Exam 5: Time Value of Money

Your aunt is about to retire,and she wants to sell some of her stock and buy an annuity that will provide her with income of $50,000 per year for 30 years,beginning a year from today.The going rate on such annuities is 7.25%.How much would it cost her to buy such an annuity today?

Your father paid $10,000 (CF at t = 0)for an investment that promises to pay $750 at the end of each of the next 5 years,then an additional lump sum payment of $10,000 at the end of the 5th year.What is the expected rate of return on this investment?

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

You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%,compounded monthly.If you invest $5,000 at the beginning of each month,how many months would it take for your account to grow to $250,000? Round fractional months up.

You are negotiating to make a 7-year loan of $25,000 to Breck Inc.To repay you,Breck will pay $2,500 at the end of Year 1,$5,000 at the end of Year 2,and $7,500 at the end of Year 3,plus a fixed but currently unspecified cash flow,X,at the end of each year from Year 4 through Year 7.Breck is essentially riskless,so you are confident the payments will be made.You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan.What cash flow must the investment provide at the end of each of the final 4 years,that is,what is X?

Starting to invest early for retirement reduces the benefits of compound interest.

You have a chance to buy an annuity that pays $2,500 at the end 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?

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

You plan to invest in securities that pay 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?

You want to quit your job and return to school for an MBA degree 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?

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.

A $150,000 loan is to be amortized over 7 years,with annual end-of-year payments.Which of these statements is CORRECT?

Suppose the U.S.Treasury 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?

Which of the following statements regarding a 15-year (180-month)$125,000,fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

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

Which of the following statements is CORRECT?

What is the present value of the following cash flow stream at a rate of 6.25%? ​ ​ ​​

You want to go to Europe 5 years from now,and you can save $3,100 per year,beginning one year from today.You plan to deposit the funds in a mutual fund that you think will return 8.5% per year.Under these conditions,how much would you have just after you make the 5th deposit,5 years from now?

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

You plan to 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?