Exam 5: The Time Value of Money

How much would you be willing to pay (rounded to the nearest dollar)for a 20-year annuity due if the payments are $4,500 per year and you want to earn a rate of return equal to 5.5% per year?

A compound annuity involves depositing or investing a single sum of money and allowing it to compound for a certain number of years.

A rational investor would prefer to receive $1,200 today rather than $100 per month for 12 months.

If you want to have 1$2,500 in 57 months,how much money must you put in a savings account today? Assume that the savings account pays 4.5% and it is compounded quarterly (round to nearest $1).

At what rate must $500 be compounded annually for it to grow to $1,079.46 in 10 years?

Assume you are to receive a 10-year annuity with annual payments of $100.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 20 years from today,and the account will continue to earn 9% for the entire 20-year period.What will be the value in your account at the end of Year 20 (rounded to the nearest dollar)?

A bond matures in 20 years,at which time it pays the owner $1,000.It also pays $70 at the end of each of the next 20 years.If similar bonds are currently yielding 8%,what is the market value of the bond?

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.

You bought a racehorse that has had a winning streak for four years,bringing in $500,000 at the end of each year before dying of a heart attack.If you paid $1,518,675 for the horse 4 years ago,what was your annual return over this 4-year period?

Leigh Delight Candy,Inc.is choosing between two bonds in which to invest their cash.One is being offered from Hershey's and will mature in 10 years and pay $30 each quarter.The other alternative is a Mars' bond that will mature in 20 years and pay $30 each quarter.What would be the present value of each bond if the discount rate is 10% compounded quarterly,and each bond pays $1,000 at maturity?

Cindy wants $2.5 million for her retirement at age 65.Cindy is 25 years old today and plans to deposit equal amounts each year starting on her 26^th birthday and ending on her 65^th birthday.If her investments earn 6% per year,how much must each deposit be?

The present value of a single future sum of money is inversely related to both the number of years until payment is received and the discount rate.

A financial advisor tells you that you can make your child a millionaire if you just start saving early.You decide to put an equal amount each year into an investment account that earns 7.5% interest per year,starting on the day your child is born.How much would you need to invest each year (rounded to the nearest dollar)to accumulate a million for your child by the time he is 35 years old? (Your last deposit will be made on his 34^th birthday.)

At an annual interest rate of 9%,an initial sum of money will double approximately every 8 years.

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?

If the future value of annuity A is greater than the future value of annuity B,then the present value of annuity A must also be greater than the present value of annuity B.

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?

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

A return of 12% compounded annually is the same as a return of 1% per month.

You borrow $25,000 to buy a car,and agree to make 48 monthly payments of $607.39 to repay the loan.What annual rate of interest,which is being compounded monthly,are you being charged?