Chapter 5. Practice problems with solution (Source: Test Bank)

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1 Chapter 5 Practice problems with solution (Source: Test Bank) 160. Robin invested $10,000 in an account that pays 5 percent simple interest. How much more could she have earned over a 40-year period if the interest had compounded annually? A. $38, B. $38, C. $40, D. $48, E. $50, LO3: Simple vs. Compound Interest 161. Alex and Courtney are each investing $1,200 today in a savings account. Alex will earn 4 percent interest compounded annually. Courtney will earn 4 percent simple interest. After five years Alex will have more than Courtney. A. $19.98 B. $20.13 C. $20.17 D. $20.21 E. $20.28 LO3: Simple vs. Compound Interest

2 162. What is the future value of $4,160 invested for eight years at 8.5 percent compounded annually? A. $6, B. $7, C. $8, D. $8, E. $8, LO1: Future Value 163. Today, you earn a salary of $37,800. What will your annual salary be twelve years from now if you receive annual raises of 3.6 percent? A. $55, B. $56, C. $56, D. $57, E. $58, LO1: Future Value

3 164. You own a stamp collection that is currently valued at $24,500. If the value increases by 5.5 percent annually, how much will the collection be worth when you retire 40 years from now? A. $204, B. $204, C. $205, D. $206, E. $208, LO1: Future Value 165. Your goal is to build your first home seven years from now. The home that you desire currently costs $215,900. New home prices are increasing by 4.2 percent annually. If home prices continue rising at that pace, how much will your home cost when you are ready to build seven years from now? A. $281, B. $284, C. $287, D. $292, E. $295, LO1: Future Value 166. Today, your grandmother gave you a gift of $25,000 to help pay for your college education. She told you that this amount was the result of a one-time investment at 8 percent interest 13 years ago. How much did your grandmother originally invest? A. $9, B. $9, C. $9, D. $9, E. $9, LO2: Present Value

4 167. What is the present value of $36,500 to be received five years from today if the discount rate is 6.75 percent? A. $26, B. $26, C. $26, D. $28, E. $28, LO2: Present Value 168. You would like to give your daughter $50,000 towards her college education sixteen years from now. How much money must you set aside today for this purpose if you can earn 7.8 percent on your funds? A. $14, B. $15, C. $15, D. $16, E. $16, LO2: Present Value 169. One year ago, you invested $5,000. Today, your investment is worth $6, What rate of interest did you earn? A percent B percent C percent D percent E percent LO3: Interest Rate for a Single Period

5 170. Thirty years ago, your father invested $6,000. Today that investment is worth $67, What is the average rate of return your father earned on this investment? A percent B percent C percent D percent E percent LO3: Interest Rate for Multiple Periods 171. Twenty years ago, Max invested $10,000. Thirty years ago, Julie invested $5,000. Today, both Max and Julie's investments are each worth $35,000. Which one of the following statements is correct concerning their investments? Assume that they will continue earning the same rate of return. A. Two years from now, Max's investment will be worth more than Julie's. B. Last year, Julie's investment was worth more than Max's. C. Max has earned more interest on interest than Julie. D. Julie has earned an average annual interest rate of 6.7 percent. E. Max has earned an average annual interest rate of 6.41 percent. LO3: Interest Rate for Multiple Periods Level: Intermediate 172. New Metals, Inc. is planning on expanding their operations when the economy strengthens in a few years. At that time they will need to purchase additional equipment. Four years ago, they set aside $300,000 in a special account for this purpose. Today, that account is worth $383, What rate of interest is New Metals earning on this money? A percent B percent C percent D percent E percent LO3: Interest Rate for Multiple Periods

6 173. Kay purchased some land costing $124,600. Today, that same land is valued at $179,400. How long has she owned this land if the price of land has been increasing at 6 percent per year? A years B years C years D years E years LO4: Number of Time Periods 174. When you were 26 years old, you received an inheritance of $1,500 from your grandfather. You invested that amount in Nu-Wave stock and have not touched the investment since then. Today, this investment is worth $109, Nu-Wave stock has earned an average rate of return of 11.3 percent per year over this time period. How old are you today? A. age 57 B. age 59 C. age 62 D. age 64 E. age 66 LO4: Number of Time Periods 175. Your goal is to have $50,000 in cash to build a new home twelve years from now. Your plan is to make one deposit today to fund this goal. How much more will you have to deposit today to fund this goal if you can only earn 4 percent on your savings rather than 5 percent? A. $3, B. $3, C. $3, D. $3, E. $3, LO3: Present Value and Rate Changes

7 176. Your goal is to have two separate investments that will be worth $10,000 each ten years from today. Investment A will pay 6 percent interest. Investment B will pay 6.5 percent interest. You will make a one-time deposit into each account today. What is the difference between the amount you must invest today in Investment A as compared to the amount you must invest today in Investment B if you are to reach your goal in ten years? A. $ B. $ C. $ D. $ E. $ LO3: Present Value and Rate Changes 177. Twenty years from now, you would like to purchase a cottage located on the shores of your favourite lake. You expect that you will have $250,000 available at that time for this purchase. You could afford a home that is currently selling for if the homes increase in value by 3 percent annually, but if the homes increase in value by 5 percent annually, you can only afford a home priced at today. A. $127,023; $92,687 B. $138,419; $94,222 C. $138,419; $114,097 D. $144,676; $100,469 E. $144,676; $111,068 LO3: Present Value and Rate Changes Level: Intermediate

8 178. You would like to invest some money today such that your investment will be worth $100,000 fifteen years from now. Your broker gives you two options. First, you can invest at a guaranteed annual rate of 4 percent. Or, you can invest in stocks and hopefully earn an average of 7 percent per year. How much more will you have to invest today if you opt for the fixed rate rather than the stocks? A. $18, B. $18, C. $18, D. $18, E. $19, LO3: Present Value and Rate Changes 179. Omar has an investment valued at $12,345 today. He made a one-time investment at 6.5 percent four years ago. Leon has an investment that is also valued at $12,345 today. Leon invested four years ago at 7.5 percent. Omar originally invested and Leon invested. A. $9,568.24; $9, B. $9,596.05; $9, C. $9,608.14; $9, D. $9,633.33; $9, E. $9,652.18; $9, LO3: Present Value and Rate Changes

9 180. When you retire thirty years from now, you want to have $750,000. You think you can earn an average of 9 percent on your money. To meet this goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum five years from today. How much more will you have to deposit as a lump sum if you wait for five years before making the deposit? A. $28, B. $29, C. $30, D. $36, E. $38, LO4: Present Value and Time Changes 181. Jeanette needs $15,000 as a down payment for a house six years from now. She earns 3.5 percent on her savings. Jeanette can either deposit one lump sum today for this purpose or she can wait a year and deposit a lump sum. How much additional money must Jeanette deposit if she waits for one year rather than making the deposit today? A. $ B. $ C. $ D. $ E. $ LO4: Present Value and Time Changes

10 182. Theresa wants to save $10,000 so that she can surprise her husband with a vacation six years from now. She can earn 7 percent on her savings. How much more will she have to deposit if she waits one more year before investing versus if she deposits one lump sum today? A. $ B. $ C. $ D. $ E. $ LO4: Present Value and Time Changes 183. Moe and Joe are twins. Moe invested $1,000, earned 9 percent annually, and now has $1, Joe invested $1,000, earned 6.47 percent, and now has $1, Joe invested his money years before Moe. A. 2.5 years B. 2.8 years C. 3.0 years D. 3.2 years E. 3.5 years LO4: Present Value and Time Changes 184. Sue invested $5,000 eleven years ago at 12 percent. Terri has the same amount saved today as Sue has. Terri also earns 12 percent but she only invested $2,500. How long ago did Terri invest her money? A years B years C years D years E years LO4: Present Value and Time Changes

11 185. You have just been awarded a $200,000 insurance settlement. The insurance company has offered to invest this amount at a guaranteed interest rate of 4.5 percent for ten years. You think you can invest this money yourself and earn an average return of 8 percent. If you are able to do that, how much more will your settlement be worth ten years from now than if you had left the funds with the insurance company? A. $78, B. $86, C. $118, D. $121, E. $137, LO3: Future Value and Rate Changes 186. You have just landed your first job. Part of the offer includes a $4,000 new employee bonus which is intended to cover your relocation costs. You have determined that you can move yourself for $1,000. Thus, you have decided to open an Individual Retirement Account with the remaining $3,000. How much more will this investment be worth 35 years from now if you can earn an average rate of return of 9.5 percent rather than 9 percent? A. $10, B. $10, C. $11, D. $11, E. $11, LO3: Future Value and Rate Changes

12 187. You deposit $3,000 in a retirement account today at 5.5 percent interest. How much more money will you have if you leave the money invested for forty-five years rather than forty years? A. $7, B. $7, C. $7, D. $7, E. $7, LO4: Future Value and Time Changes 188. You collect model airplanes. One particular model is currently valued at $275. If this model increases in value by 5 percent annually, it will be worth six years from now and twelve years from now. A. $368.01; $ B. $368.01; $ C. $368.53; $ D. $368.53; $ E. $368.53; $ LO4: Future Value and Time Changes 189. Frank invests $2,500 in an account that pays 6 percent simple interest. How much money will he have at the end of four years? A. $2,650 B. $3,100 C. $3,156 D. $3,163 E. $10,600 Ending value = $2,500 + ($2, ) = $3, LO3: Simple Interest

13 190. Faith invests $4,500 in an account that pays 4 percent simple interest. How much money will she have at the end of eight years? A. $4,680 B. $5,367 C. $5,940 D. $6,122 E. $6,159 Ending value = $4,500 + ($4, ) = $5, LO3: Simple Interest 191. Jessica invests $3,000 in an account that pays 5 percent simple interest. How much more could she have earned over a 7-year period if the interest had compounded annually? A. $ B. $ C. $ D. $ E. $ Ending value at 5 percent simple interest = $3,000 + ($3, ) = $4,050.00; Ending value at 5 percent compounded annually = $3,000 (1 +.05) 7 = $4,221.30; Difference = $4, $4, = $ LO3: Simple versus Compound Interest

14 192. Jeff invests $3,000 in an account that pays 7 percent simple interest. How much more could he have earned over a 20-year period if the interest had compounded annually? A. $2, B. $3, C. $3, D. $4, E. $4, Ending value at 7 percent simple interest = $3,000 + ($3, ) = $7,200.00; Ending value at 7 percent compounded annually = $3,000 (1 +.07) 20 = $11,609.05; Difference = $11, $7, = $4, LO3: Simple versus Compound Interest 193. What is the future value of $3,497 invested for 15 years at 7.5 percent compounded annually? A. $7, B. $10, C. $14, D. $14, E. $15, Future value = $3,497 ( ) 15 = $10, LO1: Future Value

15 194. Today, you earn a salary of $42,500. What will be your annual salary 10 years from now if you earn annual raises of 3.2 percent? A. $56, B. $57, C. $58, D. $59, E. $59, Future value = $42,500 ( ) 10 = $58, LO1: Future Value 195. You own a classic automobile that is currently valued at $67,900. If the value increases by 8 percent annually, how much will the automobile be worth 15 years from now? A. $199, B. $212, C. $214, D. $215, E. $218, Future value = $67,900 (1 +.08) 15 = $215, LO1: Future Value

16 196. You hope to buy your dream house 3 years from now. Today, your dream house costs $247,900. You expect housing prices to rise by an average of 7.5 percent per year over the next 3 years. How much will your dream house cost by the time you are ready to buy it? A. $292, B. $294, C. $298, D. $307, E. $309, Future value = $247,900 ( ) 3 = $307, LO1: Future Value 197. Your grandmother invested one lump sum 42 years ago at 3.5 percent interest. Today, she gave you the proceeds of that investment which totaled $28, How much did your grandmother originally invest? A. $4,500 B. $6,650 C. $7,200 D. $7,500 E. $9,000 Present value = $28, [1 / ( ) 42 ] = $6, LO2: Present Value

17 198. What is the present value of $36,800 to be received 6 years from today if the discount rate is 12 percent? A. $18, B. $19, C. $19, D. $20, E. $20, Present value = $36,800 [1 / (1 +.12) 6 ] = $18, LO2: Present Value 199. You would like to give your daughter $50,000 towards her college education 15 years from now. How much money must you set aside today for this purpose if you can earn 9 percent on your investments? A. $12, B. $12, C. $13, D. $14, E. $14, Present value = $50,000 [1 / (1 +.09) 15 ] = $13, LO2: Present Value

18 200. One year ago, you invested $2,500. Today it is worth $2, What rate of interest did you earn? A percent B percent C percent D percent E percent $2, = $2,500 (1 + r) 1 ; r = percent LO3: Interest Rates 201. Thirty years ago, your father invested $11,000. Today, that investment is worth $287,047. What is the average annual rate of return your father earned on his investment? A percent B percent C percent D percent E percent $287,047 = $11,000 (1 + r) 30 ; r = percent LO3: Interest Rates

19 202. Twelve years ago, Jake invested $2,000. Six years ago, Tami invested $4,000. Today, both Jake's and Tami's investments are each worth $9,700. Assume that both Jake and Tami continue to earn their respective rates of return. Which one of the following statements is correct concerning these investments? A. Three years from today, Jake's investment will be worth more than Tami's. B. One year ago, Tami's investment was worth more than Jake's. C. Jake has earned a higher rate of return than Tami. D. Tami has earned an average annual interest rate of percent. E. Jake has earned an average annual interest rate of percent. Jake $9,700 = $2,000 (1 + r) 12 ; r = percent; Tami: $9,700 = $4,000 (1 + r) 6 ; r = percent; The correct answer states that Tami earned percent interest. LO3: Interest Rates

20 203. Tropical Tans is saving money to build a new salon. Three years ago, they set aside $12,000 for this purpose. Today, that account is worth $16,418. What rate of interest is Tropical Tans earning on this money? A percent B percent C percent D percent E percent $16,418 = $12,000 (1 + r) 3 ; r = percent. LO3: Interest Rates 204. Five years ago, Precision Tool set aside $50,000 in case of a financial emergency. Today, that account has increased in value to $64,397. What rate of interest is the firm earning on this money? A percent B percent C percent D percent E percent $64,397 = $50,000 (1 + r) 5 ; r = 5.19 percent LO3: Interest Rates