Chapter 9

Olivia borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is (Pick the closest answer.) a. $942 b. $1,125 c. $1,482 d. $2,641

C PV 4,500 FV 0 N 4 I/Y 12 → PMT = -$1,481.55

Consolidated Freightways is financing a new truck with a loan of $60,000 to be repaid in six annual end-of-year installments of $13,375. What annual interest rate is Consolidated Freightways paying? Pick the closest answer. a. 7% b. 8% c. 9% d. 10%

C PV 60,000 PMT -13,375 N 6 FV 0 → I/Y = 9%

In future value or present value problems, unless stated otherwise, cash flows are assumed to be a. at the end of a time period. b. at the beginning of a time period. c. in the middle of a time period. d. spread out evenly over a time period.

A

Interest earned only on an investment's principal or original amount is referred to as: a. simple interest b. compound interest c. discount interest d. annuity interest

A

Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments. The interest paid in the first year is (Pick the closest answer.) a. $1,155 b. $2,481 c. $144 d. $1,327

A

A loan that is repaid in equal payments over a specified time period is referred to as a (n): a. discounted loan b. amortized loan c. simple interest-free loan d. inflation-indexed loan

B

The amount earned on a deposit becomes part of the principal at the end of a period and can earn a return in future periods is called a. discount interest. b. compound interest. c. primary interest. d. future value.

B

A famous athlete is awarded a $9 million contract that stipulates equal payments to be made monthly over a period of five years. To determine what lump sum has the same value as the contract today, you would need to use: a. present value of a single lump sum b. future value of a single lump sum c. present value of an annuity d. future value of an annuity

C

A loan that is repaid in equal payments over a specified time period is called a (n) a. discount loan b. balloon loan c. amortized loan d. none of the above

C

A series of equal payments or receipts that occur at the beginning of each of a number of time periods is referred to as: a. an ordinary annuity b. a deferred annuity c. an annuity due d. an extraordinary annuity

C

The future value of a dollar ________ as the interest rate increases and ________ the farther in the future is the funds are to be received. a. decreases; decreases. b. decreases; increases. c. increases; increases. d. increases; decreases.

C

The method of calculating interest on a loan that is set by law is called the: a. negotiated legal rate (NLR) b. effective annual rate (EAR) c. annual percentage rate (APR) d. none of the above

C

The basic future and present value equations contain four variables. Which one of the following is not included? a. present value (PV) b. future value (FV) c. interest rate (r) d. inflation rate (I) e. number of periods (n)

D

The interest rate that measures the true interest rate when compounding occurs more frequently than once a year is called the: a. annual percentage rate b. compound rate of interest c. stated rate of interest d. effective annual rate

D

The time value concept/calculation used in amortizing a loan is a. future value of a dollar b. future value of an annuity c. present value of a dollar d. present value of an annuity

D

A ski chalet in Vail now costs $250,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 10 years before Larry and his wife retire from successful investment banking careers. How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 13 percent in order to buy the ski chalet upon retirement? Pick the closest answer. a. $8,333 b. $13,572 c. $25,005 d. $22,109

D PV 250,000 N 10 I/Y 5 → FV = $407,222.66 FV 407,222.66 N 10 I/Y 13 PV 0 → PMT = -$22,107.94

An annuity due may also be referred to as a deferred annuity.

F

An ordinary annuity exists when the equal payments occur at the beginning of each time period.

F

As the number of periods increases, present value increases.

F

A fixed-rate mortgage is an example of an annuity.

T

A loan amortization schedule shows the breakdown of each payment between interest and principal, as well as the remaining balance after each payment.

T

An amortized loan is repaid in equal payments over a specified time period.

T

An annuity is a series of equal payments that occur over a number of time periods.

T

The _________ value of a savings or investment is its amount or value at the current time. a. present b. future c. book d. none of the above

A

The interest rate determined by multiplying the interest rate charged per period by the number of periods in a year is called the: a. annual percentage rate b. compound rate of interest c. stated rate of interest d. effective annual rate

A

You need to have $35,000 on hand to buy a new Lexus five years from today. To achieve that goal, you want to know how much you must invest today in a certificate of deposit guaranteed to return you 3% per year. To help determine how much to investment today, you will use: a. present value of a single lump sum b. future value of a single lump sum c. present value of an annuity d. future value of an annuity

A

Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments. Calculate the loan balance at the end of the second year. (Pick the closest answer.) a. $7,700.17 b. $5,536.18 c. $8,164.05 d. $9,113.72

A ANNUAL PAYMENT: PV 10,500 N 6 I/Y 11 FV 0 → PMT = - $2,481.91 INTEREST PAID IN 1ST PAYMENT: 10,500(0.11) = $1,155 PRINCIPAL PAID IN 1ST PAYMENT: 2,481.91 - 1,155 = $1,326.91 LOAN BALANCE END OF 1ST YEAR: 10,500 - 1,326.91 = $9,173.09 INTEREST PAID IN 2ND PAYMENT: 9,173.09(0.11) = $1,009.04 PRINCIPAL PAID IN 2ND PAYMENT: 2,481.91 - 1,009.04 = $1,472.87 LOAN BALANCE END OF 2ND YEAR: 9,173.04 - 1,472.87 = $7,700.17

If the quarterly rate of interest is 2.5% and interest is compounded quarterly, then the EAR is (Pick the closest answer.): a. 10.38% b. 10.00% c. 2.50% d. none of the above

A EAR = (1 + 2.5%)^4 -1 = 1.1038 - 1 = 10.38%

Assume your bank has a choice between two deposit accounts. Account A has an annual percentage rate of 7.55 percent but with interest compounded monthly. Account B has an annual percentage rate of 7.45 percent with interest compounded quarterly. Which account provides the highest effective annual return? a. Account A b. Account B c. Both provide the same effective annual return. d. We don't have sufficient information to make a choice.

A It has a higher nominal interest rate and compounds more frequently

The present value of an annuity of $5,000 to be received at the end of each of the 6 years at a discount rate of 4% would be (Pick the closest answer.): a. $26,210 b. $33,165 c. $3,950 d. none of the above

A PMT +5,000 FV 0 N 6 I/Y 4→ PV = -$26,210.68

Shannon plans to fund his individual retirement account (IRA) with the maximum contribution of $2,500 at the end of each year for the next 30 years. If Shannon can earn 10 percent on his contributions, how much will he have at the end of the tenth year? Pick the closest answer. a. $39,843.56 b. $411,235 c. $23,567 d. $41,124

A PMT -2,500 N 10 I/Y 10 PV 0 → FV = $39,843.56

The future value of $100 received today and deposited at 6 percent for four years is (Pick the closest answer. ) a. $126. b. $ 79. c. $124. d. $116.

A PV -100 N 4 I/Y 6 → FV = $126.25

If a Canadian Savings bond can be purchased for $29.50 and has a maturity value at the end of 25 years of $100, what is the annual rate of return on the bond? Pick the closest answer. a. 5% b. 6% c. 7% d. 8%

A PV -29.50 FV 100 N 25 → I/Y = 5%

If $1,000 were invested now at a 12% interest rate compounded annually, what would be the value of the investment in two years? Pick the closest answer. a. $1,254 b. $1,210 c. $1,188 d. $1,160

A PV 1,000 N 2 I/Y 12 → FV = $1,254.40

Your college has agreed to give you a $10,000 tuition loan. As part of the agreement, you must repay $12,600 at the end of the three-year period. What interest rate is the college charging? a. 8% b. 9% c. 11% d. 6%

A PV 10,000 FV -12,600 N 3 → I/Y = 8%

Assume that a borrower is willing to pay you $2,000 at the end of three years in return for a sum of money now. To receive a return of 10%, how much are you willing to lend now? Pick the closest answer. a. $1,502 b. $1,786 c. $1,802 d. $1,818

A PV 2,000 N 3 I/Y 10 → PV = $1,502.63

The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ________. a. $253 b. $252 c. $158 d. $135

A PV 200 N 6 I/Y 4 → FV = $253.06

CLAIRE bought 100 shares of Minnesota Mining and Manufacturing in June, 1987 for $38 a share for a total investment of $3,800. She sold the shares in June, 1996 for $8,960. What is Cecilia's annual rate of return on her investment? Pick the closest answer. a. 10% b. 10.6% c. 11% d. 11.2%

A PV 3,800 N 9 FV 8,960 → I/Y = 10%

Tracey deposits $5,000 in a five-year certificate of deposit paying 6% compounded semi-annually. How much will Tracey have at the end of the five-year period? Pick the closest answer. a. $6,720 b. $6,690 c. $6,596 d. $6,910

A PV 5,000 I/Y 3 N 10 → FV = $6,719.58

Suppose you receive $3,000 a year in Years One through Four, $4,000 a year in Years Five through Nine, and $2,000 in Year 10, with all the money to be received at the end of the year. If your discount rate is 12%, what is the present value of these cash flows? Pick the closest answer. a. 18,926.12 b. 19,560.80 c. 20,651.24 d. 24,175.00

A YR 1-4: PMT 3,000 FV 0 N 4 I/Y 12 → PV0 = $9,112.05 YR 5-9: PMT 4,0000 FV 0 N 5 I/Y 12 → PV5 = $14,419.10 BACK TO NOW: FV 14,419.10 N 4 I/Y 12 → PV = $9,163.60 YR 10: FV 2,000 N 10 I/Y 12 → PV = $643.95 TOTAL: 9,112.05 + 9,163.60 + 643.95 = $18,919.60

Suppose you have a choice of two equally risky annuities, each paying $1,000 per year for 20 years. One is an annuity due, while the other is an ordinary annuity. Which annuity would you choose? a. the ordinary annuity b. the annuity due c. either one because the annuities have the same present value d. without information about the appropriate interest rate, we cannot tell which annuity is better

B

Which of the following characteristics is not descriptive of an amortization schedule? a. Each payment is the same. b. The same dollar amount of interest is paid with each payment. c. Payment on principal increases with each total payment. d. Balance owed is reduced by each payment.

B

Kristen has just purchased a used Mercedes for $18,995. She plans to make a $2,500 down payment on the new car. What is the amount of her monthly payment on the remaining loan if she must pay 12% annual interest on a 24-month car loan? Pick the closest answer. a. $759.53 b. $776.48 c. $894.16 d. $899.87

B $18,995 - $2,500 = $16,495 PV 16,495 N 24 I/Y 1 FV 0 → PMT = $776.48

A generous benefactor to the local university plans to make a one-time endowment which would provide the university with $150,000 per year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment be? Pick the closest answer. a. $300,000 b. $3,000,000 c. $750,000 d. $1,428,571

B (ENDOWMENT) × 5% = $150,000 ENDOWMENT = 150,000/0.05 = $3,000,000

If the stated or nominal interest rate is 10 percent and the inflation rate is 5 percent, the net or differential compounding rate would be ________ percent a. ten b. five c. two d. fifteen

B 10% - 5% = 5%

The present value of $1,000 received at the end of year 1, $1,200 received at the end of year 2, and $1,300 received at the end of year 3, assuming an opportunity cost of 7 percent, is (Pick the closest answer.) a. $2,500 b. $3,043 c. $6,516 d. $2,856

B 1ST DEPOSIT: PV 1,000 N 1 I/Y 7 → PV = $934.58 2ND DEPOSIT: PV 1,200 N 2 I/Y 12 → PV = $1,048.13 3RD DEPOSIT: PV 1,300 N 3 I/Y 12 → PV = $1,061.87 TOTAL $3,044.58

If the quarterly rate of interest is 2.5% and interest is compounded quarterly, then the APR is (Pick the closest answer.): a. 10.38% b. 10.00% c. 2.50% d. none of the above

B APR = 2.5% × 4 = 10%

The present value of an annuity of $5,000 to be received at the beginning of each of the 6 years at a discount rate of 4% would be (Pick the closest answer.): a. $26,210 b. $27,258 c. $3,950 d. none of the above

B BGN PMT 5,000 N 6 I/Y 4 FV 0 → PV = -$27,259.11

Larry deposited $5,000 in a savings account that paid 8% interest compounded quarterly. What is the effective rate of interest? a. 8.00% b. 8.24% c. 8.33% d. 8.46%

B EAR = (1 + R)^m - 1 = (1.02)^4 - 1 = 8.24%

Lance would like to send his parents on a cruise for their 25th wedding anniversary. He expects the cruise will cost $15,000 and he has 5 years to accumulate this money. How much must Lance deposit at the end of each year in an account paying 10 percent interest in order to have enough money to send his parents on the cruise? Pick the closest answer. a. $1,862 b. $2,457 c. $3,000 d. $2,234

B FV 15,000 PV 0 N 5 I/Y 10 → PMT = -$2,456.96

You need $8,000 four years from now for a down payment on your future house. How much money must you deposit today if your credit union pays 5% interest compounded annually? Pick the closest answer. a. $6,269.59 b. $6,581.62 c. $6,394.12 d. $6,189.83

B FV 8,000 N 4 I/Y 5 → PV = $6,581.62

If you have an account with a 21.5% annual percentage rate where interest is compounded quarterly, what is the effective annual rate of interest? Pick the closest answer. a. 23.75% b. 23.3% c. 21.5% d. none of the above

B INTEREST PER QUARTER= 21.5/4 = 5.375% EAR = (1 + 0.05375)^4 - 1 = 1.23296 -1 = 23.3%

The future value of an ordinary annuity of $1,000 each quarter for 10 years, deposited at 12 percent compounded quarterly is (Pick the closest answer.) a. $17,549 b. $75,401 c. $93,049 d. $11,200

B PMT -1,000 N 40 I/Y 3 PV 0 → FV = $75,401.26

Claire makes annual end-of-year payments of $5,043.71 on a four-year loan with an interest rate of 13 percent. The original principal amount was (Pick the closest answer.) a. $24,462 b. $15,000 c. $3,092 d. $20,175

B PMT -5,043.71 N 4 I/Y 13 FV 0 → PV = $15,002.37

If we will receive $100 per year beginning one year from now for a period of three years with a 12% discount rate, what would be the value of our investment today? Pick the closest answer. a. $230 b. $240 c. $250 d. $260

B PMT 100 FV 0 N 3 I/Y 12 → PV = $240.18

The present value of an annuity of $5,000 to be received at the end of every six months for over 6 years at a 4% annual rate would be (Pick the closest answer.): a. $26,210 b. $52,875 c. $3,950 d. none of the above

B PMT 5,000 N 12 I/Y 2 FV 0 → PV = -$52,876.71

You have just won a lottery! You will receive $50,000 a year beginning one year from now for 20 years. If your required rate of return is 10%, what is the present value of your winning lottery ticket? Pick the closest answer. a. $418,250 b. $425,700 c. $444,640 d. $453,850

B PMT 50,000 N 20 I/Y 10 FV 0 → PV = $425,678.19

Shelby was given a gold coin originally purchased for $1 by her great-grandfather 50 years ago. Today the coin is worth $450. The rate of return realized on the sale of this coin is approximately equal to (Pick the closest answer.) a. 8% b. 13% c. 50% d. cannot be determined with the given information

B PV -1 FV 450 N 50 → I/Y = 13%

Megan puts $1,000 in a savings passbook that pays 4% compounded quarterly. How much will she have in her account after five years? Pick the closest answer. a. $1,200.50 b. $1,220.20 c. $1,174.80 d. $1,217.50

B PV -1,000 N 20 I/Y 1 → FV = $1,220.19

Megan owns stock in a company which has consistently paid a growing dividend over the last five years. At the end of the first year Megan owned the stock, she received $1.71 per share and in the fifth year, she received $2.89 per share. What is the growth rate of the dividends during this time? Pick the closest answer. a. 7 percent b. 14 percent c. 12 percent d. 5 percent

B PV -1.71 FV 2.89 N 4 → I/Y = 14.02%

$2,000 invested today at 6% in 3 years would result in a future value of (Pick the closest answer): a. $2,000 b. $2,382 c. $6,362 d. none of the above

B PV -2,000 N 3 I/Y 6 → FV = $2,382.03

The future value of $200 received today and deposited at 8 percent for three years is (Pick the closest answer.) a. $248. b. $252. c. $158. d. $200.

B PV -200 N 3 I/Y 8 → FV = $251.94

Taylor deposits $2,000 per year at the end of the year for the next 20 years into an IRA account that pays 6%. How much will Taylor have on deposit at the end of 20 years? Pick the closest answer. a. $67,520 b. $73,572 c. $81,990 d. $75,686

B PV 0 N 20 I/Y 6 PMT -2,000 → FV = $73, 571.18

An investment will mature in 20 years. Its maturity value is $1,000. If the discount rate is 7%, what is the present value of the investment? Pick the closest answer. a. $178 b. $258 c. $276 d. $362

B PV 1,000 N 20 I/Y 7 → PV = $258.42

In 1983, the average tuition for one year in the MBA program at a university was $3,600. Thirty years later, in 2013, the average tuition was $27,400. What is the compound annual growth rate in tuition (rounded to the nearest whole percentage) over the 30-year period? Pick the closest answer. a. 6% b. 7% c. 8% d. 10%

B PV 3,600 FV -27,400 N 30 → I/Y = 7.0%

In 1976, the average price of a domestic car was $5,100. Twenty years later, in 1996, the average price was $16,600. What was the annual growth rate in the car price over the 20-year period? Pick the closest answer. a. 5% b. 6% c. 7% d. 8%

B PV 5,000 FV -16,600 N 20 → I/Y = 6.18%

You want to buy a Volvo in seven years. The car is currently selling for $50,000, and the price will increase at a compound rate of 10% per year. You can presently invest in high-yield bonds earning a compound annual rate 14% per year. How much must you invest at the end of each of the next seven years to be able to purchase your dream car in seven years? Pick the closest answer. a. $8,831.46 b. $9,080.20 c. $9,125.42 d. $9,282.09

B PV 50,000 N 7 I/Y 10 → FV = $97,435.86 COST OF CAR PV 0 FV 97,435.86 N 7 I/Y 14 → PMT = $9,080.28

Your current bank is paying 6.25% simple interest rate. You can move your savings account to Harris Bank that pays 6.25% compounded annually or to First Chicago bank paying 6% compounded semi-annually. To maximize your return you would choose: a. your current bank b. Harris Bank c. First Chicago ban d. you are indifferent, because the effective interest rate for all three banks is the same

B a. NOT AS GOOD AS ANNUAL COMPOUNDING IN HARRIS BANK b. EAR = 6.25% c. EAR = (1 + .03)^2 - 1 = 1.0609 - 1 = 6.09%

When solving for the future value of an amount deposited now, which one of the following factors would not be part of the calculation? a. present value amount b. 1 plus the interest rate c. 1 divided by the sum of 1 plus the interest rate d. number of periods to compound over

C

Which of the following statements is false? a. For a given APR, more frequent compounding results in additional return on the investment. b. An amortized loan is repaid in equal payments over a specified time period. c. The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year. d. Each of the above statements is true.

C

Which of the following terms best describes an annuity due? a. a perpetuity b. unequal payments c. payment at beginning of year d. payment at the end of the year

C

A hospital received a contribution to its endowment fund of $2 million. The hospital can never touch the principal, but it can use the earnings. At an assumed interest rate of 9.5 percent, how much can the hospital earn to help its operations each year? Pick the closest answer. a. $95,000 b. $19,000. c. $190,000. d. $18,000.

C $2,000,000(0.095) = 190,000

A wealthy inventor has decided to endow her favorite art museum by establishing funds for an endowment which would provide $1,000,000 per year forever. She will fund the endowment upon her fiftieth birthday 10 years from today. She plans to accumulate the endowment by making annual end-of-year deposits into an account. The rate of interest is expected to be 5 percent in all future periods. How much must the scientist deposit each year to accumulate to the required amount? Pick the closest answer. a. $1,875,333 b. $736,000 c. $1,590,091 d. $943,396

C (ENDOWMENT)(0.05) = 1,000,000 → ENDOWMENT = 1,000,000/.05 = $20,000,000 FV 20,000,000 PV O N 10 I/Y 5 → PMT = -$1,590,091

$100 is received at the beginning of year 1, $200 is received at the beginning of year 2, and $300 is received at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is ________. Pick the closest answer. a. $1,536 b. $672 c. $727 d. $1,245

C 1ST DEPOSIT: PV 100 N 3 I/Y 12 → FV = $140.49 2ND DEPOSIT: PV 200 N2 I/Y 12 → FV = $250.88 3RD DEPOSIT: PV 300 N 1 I/Y 12 → FV = $336.00 TOTAL $727.37

Your subscription to Consumer Reports is about to expire. You may renew it for $24 a year or, instead, you may get a lifetime subscription to the magazine for a onetime payment of $400 today. Payments for the regular subscription are made at the beginning of each year. Using a discount rate of 5%, how many years does it take to make the lifetime subscription the better deal? Pick the closest answer. a. 25 years b. 28 years c. 30 years d. 40 years

C BGN MODE PV 400 FV 0 PMT -24 I/Y 5 → N = 32.3

Suppose you were going to save $1,000 per year for three years at a 10% interest rate compounded annually, with the first investment occurring today. What would be the future value of this investment? Pick the closest answer. a. $2,124 b. $2,310 c. $3,641 d. $3,812

C BGN PMT -1,000 N 3 I/Y 10 PV 0 → FV = $3,641

What is the highest effective rate attainable with a 12 percent nominal rate? Pick the closest answer. a. 12.00% b. 12.55% c. 12.75% d. 12.95%

C DAILY: (1+.12/365)^365 - 1 = (1.0003288)^365-1 = 12.72%

If the APR is 12% and interest is compounded monthly, then the EAR is (Pick the closest answer.): a. 12.00% b. 1.00% c. 12.68% d. none of the above

C EAR = (1 + 1%)^12 -1 = 1.1268 - 1 = 12.68%

Taylor has just accepted a job as a stockbroker. He estimates his gross pay each year for the next three years is $35,000 in year 1, $21,000 in year 2, and $32,000 in year 3. The present value of these cash flows, if they are discounted at 4%, is closest to a. $79,452.30 b. $80,294.50 c. $81,517.1 d. $88,000

C FV 35,000 N 1 I/Y 4 → PV = $33,653.85 FV 21,000 N 2 I/Y 4 → PV = $19,415.68 FV 32,000 N 3 I/Y 4 → PV = $28,447.88 ---------------- $81,517.41

Kristen has planned to start her college education four years from now. To pay for her college education, she has decided to save $1,000 each quarter for the next four years in a bank account paying 12 percent interest. How much will she have at the end of the fourth year? Pick the closest answer. a. $1,574 b. $19,116 c. $20,157 d. $16,000

C PMT -1,000 N 16 OI/Y 3 PV 0 → FV = $20,156.88

The future value of an ordinary annuity of $5,000 invested at 8% in 5 years would result in a value of (Pick the closest answer.): a. $25,000 b. $7,345 c. $29,335 d. none of the above

C PMT -5,000 PV 0 N 5 I/Y 8 → FV = $29,333.00

You deposit $1,000 in a long-term certificate of deposit with an interest rate of 9%. How many years will it take for you to triple your deposit? Pick the closest answer. a. 11 years b. 12 years c. 13 years d. 14 years

C PV -1,000 FV 3,000 I/Y 9 → N = 12.75

Collin plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years. If Collin can earn 10 percent on his contributions, how much will he have at the end of the tenth year? Pick the closest answer. a. $12,290 b. $20,000. c. $31,874. d. $51,880.

C PV 0 PMT -2,000 N 10 I/Y 10 → FV = $31,874.85

You borrow $10,000 to pay for your college tuition. The loan is amortized over a three-year period with an interest rate of 18%. What is your remaining balance at the end of Year Two? Pick the closest answer. a. $7,201 b. $4,599 c. $3,898 d. $3,303

C PV 10,000 FV 0 I/Y 18 N 3 → PMY = $4,599.24 YR1: INT = $1,800 → PRIN = 4,599.24 - 1,800 = $2,799.24 END BAL = 10,000 - 2,799.24 = $7,200.76 YR2: INT 7,200.76(0.18) = $1,296.14 → PRIN 4,599.24 - 1,296.14 = $3,303.10 END BAL 7,200.76 - 3,303.10 = $3,897.66

You put $2,000 in an IRA account at Northern Trust. This account pays a fixed interest rate of 8% compounded quarterly. How much money do you have in five years? Pick the closest answer. a. $2,914 b. $2,938 c. $2,972 d. $2,999

C PV 2,000 N 20 I/Y 2 → FV = $2,971.89

Assume a lender offers you a $25,000, 10%, three-year loan that is to be fully amortized with three annual payments. The first payment will be due one year from the loan date. How much will you have to pay each year? Pick the closest answer. a. $8,042 b. $9,026 c. $10,053 d. $11,120

C PV 25,000 FV 0 N 3 I/Y 10 → PMT = $10,052.87

When compounding more than once a year, the true opportunity costs measure of the interest rate is indicated by the: a. annual percentage rate b. contract rate c. stated rate d. effective annual rate

D

Which of the following statements is false? a. The present value of a future sum decreases as the discount rate increases. b. If the present value of a sum is equal to its future value, the interest rate must be zero. c. If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series. d. For a given APR, the present value of a future sum decreases as the number of discounting periods per year decreases.

D

Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments. Calculate the loan balance at the end of the first year. (Pick the closest answer.) a. $8,934.24 b. $9,345 c. $8,018.91 d. $9,173.09

D ANNUAL PAYMENT: PV 10,500 N 6 I/Y 11 FV 0 → PMT = - $2,481.91 INTEREST PAID IN 1ST PAYMENT: 10,500(0.11) = $1,155 PRINCIPAL PAID IN 1ST PAYMENT: 2,481.91 - 1,155 = $1,326.91 LOAN BALANCE: 10,500 - 1,326.91 = $9,173.09

Megan is planning for her son's college education to begin five years from today. Megan estimates the yearly tuition, books, and living expenses to be $5,000 per year for a four-year degree. How much must Carol deposit today, at an interest rate of 8 percent, for her son to be able to withdraw $5,000 per year for four years of college? Pick the closest answer. a. $20,000 b. $13,620 c. $39,520 d. $12,173

D Money needed at the beginning of the first year of college: BGN PMT -5,000 N 4 1/Y 8 FV 0 → PV = $17,885.48 TODAY: FV 17,885.48 N 5 I/Y 8 → PV = $12,172.56 OR money needed today for: 1st TUITION: FV 5,000 N 5 I/Y 8 → PV = $3,402.92 2ND TUITION: FV 5,000 N 6 I/Y 8 → PV = $3,150.85 3RD TUITION: FV 5,000 N 7 I/Y 8 → PV = $2,917.45 4TH TUITION: FV 5,000 N 8 I/Y 8 → PV = $2,701.34 TOTAL $12,172.56

Lance deposits $2,000 per year at the end of the year for the next 15 years into an IRA account that currently pays 7%. How much will Lance have on deposit at the end of the 15 years? Pick the closest answer. a. $39,981 b. $46,753 c. $49,002 d. $50,258

D PMT -2,000 N 15 I/Y 7 PV 0 → FV = $50,258.04

The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is (Pick the closest answer.) a. $288 b. $1,896. c. $1,750. d. $1,558.

D PMT -350 N 5 I/Y 4 FV 0 → PV = $1,558.14

Lance plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If he can earn 12 percent on his contributions, how much will he have at the end of the twentieth year? Pick the closest answer. a. $19,292. b. $14,938. c. $40,000. d. $144,104.

D PV 0 PMT -2,000 N 20 I/Y 12 → FV = $144,104.88

What would be the future value of a CD of $1,000 for two years if the bank offered a 10% interest rate compounded semiannually? Pick the closest answer. a. $1,720 b. $1,960 c. $1,200 d. $1,216

D PV 1,000 N 4 I/Y 5 → FV = $1,215.51

Jonathan wishes to accumulate $1 million by making equal annual end-of-year deposits over the next 20 years. If he can earn 10 percent on his investments, how much must he deposit at the end of each year? Pick the closest answer. a. $14,900 b. $50,000 c. $117,453 d. $17,460

D FV 1,000,000 I/Y 10 N 20 PV 0 → PMT = -$17,459.62

Taylor owns stock in a company which has consistently paid a growing dividend over the last 10 years. At the end of the first year Taylor owned the stock, he received $4.50 per share and in the 10th year, he received $4.92 per share. What is the growth rate of the dividends during this time? Pick the closest answer. a. 8% b. 4% c. 2% d. 1%

D PV -4.50 FV 4.92 N 9 → I/Y = 1%

At very high interest rates the "Rule of 72" will result in a small estimation error for the estimate of the time for an investment to double.

F

Because interest compounds, the annual percentage rate formula will overstate the true interest cost of a loan.

F

For a given discount rate, an ordinary annuity and an annuity due have the same present value.

F

If the interest rate is 0% for 10 years, then the present value will be less than the future value.

F

Level cash flow amounts that occur at the end of each period, starting at the end of the first period, are an annuity due.

F

Simple interest is interest earned on the investment's principal and subsequently-earned interest.

F

The annual percentage rate (APR) overstates the true or effective interest cost.

F

The annual percentage rate is the true opportunity cost measure of the interest rate.

F

The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year.

F

The interest portion increases and the principal portion decreases over time under a typical loan amortization schedule.

F

With compound interest, interest is earned only on the investment's principal.

F

The present value of a $100 deposit in 10 years at 10% is $259.37.

F FV 100 N 10 I/Y 10 → PV = $38.55

The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $1,593.74 is 15%.

F PMT -100 FV 1,593.74 N 10 PV 0 → I/Y = 10%

The present value of a $100 ordinary annuity deposited for 10 years at 10% is $1,593.74.

F PMT 100 N 10 I/Y 10 FV 0 → PV = $614.46

It will take approximately 9.6 years for a $100 deposit to result in a future value of $600 if I can earn 10% on my deposit.

F PV -100 FV 600 I/Y 10 → N = 18.8 years

If I earn 3% on my deposit of $500, it will take 9 years before I have $550.

F PV -500 FV 550 I/Y → N = 3.22 years

The future value of a $100 ordinary annuity deposited for 10 years at 10% is $614.46.

F PV 0 PMT 100 N 10 I/Y 10 → FV = $1,593.74

The future value of a $100 deposit in 10 years at 10% compounded annually is $38.55.

F PV 100 N 10 I/Y 10 → FV = $259.37

As the interest rate increases, present value decreases.

T

At a zero interest rate, the present value of $1 remains at $1 and is not affected by time.

T

At very low interest rates, the "Rule of 72" does not approximate the compounding process well.

T

Compound interest is interest earned on interest in addition to interest earned on the principal.

T

Compounding means that interest earned each year, plus the principal, will be reinvested at the stated rate.

T

Discounting is an arithmetic process whereby a future sum decreases at a compounding interest rate over time to reach a present value.

T

For the same annual percentage rate, more frequent compounding increases the future value of an investor's funds more quickly.

T

If the compound inflation rate were greater than the compound interest rate, future purchasing power on our savings would fall.

T

Money has a time value so long as interest is earned by saving or investing money.

T

The Rule of 72 is an estimate of how long it would take to double a sum of money at a given interest rate.

T

The effective annual rate (EAR) is sometimes called the annual effective yield.

T

The effective annual rate (EAR) is the true opportunity cost measure of the interest rate.

T

The method of calculating the annual percentage rate (APR) is set by law.

T

When the annual interest rate stays the same, more frequent interest compounding helps savers earn more interest over the course of the year.

T

The present value of a $100 deposit in 10 years at 10% compounded annually is $38.55.

T FV 100 N 10 I/Y 10 → PV = $38.55

The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $1,593.74 is 10%.

T PMT -100 FV 1,593.74 N 10 PV 0 → I/Y = 10%

The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $614.46 is negative 11.45%.

T PMT -100 N 10 FV 614.46 PV 0 → I/Y = -11.45%

The present value of a $100 ordinary annuity deposited for 10 years at 10% is $614.46.

T PMT 100 N 10 I/Y 10 FV 0 → PV = $614.46

$1000 deposited in a bank that earns 7% per year will become approximately $7,600 in 30 years.

T PV -1,000 I/Y 7 N 3 → FV = $7,612.26

It will take approximately 18.8 years for a $100 deposit to grow to $600 if I can earn 10% on my deposit.

T PV -100 FV 600 I/Y 10 → N = 18.8 years

The return provided by $100 deposited for 10 years that results in a future value of $614.46 is 19.91%.

T PV -100 N 10 FV 614.46 → I/Y = -19.91%

The future value of a $100 ordinary annuity deposited for 10 years at 10% is $1,593.74.

T PV 0 PMT 100 N 10 I/Y 10 → FV = $1,593.74

The future value of a $100 deposit in 10 years at 10% compounded annually is $259.37.

T PV 100 N 10 I/Y 10 → FV = $259.37