Exam 4: The Time Value of Money

You want to go on a boat cruise on your 27th birthday.You have priced these cruises and found that they currently cost R30,000.You believe that the price will increase by 5 percent per year until you are ready to go on it.You can presently invest to earn 14 percent.If you just turned 20 years old, how much must you invest at the end of each of the next 7 years to be able to go on the boat cruise in 7 years?

What is the future value of a 5-year ordinary annuity with annual payments of R200, evaluated at a 15 percent interest rate?

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?

You are considering an investment in a 40-year security.The security will pay R25 a year at the end of each of the first three years.The security will then pay R30 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 R360.39.Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e., for 17 years)?

Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday.She is saving money today for her retirement and is establishing a retirement account with your office.She would like to withdraw money from her retirement account on her birthday each year until she dies.She would ideally like to withdraw R50,000 on her 85th birthday, and increase her withdrawals 10 percent a year through her 89th birthday (i.e., she would like to withdraw R73,205 on her 89th birthday).She plans to die on her 90th birthday, at which time she would like to leave R200,000 to her descendants.Your client currently has R100,000.You estimate that the money in the retirement account will earn 8 percent a year over the next 15 years.Your client plans to contribute an equal amount of money each year until her retirement.Her first contribution will come in one year; her tenth and final contribution will come in ten years (on her 85th birthday).How much should she contribute each year in order to meet her objectives?

If a 5-year regular annuity has a present value of R1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment?

You have just purchased a life insurance policy that requires you to make 40 semi-annual payments of R350 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 semi-annually.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?

Your lease calls for payments of R500 at the end of each month for the next 12 months.Now your landlord offers you a new 1-year lease which calls for zero rent for 3 months, then rental payments of R700 at the end of each month for the next 9 months.You keep your money in a bank time deposit that pays a simple annual rate of 5 percent.By what amount would your net worth change if you accept the new lease? (Hint: Your return per month is 5%/12 = 0.4166667%.)

Compounding is the process of converting today's values, which are termed present value, to future value.

What is the effective annual return (EAR) for an investment that pays 10 percent compounded annually?

You have just taken out a 30-year, R120,000 mortgage on your new home.This mortgage is to be repaid in 360 equal end-of-month instalments.If each of the monthly instalments is R1,500, what is the effective annual interest rate on this mortgage?

Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will

Solving for the interest rate associated with a stream of uneven cash flows, without the use of a calculator, usually involves a trial and error process.

Suppose that the present value of receiving a guaranteed R450 in two years is R385.80.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?

Which of the following payments (receipts) would probably not be considered an annuity due? Based on your knowledge and using logic, think about the timing of the payments.

Assume you are to receive a 20-year annuity with annual payments of R50.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 have determined the profitability of a planned project by finding the present value of all the cash flows form that project.Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?

Cash flow time lines are used primarily for decisions involving paying off debt or investing in financial securities.They cannot be used when making decisions about investments in physical assets.

Suppose someone offered you your choice of two equally risky annuities, each paying R5,000 per year for 5 years.One is an annuity due, while the other is a regular (or deferred) annuity.If you are a rational wealth-maximising investor which annuity would you choose?

Which of the following statements is most correct?