Exam 4: The Time Value of Money

You are currently saving for your child's college education.The current cost of college is R10,000 a year.You expect that college costs will continue to increase at a rate of 5 percent a year.Your child is scheduled to begin attending a four-year college 10 years from now .You currently have R25,000 in an account which earns 6 percent after taxes.You would like to have all of the necessary savings by the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the next 10 years in order to provide the necessary amount.(You want to make 10 equal contributions starting in Year 0 and ending at Year 9.) How much should you contribute to the account each year in order to fully provide for your child's education?

All else equal, a rand received sooner is worth more than a rand received at some later date, because the sooner the rand is received the more quickly it can be invested to earn a positive return.

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.

You deposited R1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to finish your last year in college.Eighteen months later, you decide to go to the Durban to become a scuba diving instructor rather than continue in school, so you close out your account.How much money will you receive?

Assume that you will receive R2,000 a year in Years 1 through 5, R3,000 a year in Years 6 through 8, and R4,000 in Year 9, with all cash flows to be received at the end of the year.If you require a 14 percent rate of return, what is the present value of these cash flows?

Mphela Electronics needs to arrange financing for its expansion program.Bank A offers to lend Mphela the required funds on a loan where interest must be paid monthly, and the quoted rate is 8 percent.Bank B will charge 9 percent, with interest due at the end of the year.What is the difference in the effective annual rates charged by the two banks?

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 maximise 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?

Assume that you can invest to earn a stated annual rate of return of 12 percent, but where interest is compounded semi-annually.If you make 20 consecutive semi-annual deposits of R500 each, with the first deposit being made today, what will your balance be at the end of Year 20?

The difference between the PV of an annuity due and the PV of an ordinary annuity is that each of the payments of the annuity due is discounted by one more year.

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 R17,000 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 R25,000 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 R17,000 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.)

You have the opportunity to buy a perpetuity which pays R1,000 annually.Your required rate of return on this investment is 15 percent.You should be essentially indifferent to buying or not buying the investment if it were offered at a price of

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 R1,000 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 R100 per year to help cover their children's costs.All payments occur at the end of the relevant period, and the R100/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.

Which of the following statements is correct?

Find the present value of an income stream which has a negative flow of R100 per year for 3 years, a positive flow of R200 in the 4th year, and a positive flow of R300 per year in Years 5 through 8.The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years.Thus, a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years.All payments occur at year-end.

You can deposit your savings at Vegetable Bank, which offers to pay 12.6 percent interest compounded monthly, or at Fruit Bank, which will pay interest of 11.5 percent compounded daily.(Assume 365 days in a year.) Which bank offers the higher effective annual rate?

If R100 is placed in an account that earns a simple 4 percent, compounded quarterly, what will it be worth in 5 years?

Your employer has agreed to make 80 quarterly payments of R400 each into a trust account to fund your early retirement.The first payment will be made 3 months from now.At the end of 20 years (80 payments), you will be paid 10 equal annual payments, with the first payment to be made at the beginning of Year 21 (or the end of Year 20).The funds will be invested at a simple rate of 8.0 percent, quarterly compounding, during both the accumulation and the distribution periods.How large will each of your 10 receipts be? (Hint: You must find the EAR and use it in one of your calculations.)

The greater the number of compounding periods within a year, the greater the future value of a lump sum invested initially, and the greater the present value of a given lump sum to be received at maturity.

You just graduated, and you plan to work for 10 years and then to leave for the Australian "Outback" bush country.You figure you can save R1,000 a year for the first 5 years and R2,000 a year for the next 5 years.These savings cash flows will start one year from now.In addition, your family has just given you a R5,000 graduation gift.If you put the gift now, and your future savings when they start, into an account which pays 8 percent compounded annually, what will your financial "stake" be when you leave for Australia 10 years from now?

Which of the following statements is correct?