Exam 5: Time Value of Money

The payment made each period on an amortized loan is constant,and it consists of some interest and some principal.The closer we are to the end of the loan's life,the greater the percentage of the payment that will be a repayment of principal.

Which of the following statements is CORRECT?

Your brother's business obtained a 30-year amortized mortgage loan for $400,000 at a nominal annual rate of 7.0%,with 360 end-of-month payments.The firm can deduct the interest paid for tax purposes.What will the interest tax deduction be for Year 1?

You agree to make 24 deposits of $500 at the beginning of each month into a bank account.At the end of the 24th month,you will have $12,800 in your account.If the bank compounds interest monthly,what nominal annual interest rate will you be earning?

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.

You have a chance to buy an annuity that pays $5,700 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?

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 $170,000? Round fractional months up.

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.

Which of the following statements is CORRECT?

Your father's employer was just acquired,and he was given a severance payment of $305,000,which he invested at a 7.5% annual rate.He now plans to retire,and he wants to withdraw $35,000 at the end of each year,starting at the end of this year.How many years will it take to exhaust his funds,i.e. ,run the account down to zero?

You just deposited $8,000 in a bank account that pays a 4.0% nominal interest rate,compounded quarterly.If you also add another $5,000 to the account one year (4 quarters)from now and another $7,500 to the account two years (8 quarters)from now,how much will be in the account three years (12 quarters)from now?

Which of the following statements is CORRECT?

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 buy a new sports car 3 years from now,and you plan to save $6,700 per year,beginning one 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 3rd deposit,3 years from now?

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 $78,000 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?

John and Daphne are saving for their daughter Ellen's college education.Ellen just turned 10 (at t = 0),and she will be entering college 8 years from now (at t = 8).College tuition and expenses at State U.are currently $14,500 a year,but they are expected to increase at a rate of 3.5% a year.Ellen should graduate in 4 years--if she takes longer or wants to go to graduate school,she will be on her own.Tuition and other costs will be due at the beginning of each school year (at t = 8,9,10,and 11). So far,John and Daphne have accumulated $18,000 in their college savings account (at t = 0).Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1,2,3,and 4).Then they plan to make 3 equal annual contributions in each of the following years,t = 5,6,and 7.They expect their investment account to earn 9%.How large must the annual payments at t = 5,6,and 7 be to cover Ellen's anticipated college costs?

Which of the following bank accounts has the highest effective annual return?

You are negotiating to make a 7-year loan of $20,000 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?

All other things held constant,the present value of a given annual annuity increases as the number of periods per year increases.

Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.