Exam 4: Time Value of Money

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

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?

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

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

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?

When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage declines in the loan's later years.

Your uncle just won the weekly lottery, receiving $375,000, which he invested at a 7.5% annual rate.He now has decided to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year.What is the maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)

Your investment advisor has recommended your invest in bonds that pay 6.0%, compounded annually.If you invest $10,000 today, how many years will it take for your investment to grow to $30,000?

Ten years ago, Kronan Corporation earned $0.50 per share.Its earnings this year were $2.20.What was the growth rate in earnings per share (EPS) over the 10-year period?

The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant.

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date.

The going rate of interest on a 5-year treasury bond is 4.25%.You have one that will pay $2,500 five years from now.How much is the bond worth today?

Your investment account pays 8.0%, compounded annually.If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

Of the following investments, which would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.

After receiving a reward for information leading to the arrest of a notorious criminal, you are considering investing it in an annuity that pays $5,000 at the end of each year for 20 years.You could earn 5% on your money in other investments with equal risk.What is the most you should pay for the annuity?

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years.How much interest would you have to pay in the first year?

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.

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?