Exam 5: Time Value of Money

Your aunt has $270,000 invested at 5.5%,and she now wants to retire.She wants to withdraw $45,000 at the beginning of each year,beginning immediately.She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account.For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end?

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 $450,000? Round fractional months up.

You are considering two equally risky annuities,each of which pays $5,000 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?

You have a chance to buy an annuity that pays $13,700 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 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 $15,000?

What's the present value of a perpetuity that pays $3,800 per year if the appropriate interest rate is 5%?

You want to buy a new sports car 3 years from now,and you plan to save $6,200 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?

You deposit $825 today in a savings account that pays 6% interest,compounded annually.How much will your account be worth at the end of 25 years?

Jose now has $500.How much would he have after 6 years if he leaves it invested at 7.0% with annual compounding?

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

Your bank offers to lend you $114,400 at an 8.5% annual interest rate to start your new business.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?

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

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 6.50%,but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year.What is the effective annual rate on the loan?

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

You inherited an oil well that will pay you $39,000 per year for 25 years,with the first payment being made today.If you think a fair return on the well is 7.5%,how much should you ask for it if you decide to sell it?

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.

Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR)on their monthly statements.If the APR is stated to be 24.50%,with interest paid monthly,what is the card's EFF%?

If a bank compounds savings accounts quarterly,the effective annual rate will exceed the nominal rate.

​Suppose you just won the state lottery,and you have a choice between receiving $3,025,000 today or a 20-year annuity of $250,000,with the first payment coming one year from today.What rate of return is built into the annuity? Disregard taxes.

How much would $20,000 due in 50 years be worth today if the discount rate were 7.5%?