Exam 5: Time Value of Money

You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4. What rate of return would you earn if you bought this asset?

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 (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift which you will deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?

If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series.

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate?

You deposit $500 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?

Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.

Your father paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year. What is the expected rate of return on this investment?

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

Your Aunt Ruth has $500,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. How many years will it take to exhaust her funds, i.e., run the account down to zero?

Which of the following statements is CORRECT?

The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant.

Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

A $150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?

Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, starting at the end of this year. 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?

Which of the following statements is CORRECT?

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?

Suppose a State of California bond will pay $1,000 eight years from now. If the going interest rate on these 8-year bonds is 5.5%, how much is the bond worth today?

Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.