Exam 4: Time Value of Money

Your older brother turned 35 today, and he is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today.He will invest in a mutual fund that's expected to provide a return of 7.5% per year.He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90.Under these assumptions, how much can he spend each year after he retires? His first withdrawal will be made at the end of his first retirement year.

A time line is not meaningful unless all cash flows occur annually.

Julian and Jonathan are twin brothers (and so were born on the same day).Today, both turned 25.Their grandfather began putting $2,500 per year into a trust fund for Julian on his 20th birthday, and he just made a 6th payment into the fund.The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Julian's 65th birthday.The grandfather set things up this way because he wants Julian to work, not be a "trust fund baby," but he also wants to ensure that Julian is provided for in his old age. Until now, the grandfather has been disappointed with Jonathan and so has not given him anything.However, they recently reconciled, and the grandfather decided to make an equivalent provision for Jonathan.He will make the first payment to a trust for Jonathan today, and he has instructed his trustee to make 40 additional equal annual payments until Jonathan 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 Jonathan's trust today and each subsequent year to enable him to have the same retirement nest egg as Julian after the last payment is made on their 65th birthday?

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?

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?

A new investment opportunity for you is an annuity that pays $550 at the beginning of each year for 3 years.You could earn 5.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?

You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4.What rate of return would you earn if you bought this asset?

Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.

What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?

Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?

What is the present value of the following cash flow stream at a rate of 8.0%?

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding.What is the effective annual rate?

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?

You want to purchase a motorcycle 4 years from now, and you plan to save $3,500 per year, beginning immediately.You will make 4 deposits in an account that pays 5.7% interest.Under these assumptions, how much will you have 4 years from today?

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 8% is CORRECT?

You are considering two equally risky annuities, each of which pays $25,000 per year for 10 years.Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due.Which of the following statements is CORRECT?

Which of the following statements regarding a 20-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?

Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

Midway through the life of an amortized loan, the percentage of the payment that represents interest could be equal to, less than, or greater than to the percentage that represents repayment of principal.The proportions depend on the original life of the loan and the interest rate.