Exam 4: Time Value of Money

Steve and Ed are cousins who were both born on the same day.Both turned 25 today.Their grandfather began putting $2,500 per year into a trust fund for Steve on his 20th birthday,and he just made a sixth payment into the fund.The grandfather (or his estate's trustee) will continue with these $2,500 payments until a 46th and final payment is made on Steve's 65th birthday.The grandfather set things up this way because he wants Steve to work,not to be a "trust fund baby," but he also wants to ensure that Steve is provided for in his old age.​Until now,the grandfather has been disappointed with Ed,hence has not given him anything.However,they recently reconciled,and the grandfather decided to make an equivalent provision for Ed.He will make the first payment to a trust for Ed later today,and he has instructed his trustee to make additional equal annual payments each year until Ed turns 65,when the 41st and final payment will be made.If both trusts earn an annual return of 8%,how much must the grandfather put into Ed's trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday?

Suppose you are buying your first house for $210,000,and are making a $20,000 down payment.You have arranged to finance the remaining amount with a 30-year,monthly payment,amortized mortgage at a 6.5% nominal interest rate.What will your equal monthly payments be?

How much would $1,growing at 3.5% per year,be worth after 75 years?

You plan to borrow $75,000 at a 7% annual interest rate.The terms require you to amortize the loan with 10 equal end-of-year payments.How much interest would you be paying in Year 2?

Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest,compounded annually.How much will you have when the CD matures?

What would the future value of $125 be after 8 years at 8.5% compound interest?

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%,compounded semiannually?

You plan to borrow $30,000 at a 7% annual interest rate.The terms require you to amortize the loan with six equal end-of-year payments.How much interest would you be paying in Year 2?

A Canada government bond promises to pay a lump sum of $1,000 exactly 3 years from today.The nominal interest rate is 6%,semiannual compounding.Which of the following statements is correct?

You are considering investing in a bank account that pays a nominal annual rate of 6%,compounded monthly.If you invest $5,000 at the end of each month,how many months will it take for your account to grow to $200,000? Round fractional years up.

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

What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%,compounded monthly?

Which of the following is a benefit that derives from beginning to save for retirement early?

Suppose an investor plans to invest a given sum of money.She can earn an effective annual rate of 5% on Security A,while Security B will provide an effective annual rate of 12%.Within 11 years' time,the compounded value of Security B will be more than twice the compounded value of Security A.(Ignore risk,and assume that compounding occurs annually.)

At a rate of 6.5%,what is the future value of the following cash flow stream: $0 at Time 0; $75 at the end of Year 1; $225 at the end of Year 2; $0 at the end of Year 3; and $300 at the end of Year 4?

You want to buy a new sports car 3 years from now,and you plan to save $4,200 per year,beginning 1 year from today.You will deposit your savings in an account that pays 5.2% interest.How much will you have just after you make the third deposit,3 years from now?

You just deposited $2,500 in a bank account that pays a 12% nominal interest rate,compounded quarterly.If you also add another $5,000 to the account one year (12 months) from now and another $7,500 to the account 2 years from now,how much will be in the account 3 years (12 quarters) from now?

You plan to invest some money in a bank account.Which of the following banks provides you with the highest effective rate of interest?

Suppose the Government of Canada offers to sell you a bond for $747.25.No payments will be made until the bond matures 5 years from now,at which time it will be redeemed for $1,000.What interest rate would you earn if you bought this bond at the offer price?

Your uncle has $375,000 and wants to retire.He expects to live for another 25 years,and he also expects to earn 7.5% on his invested funds.How much could he withdraw at the beginning of each of the next 25 years and end up with zero in the account?