Deck 6: Mathematics of Finance

Question 1

If you lend $3,500 to a friend for 19 months at 8% annual simple interest, find the future value of loan. Round your answer to the nearest cent. ​

A) $4,386.67
B) $8,820.00
C) $3,998.75
D) $3,943.33
E) $3,887.92

Answer 1

$3,943.33

Question 2

Write the fourth term of the sequence whose n^th term is ? ​

A)
B)
C)
D)
E)

Answer 2

Question 3

What is the present value of an investment at 15% annual simple interest if it is worth $924.50 in 6 months? Round your answer to the nearest cent. ​

A) $860.00
B) $870.00
C) $850.00
D) $914.50
E) $934.50

Answer 3

$860.00

Question 4

How long does it take for $6,000 invested at 9% annual simple interest to be worth $10,500? Round your answer to two decimal places. ​

A) 30.56 years
B) 83.33 years
C) 8.33 years
D) 4.76 years
E) 0.83 years

Question 5

What are the next three terms in the arithmetic sequence 7, 0, -7,...? ​

A) -14, -21, -28
B) 14, 21, 28
C) -7, -14, -21
D) -7, 21, -28
E) 7, 14, 28

Question 6

Find I: . ​ ​

A) $1,026
B) $1,197
C) $855
D) $342
E) $1,140

Question 7

Andre De Quadros bought a $2,000, 9-month certificate of deposit (CD) that would earn 8.5% annual simple interest. What is the value of the CD when it matures? Round your answer to to the nearest cent. ​

A) $2,042.50
B) $2,085.00
C) $2,170.00
D) $2,113.33
E) $2,127.50

Question 8

Find the 63th term of the arithmetic sequence with first term 25 and tenth term 61. ​

A) 285
B) 281
C) 269
D) 277
E) 273

Question 9

An investor owns several apartment buildings. The taxes on these buildings total $2,000 per year and are due before April 1. The late fee is 0.5% per month up to 6 months, at which time the buildings are seized by the authorities and sold for back taxes. If the investor has $2,000 available on March 31, how much money will he save by investing the money at 9% and paying the taxes and the penalty on September 30 instead of paying the taxes at that time? Round your answer to the nearest cent. ​

A) $120.00
B) $84.00
C) $30.00
D) $75.00
E) $48.00

Question 10

What does the number 0.06 represent in the given equation: . ​

A) annual interest rate
B) interest
C) future value
D) time
E) principal

Question 11

What are d and a₁ in the following arithmetic sequence? ​
5, 10, 15,...
​

A)
B)
C)
D)
E)

Question 12

A student has a savings account earning 8% simple interest. She must pay $1,400 for first-semester tuition by September 1 and $1,400 for second-semester tuition by January 1. How much must she earn in the summer (by September 1) in order to pay the first-semester bill on time and still have the remainder of her summer earnings grow to $1,400 between September 1 and January 1? Round your answer to two decimal places. ​

A) $2,781.58
B) $2,772.55
C) $2,763.64
D) $2,746.15
E) $2,784.18

Question 13

What is the fifth term of the sequence whose n^th term is ? ​

A)
B)
C)
D)
E)

Question 14

$3,000 is invested for 15 months at an annual simple interest rate of 12%. How much interest will be earned? Round your answer to the nearest dollar. ​

A) $4,503
B) $5,400
C) $450
D) $397
E) $543

Question 15

Leah Hagel bought a $4,000, 9-month certificate of deposit (CD) that would earn 7% annual simple interest. Three months before the CD was due to mature, Leah needed her CD money, so a friend agreed to lend her money and receive the value of the CD when it matured. If their agreement allowed the friend to earn a 11% annual simple interest return on her loan to Leah, how much did Leah receive from her friend? Round your answer to the nearest cent. ​

A) $4,325.78
B) $4,061.09
C) $3,990.52
D) $4,171.76
E) $3,922.36

Question 16

If you borrow $1,400 for 6 years at 7% annual simple interest, how much must you repay at the end of the 3 years? Round your answer to the nearest dollar. ​

A) $2,114
B) $7,280
C) $1,890
D) $2,086
E) $1,988

Question 17

What does the number 260 represent in the given equation: ? ​

A) principal
B) interest
C) future value
D) time
E) annual interest rate

Question 18

Find the 41th term of the arithmetic sequence with first term and common difference . ​

A)
B)
C)
D)
E)

Question 19

Suppose that in order to buy a Treasury bill (T-bill) that matures to $10,000 in 10 months, you must pay $9,750. What rate does this earn? Round your answer to one decimal place. ​

A) 4.3%
B) 1.8%
C) 3.7%
D) 2.5%
E) 3.1%

Question 20

Jenny Reed bought SSX stock for $15 per share. The annual dividend was $1.50 per share, and after 2 year(s), SSX was selling for $38 per share. Find the simple interest rate of growth of her money to the nearest hundredth of a percent. Round your answer to two decimal places. ​

A) 8.67%
B) 76.67%
C) 34.21%
D) 86.67%
E) 186.67%

Question 21

Suppose an employee has a base salary of $23,000 per year and at the end of each year a raise of $1,000 will be given. Find the employee's total income after the first 3 years. ​

A) $144,000
B) $72,000
C) $73,500
D) $37,500
E) $24,000

Question 22

Suppose an individual wants to have $160,000 available for her child's education. Find the amount that would have to be invested at annual rate 7%, compounded continuously, if the number of years until college is 10 years. Round your answer to the nearest cent. ​

A) $73,508.13
B) $66,697.92
C) $79,453.65
D) $58,860.71
E) $89,285.62

Question 23

If $8,000 is invested at an annual rate of 7.5% compounded continuously, find the future value after 7.5 years. Round your answer to the nearest cent. ​

A) $17,868.03
B) $16,160.44
C) $24,641.73
D) $14,040.44
E) $2,218,178.28

Question 24

Find the future value if $4200 is invested for 2 years at an annual rate of 11% compounded quarterly. Round your answer to the nearest cent. ​

A) $4,681.41
B) $4,434.18
C) $5,508.93
D) $5,816.09
E) $5,218.00

Question 25

What does the number 0.004 represent in the given equation: ? ​

A) number of periods
B) future value
C) principal value
D) periodic rate
E) none of these choices

Question 26

What lump sum should be deposited in an account that will earn at an annual rate of 7%, compounded quarterly, to grow to $90,000 for retirement in 20 years? Round your answer to the nearest cent. ​

A) $29,594.17
B) $5,741.36
C) $44,828.96
D) $14,219.12
E) $22,464.10

Question 27

If $11,000 had been invested in the Fictious Fund on June 30, 1991, then on June 30, 2000 the investment would have been worth $34,575.25. What interest rate compounded annually would this investment have earned? Round your answer to two decimal places. ​

A) 27.14%
B) 13.57%
C) 11.27%
D) 15.33%
E) 6.79%

Question 28

What interest will be earned if $5,800 is invested for 2 years at an annual rate of 9% compounded monthly? Round your answer to the nearest cent. ​

A) $7,586.35
B) $6,635.80
C) $7,191.44
D) $6,939.20
E) $45,884.28

Question 29

Find the interest that will result if $10,500 is invested at an annual rate of 9%, compounded continuously, for 12 years. Round your answer to the nearest cent. ​

A) $20,419.14
B) $30,919.14
C) $41,419.14
D) $30,002.97
E) $38,618.34

Question 30

Find the sum of the first 62 terms of the arithmetic sequence with first term 9 and 62​^th term 229. ​

A) 7,378
B) 7,735
C) 7,140
D) 8,568
E) 6,545

Question 31

Find S: . Round your answer to the nearest cent. ​

A) $7,394.15
B) $1,173.17
C) $4,730.70
D) $3,000.00
E) $1,885.04

Question 32

To help their son buy a car on his 16th birthday, a boy's parents invest $800 on his 11th birthday. If the investment pays an annual rate of 11% compounded continuously, how much is available on his 16th birthday? Round your answer to the nearest cent. ​

A) $1,154.33
B) $1,386.60
C) $1,265.15
D) $1,590.99
E) $2,000.75

Question 33

How much more interest will be earned if $7,500 is invested for 7 years at an annual rate of 12% compounded continuously, instead of at 12% compounded quarterly? Round your answer to the nearest cent. ​

A) $17,372.75
B) $2,802.74
C) $213.29
D) $4,315.07
E) $5,301.40

Question 34

Rank each interest rate and compounding scheme in order from highest yield to lowest yield. ​

A) 6.5% compounded semi-annually, 6.5% compounded monthly, 6.5% compounded continuously
B) 6.5% compounded monthly, 6.5% compounded continuously, 6.5% compounded semi-annually
C) 6.5% compounded continuously, 6.5% compounded semi-annually, 6.5% compounded monthly
D) 6.5% compounded continuously, 6.5% compounded monthly, 6.5% compounded semi-annually
E) 6.5% compounded semi-annually, 6.5% compounded continuously, 6.5% compounded monthly

Question 35

A new firm loses $1,600 in its first month, but its profit increases by $400 in each succeeding month for the rest of its first year. What is its profit in the twelfth month? ​

A) $6,800
B) $2,800
C) $3,200
D) $6,000
E) $4,400

Question 36

Find the sum of the first 208 terms of the arithmetic sequence 12, 10, 8,... ​

A) -39,520
B) -42,640
C) -40,560
D) -37,440
E) -44,720

Question 37

Suppose you are offered a job paying a starting salary of $23,000 with yearly raises of $1,300. How much will you receive for your 10th year on the job? ​

A) $37,300
B) $34,700
C) $32,100
D) $36,000
E) $36,100

Question 38

How long (in years) would $700 have to be invested at an annual rate of 11%, compounded continuously, to amount to $1,376? Round your answer to two decimal places. ​

A) 7.37 years
B) 6.76 years
C) 7.99 year
D) 3.69 years
E) 6.14 years

Question 39

What is the annual percentage yield (or effective annual rate) for a nominal rate of 12% compounded continuously? Round your answer to two decimal places. ​

A) 16.18%
B) 12.75%
C) 11.53%
D) 14.26%
E) 18.70%

Question 40

What is the annual percentage yield (or effective annual rate) for a nominal rate of 8% compounded quarterly? Round your answer to two decimal places. ​

A) 11.1%
B) 6.56%
C) 8.54%
D) 8.24%
E) 9.64%

Question 41

Suppose that Bob delays starting an IRA for the first 10 years he works but then makes $2,000 deposits at the end of each of the next 15 years. If the annual interest rate is 8%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? Round your answer to the nearest cent. ​

A) $79,790.73
B) $73,880.30
C) $68,407.69
D) $63,340.45
E) $93,067.90

Question 42

If inflation causes the cost of automobiles to increase by 3.5% each year, what should a car cost today if it cost $21,000 4 years ago? Round your answer to the nearest cent. ​

A) $25,525.63
B) $24,923.28
C) $24,462.21
D) $24,097.98
E) $23,803.02

Question 43

Suppose a new business makes a $2,000 profit in its first month and has its profit increase by 14% each month for the next 2 years. How much profit will the business earn in its 13^th month? Round your answer to the nearest cent. ​

A) $10,984.82
B) $9,635.81
C) $12,522.70
D) $8,452.46
E) $2,280.00

Question 44

Find the next three terms of the geometric sequence. ​
25, 5, 1,...
​

A) 0.2, 0.04, 0.008,...
B) 0.125, 1, 0.015625,...
C) 0.125, 0.015625, 0.001953125,...
D) 64, 1, 0.001953125,...
E) 1, 0.2, 0.04,...

Question 45

Emily Rideout deposits $2,000 at the end of each of the 5 years she qualifies for an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an annual interest rate of 8.1%, compounded annually. Round your answer to the nearest cent. ​

A) $17,354.45
B) $82,399.55
C) $458,820.59
D) $293,915.51
E) $12,708.91

Question 46

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 9% each month for the next 2 years. How much profit will it earn in its first year? Round your answer to the nearest cent. ​

A) $2,014.07
B) $7,523.33
C) $40,281.44
D) $20,140.72
E) $76,789.81

Question 47

How long does it take for an account containing $5,500 to be worth $13,600 if the money is invested at 12% compounded monthly? Round your answer to the one decimal place. ​

A) 8.8 years
B) 6.3 years
C) 7.6 years
D) 8.2 years
E) 9.5 years

Question 48

Suppose Emily Yu deposited $1,400 in an account that earned simple interest at an annual rate of 10% and left it there for 3 years. At the end of the 3 years, Emily deposited the entire amount from that account into a new account that earned 10% compounded quarterly. She left the money in this account for 8 years. How much did she have after the 11 years? Round your answer to the nearest cent. ​

A) $4,010.84
B) $5,197.15
C) $3,429.86
D) $3,088.77
E) $8,672.19

Question 49

Write an expression that gives the requested term or sum. ​
The sum of the first 12 terms of the geometric sequence with first term 6 and common ratio 7.
​

A)
B)
C)
D)
E)

Question 50

What is the 7th term of the geometric sequence with first term 5 and common ratio 2? ​

A) 5
B) 160
C) 3,645
D) 640
E) 320

Question 51

Find the next three terms of the geometric sequence. ​
3, 9, 27,...
​

A) 4, 12, 36,...
B) 81, 243, 729,...
C) 108, 324, 972,...
D) 27, 81, 243,...
E) 108, 243, 729,...

Question 52

Find the future value of an annuity due of $1,700 each month for 4 years if the annual interest rate is 11%, compounded monthly. Round your answer to the nearest cent. ​

A) $21,657.31
B) $63,463.93
C) $136,419.89
D) $82,443.20
E) $102,859.77

Question 53

Find S : . Round your answer to the nearest dollar. ​

A) S = $1,666,521
B) S = $104,158
C) ​S = $8,333
D) S = $416,630
E) S = $599,280

Question 54

A pump removes of the water in a container with every stroke. How much water remains in the container after 3 strokes if it originally contained 36 cm³? ​

A)
B)
C)
D)
E)

Question 55

Find the future value of an ordinary annuity of $67 paid quarterly for 4 years, if the interest rate is 6%, compounded quarterly. Round your answer to the nearest cent. ​

A) $1,350.51
B) $1,201.47
C) $1,248.83
D) $5,668.14
E) $300.37

Question 56

What does 040 represent in the following equation? ​ ​

A) future value of the annuity
B) total number of payments(periods)
C) interest rate per period
D) interest rate per year
E) none of these choices

Question 57

Which of the following expresses the sum of the first 27 terms of the geometric sequence 9, -6, 4....? ​

A)
B)
C)
D)
E)

Question 58

A sinking fund is established to discharge a debt of $70,000 in 8 years. If deposits are made at the end of each 6-month period and interest is paid at the annual rate of 6%, compounded semiannually, what is the amount of each deposit? Round your answer to the nearest cent. ​

A) $806.23
B) $1,308.65
C) $3,472.76
D) $582.57
E) $374.69

Question 59

If a population of 6 million begins to increase at a rate of 0.2% each month, in how many months will it be 9 million? Round your answer to two decimal places. ​

A) 243.48 months
B) 304.30 months
C) 202.94 months
D) 263.76 months
E) 101.57 months,

Question 60

If $6,000 is deposited at the end of each half year in an account that earns an annual rate of 6.3% compounded semiannually, how long will it be before the account contains $170,000? Round your answer to two decimal places. ​

A) 8.83 half years
B) 51.19 half years
C) 43.82 half years
D) 34.25 half years
E) 20.57 half years

Question 61

Find A_n: . Round your answer to the nearest dollar. ​

A) $86,002
B) $141,632
C) $99,394
D) $110,638
E) $108,647

Question 62

State whether the problem relates to an ordinary annuity or an annuity due. A couple has determined that they need $400,000 to establish an annuity when they retire in 25 years. How much money should they deposit at the end of each month in an investment plan that pays an annual rate of 8%, compounded monthly, so they will have the $400,000 in 25 years? ​

A) ordinary annuity
B) annuity due

Question 63

A small business owner contributes $7,000 at the end of each quarter to a retirement account that earns an annual rate of 7.5% compounded quarterly. Suppose when the account reaches $500,000, the business owner increases the contributions to $9,000 at the end of each quarter. What will the total value of the account be after 13 more years since when the account reached? Round your answer to the nearest cent. ​

A) $2,875,916.87
B) $3,408,463.68
C) $2,094,793.51
D) $1,313,670.16
E) $781,123.35

Question 64

What does 050 represent in the following equation? ​ ​

A) present value of the annuity
B) total number of payments(periods)
C) interest rate per period
D) future value of the annuity
E) interest rate per year

Question 65

If $3,000 is deposited at the beginning of each quarter into an account that earns 6% compounded quarterly, how long until the account contains $42,000? Express your answer as a whole number of quadrants. ​

A) 14 quarters
B) 13 quarters
C) 15 quarters
D) 16 quarters
E) 10 quarters

Question 66

What is the size of the payments that must be deposited at the beginning of each 6-month period in an account that pays an annual rate of 8%, compounded semiannually, so that the account will have a future value of $110,000 at the end of 11 years? Round your answer to the nearest cent. ​

A) $17,573.48
B) $7,842.69
C) $916.44
D) $3,088.34
E) $1,597.49

Question 67

A family wants to have a $160,000 college fund for their children at the end of 16 years. What contribution must be made at the end of each quarter if their investment pays an annual rate of 6.6%, compounded quarterly? Round your answer to the nearest cent. ​

A) $976.58
B) $8,819.82
C) $3,835.83
D) $1,426.89
E) $2,211.82

Question 68

Parents agree to invest $800 (at an annual rate of 8%, compounded semiannually) for their son on the December 31 or June 30 following each semester that he makes the Dean's List during his 4 years in college. If he makes the Dean's List in each of the 8 semesters, how much money will his parents have to give him when he graduates? Round your answer to the nearest cent. ​

A) $3,397.17
B) $9,604.89
C) $7,371.38
D) $2,497.28
E) $5,306.38

Question 69

State whether the problem relates to an ordinary annuity or an annuity due. A property owner has several rental units and wants to build more. How much of each month's rental income should be deposited at the beginning of each month in an account that earns an annual rate of 6.9%, compounded monthly, if the goal is to have $200,000 at the end of 7 years? ​

A) ordinary annuity
B) annuity due

Question 70

A house is rented for $3,700 per quarter, with each quarter's rent payable in advance. If money is worth 6%, compounded quarterly, and the rent is deposited in an account, what is the future value of the rent for two years? Round your answer to the nearest cent. ​

A) $20,437.99
B) $146,482.53
C) $65,803.29
D) $42,342.65
E) $31,201.50

Question 71

State whether the problem relates to an ordinary annuity or an annuity due. Mr. Gordon plans to invest $500 at the end of each month in an account that pays an annual rate of 9%, compounded monthly. After how many months will the account be worth $60,000? ​

A) ordinary annuity
B) annuity due

Question 72

A couple has determined that they need $400,000 to establish an annuity when they retire in 20 years. How much money should they deposit at the end of each month in an investment plan that pays an annual rate of 8%, compounded monthly, so they will have the $400,000 in 20 years? Round your answer to the nearest cent. ​

A) $2,186.44
B) $679.09
C) $960.30
D) $18,762.78
E) $8,758.96

Question 73

Mr. Alphin plans to invest $350 at the end of each month in an account that pays an annual rate of 9%, compounded monthly. After how many months will the account be worth $50,000? Round your answer to two decimal places. ​

A) 192.52 months
B) 57.41 months
C) 222.83 months
D) 153.26 months
E) 97.46 months

Question 74

A small business owner contributes $5,000 at the end of each quarter to a retirement account that earns an annual rate of 6% compounded quarterly. How long will it be until the account is worth $150,000? ​

A) 24.96 quarters
B) 43.11 quarters
C) 57.39 quarters
D) 69.15 quarters
E) 13.63 quarters

Question 75

A property owner has several rental units and wants to build more. How much of each month's rental income should be deposited at the beginning of each month in an account that earns an annual rate of 7.9%, compounded monthly, if the goal is to have $300,000 at the end of 5 years? Round your answer to the nearest cent. ​

A) $9,018.39
B) $4,066.80
C) $5,052.86
D) $6,537.27
E) $3,365.48

Question 76

Suppose a young couple deposits $1,100 at the end of each quarter in an account that earns an annual rate of 8.8%, compounded quarterly, for a period of 6 years. After the 6 years, they start a family and find they can contribute only $300 per quarter. If they leave the money from the first 6 years in the account and continue to contribute $300 at the end of each quarter for the next years, how much will they have in the account (to help with their child's college expenses)? Round your answer to the nearest cent. ​

A) $171,621.52
B) $226,229.22
C) $54,607.70
D) $280,836.92
E) $397,850.74

Question 77

A young executive deposits $200 at the end of each month for 5 years and then increases the deposits. If the account earns an annual rate of 8.1%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total of $300,000 after 17 years from the time the deposits were increased? Round your answer to the nearest cent. ​

A) $367.97
B) $1,952.64
C) $1,286.64
D) $900.55
E) $653.90

Question 78

State whether the problem relates to an ordinary annuity or an annuity due. Jane Adele deposits $600 in an account at the beginning of each 3-month period for 10 years. If the account pays interest at the annual rate of 6%, compounded quarterly, how much will she have in her account after 10 years? ​

A) ordinary annuity
B) annuity due

Question 79

Gail Kelley deposits $600 in an account at the beginning of each 3-month period for 8 years. If the account pays interest at the annual rate of 7%, compounded quarterly, how much will she have in her account after 8 years? Round your answer to the nearest cent. ​

A) $18,016.48
B) $57,281.19
C) $25,892.65
D) $34,941.44
E) $45,337.43

Question 80

How much is needed in an account that earns an annual rate of 8.4% compounded monthly in order to withdraw $1,200 at the end of each month for 22 years? Round your answer to the nearest cent. ​

A) $103,164.36
B) $156,715.29
C) $151,429.66
D) $144,245.22
E) $134,479.83