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.

If you put $10 in a savings account at the beginning of each month for 15 years,how much money will be in the account at the end of the 10th year? Assume that the account earns 12% compounded monthly and round to the nearest $1.

You are going to pay $100 into an account at the beginning of each of the next 40 years.At the beginning of the 41st year you buy a 30 year annuity whose first payment comes at the end of the 41st year (the accounts earn 12%).How much will you receive at the end of the 41st year (i.e.the first annuity payment).Round to nearest $100.

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 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)?

A zero coupon bond pays no annual coupon interest payments.When it matures at the end of 7.5 years it pays out $1,000.If investors wish to earn 2.35% per year on this bond investment,what is the current price of the bond? (Round to the nearest dollar.)

What is the present value of an annuity of $120 received at the end of each year for 11 years? Assume a discount rate of 7%.The first payment will be received one year from today (round to nearest $1).

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.

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?

Your son will be attending an expensive university in 12 years.You deposit $5,000 per year for 12 years,beginning today.How much money will be in the college fund 12 years from now if the fund earns 8% per year?

A car manufacturer offers either $2,000 cash back or zero percent financing for 5 years.A rational consumer will always take the cash back because money received today is worth more than money received in the future.

Your son is born today and you want to make him a millionaire by the time he is 50 years old.You deposit $10,700 in an investment account and want to know what annual interest rate must you earn in order to have the account value equal to $1,000,000 on your son's 50^th birthday.

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).

Biff deposited $9,000 in a bank account,and 10 years later he closes out the account,which is worth $18,000.What annual rate of interest has he earned over the 10 years?

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

You borrow $30,000 and agree to pay it off with one lump sum payment of $40,000 in 6 years.What annual rate of interest will you be charged?

You have a savings bond that will be worth $750 when it matures in 3 years,but you need cash today.If the current going rate of interest is 5%,what is your bond worth if you sell it today (rounded to the nearest dollar)?

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?

$10,000 invested at 10% per year for 5 years earns interest equal to $6,105.10; therefore,$10,000 invested at 10% per year for 10 years will earn interest equal to $12,210.20 (2 times $6,105.10).

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.