Exam 4: Time Value of Money

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 $1,000 a year for the first 5 years and $2,000 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 $5,000 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?

A bank pays a quoted annual (simple) interest rate of 8 percent.However, it pays interest (compounds) daily using a 365-day year.What is the effective annual rate of return?

Gomez Electronics needs to arrange financing for its expansion program.Bank A offers to lend Gomez 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?

A recent advertisement in the financial section of a magazine carried the following claim: "Invest your money with us at 14 percent, compounded annually, and we guarantee to double your money sooner than you imagine." Ignoring taxes, how long would it take to double your money at a simple rate of 14 percent, compounded annually?

Suppose an investor can earn a steady 5% annually with investment A, while investment B will yield a constant 12% annually.Within 11 years time, the compounded value of investment B will be more than twice the compounded value of investment A (ignore risk).

By definition, what type of annuity best describes payments such as rent and magazine subscriptions (assuming the costs do not change over time)?

Your employer has agreed to make 80 quarterly payments of $400 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 pa 10 equal annual payments, with the first payment to be made at the beginning of Year 21 (or the end of Year 20).Th 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.)

All else equal, the future value of a lump-sum amount invested today will increase if the

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. Year Amount 1-5 $20,000 6-10 $25,000 What should you be willing to pay right now to receive the income stream above?

Everything else equal, which of the following conditions will result in the lowest present value of an amount to be received in the future?

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

Steaks Galore needs to arrange financing for its expansion program.One bank offers to lend the required $1,000,000 on a loan which requires interest to be paid at the end of each quarter.The quoted rate is 10 percent, and the principal must be repaid at the end of the year.A second lender offers 9 percent, daily compounding (365-day year), with interest and principal due at the end of the year.What is the difference in the effective annual rates (EFF%) charged by the two banks?

Assume that you just had a child, and you are now planning for her college education.You would like to make 43 equal payments over the next 21 years (the first payment to be made immediately, all other payments to be made at 6-month intervals, with the final payment to be made at her 21st birthday) so that you will be able to cover her expected expenses while in school.You expect to pay expenses on her 18th, 19th, 20th, and 21st birthdays.Assume that the current (time period 0) annual cost of college is $6,000, that you expect annual inflation to be 8 percent for the next 5 years, and then 5 percent thereafter.If you expect to be able to earn a return of 4 percent every 6 months on your investments (a simple rate of 8 percent with semiannual compounding), what will be the amount of each of the 43 payments?

In 1958 the average tuition for one year at an Ivy League school was $1,800.Thirty years later, in 1988, the average cost was $13,700.What was the growth rate in tuition over the 30-year period?

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%?

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

You want to buy a Nissan 350Z on your 27th birthday.You have priced these cars and found that they currently sell for $30,000.You believe that the price will increase by 5 percent per year until you are ready to buy.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 purchase the Nissan in 7 years?

A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments.Given the following facts, which of these statements is correct?

You will receive a $100 annual perpetuity, the first payment to be received now, at Year 0, a $300 annual perpetuity payable starting at the end of Year 5, and a $200 semiannual (2 payments per year) perpetuity payable starting midw through Year 10.If you require an effective annual interest rate of 14.49 percent, what is the present value of all thr perpetuities together at Year 0? (Hint: The semiannual annuity can be thought of as two annual annuities.)

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.