Financial Management Chapter 5

Your best friend gave you $100 as a present six years ago. You invested this money at a 7 percent rate of interest. How much will this money be worth 10 years from today?

$295.22

You just won the lottery and want to put some money away for your child's college education. When your child goes to college 18 years from now, the cost will be $65,000. You can earn 8 percent compounded annually. How much do you need to invest today?

$16,266.19

Carlos has $2,413 saved today. He wants to buy a different vehicle as soon as he has $2,700 saved. How long does he have to wait to get his vehicle if he earns 4.5 percent compounded annually?

$2,700 = $2,413(1.045)t 1.11894 = 1.045t ln 1.11894 = t(ln 1.045) .11238 = .04402 t t = 2.55

Jessica wants to buy a house six years from now. She will need $36,000 in cash to do so. How much does she have to deposit today to achieve her goal if she can earn 7.5 percent compounded annually?

$23,326.61

You opened an investment account four years ago and deposited $1,000 at that time. The following year, you added another $1,000 to the account. You did not add any more money until today when you deposited an additional $1,000 into the account. This account has been earning 13.5 percent annually. How much is in the account today after your latest deposit?

$4,121.66

Your best friend borrowed $5,000 from you three years ago. At that time, it was agreed that you would charge him 5 percent interest compounded annually. The day after he borrowed the money, he skipped town and you had not heard from his until this morning. This morning he contacted you, apologized, and wants to meet you this afternoon to repay you the entire amount he now owes you. How much will he need to pay you this afternoon?

$5,788.13

Today, Tomas is borrowing $4,600 at an 8.5 percent rate of interest. He has agreed to repay both the principal and the interest in one lump sum five years from now. How much will he owe at the end of the loan period?

$6,916.82

One year ago, Sondra opened an investment account paying 7.65 percent annually. She made an initial deposit of $3,000. Her goal is to have $5,000 in the account three years from today. This afternoon, she realized that she may not have deposited sufficient funds to reach her goal. How much more, if any, should she deposit into her account to ensure that she reaches her goal in three more years?

$778.50

You are going to receive $100 four years from today. If the discount rate is 5 percent compounded annually, what will be the present value of the $100 two years from today?

$90.70

Five years ago, Leslie had $23,460 in her savings account. Today, she deposited an additional $6,000. She plans to deposit another $6,000 into this account next year. How much money will she have in her account ten years from today if she earns 7.5 percent on her savings?

$93,284.88

One hundred and fifty years ago, your ancestors purchased a tract of land and built a general store at a total cost of $550. This store has been successful over the years and is now the center attraction of the town which has grown around it. Your family still owns this landmark enterprise which today has an estimated value of $1.35 million What is the annual rate of return your family has earned on this property?

5.34 percent

Currently, you earn a salary of $37,500. Your goal is to earn an annual salary of $50,000 five years from now. By what percent will your salary have to increase on an annual basis if you are to reach your goal?

5.92 Percent

According to the Rule of 72, how long will it take to double your money if you can earn a 12 percent rate of return?

6 years

One hundred years ago, your great-grandfather purchased a 300-acre farm for the princely sum of $2,500. Today, that farm is still owned by your family and is currently valued at $1.8 million. What rate of return has your family on this investment by your great-grandfather?

6.80 Percent

In a growing Midwestern town, the number of eating establishments at the end of each of the last five years are as follows: Year 1 = 143; Year 2 = 149; Year 3 = 162; Year 4 = 171; Year 5 = 178. If the number of eating establishments is expected to grow in year 6 at the same rate as the percentage increase in year 5, how many new eating establishments will be added in year 6?

7

You can invest $1,000 at 7 percent simple interest for twenty years or at 5.5 percent compounded annually for twenty years. Which one of the following is true about these investment options?

At 7 percent simple interest, you will earn $70 in interest during the second year that your money is invested.

Sun borrows $13,500 today at 7.90 percent compounded annually. The terms of the loan require him To repay the principal and interest in one lump sum three years from today. How much will he have to pay in three years?

FV = $13,500(1.0790)3 = $16,958.92

Simple interest is interest earned only in the first year of an investment.

False

Which of the following statements are correct? I. All else equal, the present value increases as the interest rate decreases. II. All else equal, the future value decreases as the period of time increases. III. All else equal, the interest rate increases as the time period decreases.

I and III only

All else equal, the present value _____ as the period of time decreases.

Increases

Rosa wants to have $50,000 in her investment account fifteen years from now. How much does she have to deposit today to achieve her goal if she can earn 9.5 percent compounded annually?

PV = $50,000[1/(1.095)^15] = $12,816.17 Enter 15 N 9.5 I/Y 50,000 FV Solve for PV -12,816.17

Kristie is investing $5,000 today at 7 percent simple interest. Suzie is investing $3,000 today at 6 percent interest, compounded annually. Both Kristie and Suzie plan on leaving this money invested for thirty years. Which one of the following statements is true?

Suzie will have 11 percent more than Kristie thirty years from now.

Suppose you are trying to find the present value of two different cash flows using the same interest rate for each cash flow. The first cash flow is $1,000 ten years from now. The second is $800 seven years from now. Which one of the following is true about the discount factors used to value the cash flows?

The factor for the cash flow 10 years away is always less than or equal to the factor for the cash flow that is received seven years from now.

All else equal, the higher the interest rate, the higher the future value of an investment will be.

True

If a lump sum of $10,000 is invested for three years at 10 percent compounded annually, it will earn a total of $3,310 in interest over that period.

True

Interest on interest is interest earned on the reinvestment of previous interest payments.

True

Cornerstone Bank pays interest of 3.5 percent compounded annually. Uptown Bank pays 3.75 percent simple interest. Which one of the following statements is true if you invest $1,000 in each bank for five years?

Uptown Bank will pay you $0.19 less interest than Cornerstone Bank over the five years.

All else equal, the present value _____ as the period of time increases.

decrease. All else equal, the present value will decrease as the period of time increases.

You invest $12,000 for fifteen years at a 7 percent rate of interest compounded annually. The dollar amount of interest you receive each year will:

increase

One hundred and thirty years ago, a settler purchased 100 acres of land in the western territories for $1 an acre. That land has remained in your family over the years and now is part of downtown Denver. Currently, the value of the land is estimated at $16.8 million. What rate of return has your family earned on this land?

9.70 percent

You opened a savings account seven years ago and deposited $1,500 at that time. Five years ago, you added another $1,200 to the account. Today, you deposited an additional $600. The rate of return is 6 percent compounded annually. How much was your account worth at the close of business today?

$4,461.32

Road Movers currently pays an annual dividend of $1.34 per share. The company's dividend policy is to increase the dividend by 3 percent annually. How long will it take for the annual dividend to reach $2.00 per share?

13.55 years

You have been offered a business opportunity that will pay you $57,000 in six years if you invest $25,000 today. What is the expected rate of return on this investment?

14.72 Percent

Your grandmother is encouraging you to learn to save. If you give her $1,000 of your earnings today, she has promised to give you back $2,000 in five years. What rate of interest is your grandmother paying?

14.87 percent

You have been offered an investment opportunity that will cost you $10,000 today in exchange for receiving $25,000 six years from today. What rate of return is being offered on this investment?

16.50 percent

Based on the Rule of 72, how many years will it take to quadruple your money if you can earn an 8 percent rate of return?

18.0 years

You need $2,000 to buy a new stereo for your car. If you have $800 to invest at 5 percent compounded annually, how long will you have to wait to buy the stereo?

18.78 years

Tao wants to buy a sports car costing $68,500. Currently, he only has $48,200 saved for this purpose. How long will he have to wait to make this purchase assuming that the car does not increase in value and that he can earn 12 percent on his investments?

3.10 Years

You are going to buy a new truck as soon as you have $500 saved as a down payment. Currently, you have $431.68 in your savings account which pays 4.5 percent interest. How long do you have to wait until you can buy the truck?

3.34 years

ABC Co. currently pays an annual dividend of $2.60 per share. At what rate must the company increase the dividend if they want to pay $3.20 a share four years from now?

5.33 percent