Exam 5: The Time Value of Money

Bob invested $2,000 in an investment fund on his 21^st birthday.The fund pays 7% interest compounded semiannually.Bob is celebrating his 50^th birthday today.Bob decides he wants to retire on his 60^th birthday and he wants to withdraw $75,000 per year,the first withdrawal on his 60^th birthday and the last withdrawal on his 90^th birthday.Bob expects to receive $100,000 from his employer on his 55^th birthday in recognition of his long service to the company.Assume Bob has not taken any money out of his investment fund since he initially funded it on his 21^st birthday,and that he will deposit the $100,000 from his employer into the investment fund on his 55^th birthday.The investment fund will be used to pay for Bob's retirement. If Bob makes no additional deposits into his investment fund,how much will be available for retirement at age 60? Since the amount in (a)is insufficient to meet his retirement goals,Bob decides to deposit equal annual amounts into the investment fund beginning on his 51^st birthday and ending on his 59^th birthday,so that he can meet his retirement goals.How much will each deposit be?

You charged $1,000 on your credit card for Christmas presents.Your credit card company charges you 26% annual interest,compounded monthly.If you make the minimum payments of $25 per month,how long will it take ( to the nearest month)to pay off your balance?

John has to pay $1,000 per month for his mortgage for another 5 years,but he is considering paying the mortgage off in one lump sum.John cannot calculate the present value of the payments using the annuity formulas because his payments are monthly and not once per year.

U)S.Savings Bonds are sold at a discount.The face value of the bond represents its value on its future maturity date.Therefore,

You decide to borrow $250,000 to build a new home.The bank charges an interest rate of 8% compounded monthly.If you pay back the loan over 30 years,what will your monthly payments be (rounded to the nearest dollar)?

The time value of money is the opportunity cost of passing up the earning potential of a dollar today.

You just invested $50,000 into an account that earns 7 percent compounded annually.At the end of each year you can withdraw $4,971.How many years can you continue to make the withdrawals?

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 30^th birthday.He wants to deposit equal annual amounts on each birthday starting on his 30^th birthday and ending on his 60^th 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.

You are 21 years old today.Your grandparents set up a trust fund that will pay you $25,000 per year for 20 years,starting on your 65^th birthday to supplement your retirement.If the trust can earn 7.5% per year,how much will your grandparents need to put in the trust fund today (rounded to the nearest ten dollars)?

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.

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.

Jimmy just bought a new Ford SUV for his business.The price of the vehicle was $40,000.Jimmy made a $5,000 down payment and took out an amortized loan for the rest.The car dealership made the loan at 8% interest compounded monthly for five years.He is to pay back the principal and interest in equal monthly installments beginning one month from now.Determine the amount of Jimmy's monthly payment.

Two brothers each open IRAs in 2009 and plan to invest $3,000 per year for the next 30 years.John makes his first deposit on January 1,2009,and will make all future deposits on the first day of the year.Bill makes his first deposit on December 31,2009,and will continue to make his 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

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?

A certificate of deposit that pays 9.8% compounded monthly is better than a similar certificate of deposit that pays 10% compounded only once per year.

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

If the interest rate is positive,a six-year ordinary annuity of $500 per year must have a present value over $3,000.

You estimate you'll need $200,000 per year for 25 years starting on your 65^th birthday to live on during your retirement.Today is your 50^th birthday and you want to make equal deposits into an account paying 9% interest per year,the first deposit today and the last deposit on your 64^th birthday.How much must each deposit be (rounded to the nearest $10)?

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.

You are going to pay $800 into an account at the beginning of each of 20 years.The account will then be left to compound for an additional 20 years until the end of year 40,when it will turn into a perpetuity.You will receive the first payment from the perpetuity at the end of the 41st year.If the account pays 14%,how much will you receive from the perpetuity each year (round to nearest $1,000)?