Exam 4: Time Value of Money

Because your mother is about to retire,she wants to buy an annuity that will provide her with $75,000 of income a year for 20 years,with the first payment coming immediately.The going rate on such annuities is 5.25%.How much would it cost her to buy the annuity today?

Which of the following statements is CORRECT?

Ellen now has $125.How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding?

Your girlfriend just won the Florida lottery.She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000,with the first payment coming one year from today.What rate of return is built into the annuity?

You want to open a sushi bar 3 years from now,and you plan to save $7,000 per year,beginning immediately.You will make 3 deposits in an account that pays 5.2% interest.Under these assumptions,how much will you have 3 years from today?

If the discount (or interest)rate is positive,the present value of an expected series of payments will always exceed the future value of the same series.

You plan to work for Strickland Corporation for 12 years after graduation and after that want to start your own business.You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6)and $15,000 annually for the following 6 years (t = 7 through t = 12).The first deposit will be made a year from today.In addition,your grandmother just gave you a $25,000 graduation gift that you will deposit immediately (t = 0).If the account earns 9% compounded annually,how much will you have when you start your business 12 years from now?

Midway through the life of an amortized loan,the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal.This is true regardless of the original life of the loan or the interest rate on the loan.

Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%,simple interest,with interest paid quarterly.An offer to lend you the $50,000 also comes from Community Bank,but it will charge 6.0%,simple interest,with interest paid at the end of the year.What's the difference in the effective annual rates charged by the two banks?

Suppose Randy Jones plans to invest $1,000.He can earn an effective annual rate of 5% on Security A,while Security B has an effective annual rate of 12%.After 11 years,the compounded value of Security B should be somewhat less than twice the compounded value of Security A.(Ignore risk,and assume that compounding occurs annually. )

A time line is meaningful even if all cash flows do not occur annually.

As a result of compounding,the effective annual rate on a bank deposit (or a loan)is always equal to or greater than the nominal rate on the deposit (or loan).

Which of the following statements is CORRECT?

You agree to make 24 deposits of $500 at the beginning of each month into a bank account.At the end of the 24^th month,you will have $13,000 in your account.If the bank compounds interest monthly,what nominal annual interest rate will you be earning?

You expect to receive $5,000 in 25 years.How much is it worth today if the discount rate is 5.5%?

What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?

You have purchased a U.S.Treasury bond for $3,000.No payments will be made until the bond matures 10 years from now,at which time it will be redeemed for $5,000.What interest rate will you earn on this bond?

If a bank compounds savings accounts quarterly,the nominal rate will exceed the effective annual rate.

Suppose you inherited $275,000 and invested it at 8.25% per year.How much could you withdraw at the beginning of each of the next 20 years?

Your uncle has $300,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $35,000 at the end of each year,beginning at the end of this year.He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account.What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer,round down to the nearest whole number. )