal annual end-of-year installments.How much must each loan payment be?