Exam 4: Time Value of Money

What is the present value of the following cash flow stream if the interest rate is 6.0% per year: 0 at Time 0; $1,000 at the end of Year 1; and $2,000 at the end of Years 2, 3, and 4?

After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years and $15,000 annually for the following 6 years, with the first deposit being made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift, which you will deposit immediately. If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?

What's the rate of return you would earn if you paid $950 for a perpetuity that pays $85 per year?

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

What's the present value of $1,500 discounted back 5 years if the appropriate interest rate is 6%, compounded semiannually?

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan).

Your aunt is about to retire, and she wants to buy an annuity that will provide her with $65,000 of income a year for 25 years, with the first payment coming IMMEDIATELY. The going rate on such annuities is 6.25%. How much would it cost her to buy the annuity today?

At a rate of 6.25%, what is the present value of the following cash flow stream: $0 at Time 0; $75 at the end of Year 1; $225 at the end of Year 2; $0 at the end of Year 3; and $300 at the end of Year 4?

Which of the following statements best describes annuities?

Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. How much would you still owe at the end of the first year, after you have made the first payment?

Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding and a 360- day year. How much could you withdraw after 8 months, assuming each month has 30 days?

If a bank pays a 4.50% nominal rate, with monthly compounding on deposits, what effective annual rate (EFF%) does the bank pay?

Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is correct?

Steve and Ed are cousins who were both born on the same day. Both turned 25 today. Their grandfather began putting $2,500 per year into a trust fund for Steve on his 20th birthday, and he just made a sixth payment into the fund. The grandfather (or his estate's trustee) will continue with these $2,500 payments until a 46th and final payment is made on Steve's 65th birthday. The grandfather set things up this way because he wants Steve to work, not to be a "trust fund baby," but he also wants to ensure that Steve is provided for in his old age. Until now, the grandfather has been disappointed with Ed, hence has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Ed. He will make the first payment to a trust for Ed later today, and he has instructed his trustee to make additional equal annual payments each year until Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Ed's trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday?

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is correct?

Your father now has $1,000,000 invested in an account that pays 9.00%. He expects inflation to average 3%, and he wants to make annual constant dollar (real) end-of-year withdrawals over each of the next 20 years and end up with a zero balance after the 20th year. How large will his initial withdrawal (and thus constant dollar (real) withdrawals) be?

Which of the following statements is INCORRECT?

Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $75 annually, beginning immediately, or you can get a lifetime subscription for $750, also payable immediately. Assuming you can earn 5.5% on your funds and the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy? Round fractional years up. (Hint: Be sure to remember that you are solving for how many years you must live, not for how many payments must be made.)

Your friend just won the lottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming 1 year from today. What rate of return is built into the annuity?

Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the BEGINNING of each year, beginning immediately. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?