Exam 4: The Time Value of Money

You are given the following cash flow information.The appropriate discount rate is 12 percent for Years 1-5 and 10 percent for Years 6-10.Payments are received at the end of the year. What should you be willing to pay right now to receive the income stream above?

As the winning contestant in a television game show,you are considering the prizes to be awarded.You must indicate to the sponsor which of the following two choices you prefer,assuming you want to maximize your wealth.Assume it is now January 1,and there is no danger whatever that the sponsor won't pay off. Which one would you choose?

At an inflation rate of 9 percent,the purchasing power of $1 would be cut in half in 8.04 years.How long to the nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4%?

You have a 30-year mortgage with a simple annual interest rate of 8.5 percent.The monthly payment is $1,000.What percentage of your total payments over the first three years goes toward the repayment of principal?

At approximately what rate would you have to invest a lump-sum amount today if you need the amount to triple in six years? Assume interest is compounded annually.

Suppose you put $100 into a savings account today,the account pays a simple annual interest rate of 6 percent,but compounded semiannually,and you withdraw $100 after 6 months.What would your ending balance be 20 years after the initial $100 deposit was made?

You have just purchased a life insurance policy that requires you to make 40 semiannual payments of $350 each,where the first payment is due in 6 months.The insurance company has guaranteed that these payments will be invested to earn you an effective annual rate of 8.16 percent,although interest is to be compounded semiannually.At the end of 20 years (40 payments),the policy will mature.The insurance company will pay out the proceeds of this policy to you in 10 equal annual payments,with the first payment to be made one year after the policy matures.If the effective interest rate remains at 8.16 percent,how much will you receive during each of the 10 years?

Which of the following statements is correct?

You are given the following cash flows.What is the present value (t = 0)if the discount rate is 12 percent?

You have just taken out a 30-year,$120,000 mortgage on your new home.This mortgage is to be repaid in 360 equal end-of-month installments.If each of the monthly installments is $1,500,what is the effective annual interest rate on this mortgage?

Susan just signed a long-term lease on a townhouse in New York City (near Central Park)that requires her to make equal monthly payments for the next five years.The payments Susan has promised to make represent a(n)__________ for the landlord.

Vegit Corporation needs to borrow funds to support operations during the summer.Vegit's CFO is trying to decide whether to borrow from the Bank of Florida or the Bank of Georgia.The loan offered by Bank of Florida has a 12.5 percent simple interest rate with annual interest payments,whereas the loan offered by the Bank of Georgia has a 12 percent simple interest rate with monthly payments.Which bank should Vegit use for the loan?

An annuity is a series of equal payments made at fixed equal-length intervals for a specified number of periods.

The effective annual rate is always greater than the simple rate as a result of compounding effects.

Assume you are to receive a 20-year annuity with annual payments of $50.The first payment will be received at the end of Year 1,and the last payment will be received at the end of Year 20.You will invest each payment in an account that pays 10 percent.What will be the value in your account at the end of Year 30?

You are considering an investment in a 40-year security.The security will pay $25 a year at the end of each of the first three years.The security will then pay $30 a year at the end of each of the next 20 years.The simple interest rate is assumed to be 8 percent,and the current price (present value)of the security is $360.39.Given this information,what is the equal annual payment to be received from Year 24 through Year 40 (i.e.,for 17 years)?

Hillary is trying to determine the cost of health care to college students,and parents' ability to cover those costs.She assumes that the cost of one year of health care for a college student is $1,000 today,that the average student is 18 when he or she enters college,that inflation in health care cost is rising at the rate of 10 percent per year,and that parents can save $100 per year to help cover their children's costs.All payments occur at the end of the relevant period,and the $100/year savings will stop the day the child enters college (hence 18 payments will be made).Savings can be invested at a simple rate of 6 percent,annual compounding.Hillary wants a health care plan which covers the fully inflated cost of health care for a student for 4 years,during years 19 through 22 (with payments made at the end of years 19 through 22).How much would the government have to set aside now (when a child is born),to supplement the average parent's share of a child's college health care cost? The lump sum the government sets aside will also be invested at 6 percent,annual compounding.

If $100 is placed in an account that earns a simple 4 percent,compounded quarterly,what will it be worth in 5 years?

Suppose that the present value of receiving a guaranteed $450 in two years is $385.80.The opportunity rate of return on similar risk investments is 8 percent.According to this information,all else equal,which of the following statements is correct?

Assume that you are graduating,that you plan to work for 4 years,and then to go to law school for 3 years.Right now,going to law school would require $17,000 per year (for tuition,books,living expenses,etc.),but you expect this cost to rise by 8 percent per year in all future years.You now have $25,000 invested in an investment account which pays a simple annual rate of 9 percent,quarterly compounding,and you expect that rate of return to continue into the future.You want to maintain the same standard of living while in law school that $17,000 per year would currently provide.You plan to save and to make 4 equal payments (deposits)which will be added to your account at the end of each of the next 4 years; these new deposits will earn the same rate as your investment account currently earns.How large must each of the 4 payments be in order to permit you to make 3 withdrawals,at the beginning of each of your 3 years in law school? (Note: (1)The first payment is made a year from today and the last payment 4 years from today,(2)the first withdrawal is made 4 years from today,and (3)the withdrawals will not be of a constant amount.)