Deck 11: The Nature of Sequences, Series, and Financial Management

Question 1

A lottery offers you a choice of $1,000,000 per year for 6 years or a lump-sum payment. What lump-sum payment (rounded to the nearest dollar) would equal the annual payments if the current interest rate is 13% compounded annually? ​

A) $3,998,440
B) $3,997,550
C) $3,988,144
D) $4,517,231
E) $4,006,956

Answer 1

$3,997,550

Question 2

State the type and answer the question. What annual deposit is necessary to have $15,000 in 5 years if all the money is deposited at 13% interest compounded annually? ​

A) Sinking fund; $2,303.83
B) Amortization; $2,314.72
C) Present value; $2,320.72
D) Sinking fund; $2,314.72
E) Future value; $2,325.61

Answer 2

Sinking fund; $2,314.72

Question 3

If $3,000 is compounded annually at 6.5% for 15 years, what is the future value?
​
Please round the answer to the nearest cent.
​
$ __________

Answer 3

7,715.52

Question 4

State the type and answer the question. What annual deposit is necessary to have $15,000 in 6 years if all the money is deposited at 9% interest compounded annually?
​
Please round the answer to the nearest cent.
​
The type is __________ (present value, future value, sinking fund); annual deposit equals $__________.

Question 5

Consider the 35-year fixed-rate home loan of $185,000 with an interest rate of 7.25%. What is the total amount of interest paid? ​

A) $325,075.05
B) $328,785.75
C) $325,080.55
D) $325,073.04
E) $325,077.06

Question 6

A lottery offers you a choice of $1,000,000 per year for 7 years or a lump-sum payment. What lump-sum payment (rounded to the nearest dollar) would equal the annual payments if the current interest rate is 12% compounded annually?
​
$ __________

Question 7

What is the monthly payment for a home costing $125,000 with a 20% down payment and the balance financed for 25 years at 10%? ​

A) Amortization; $908.70
B) Present value; $897.39
C) Present value; $910.70
D) Present value; $1,166.67
E) Sinking fund; $920.01

Question 8

Consider the 30-year fixed-rate home loan of $182,000 with an interest rate of 7.25%. What is the total amount of interest paid?
​
Please round the answer to the nearest cent.
​
$ __________

Question 9

Use a calculator to evaluate the present value of an annuity formula for the values of the variables m = $50, r = 7%, n = 12, and t = 7 years. ​ ​

A) $3,233.57
B) $3,311.86
C) $3,309.86
D) $3,312.86
E) $3,325.18

Question 10

Major Magic Corporation deposits $1,500 at the end of each month into an account paying 15% interest compounded monthly. What is the value of the account at the end of years?
​
Please round the answer to the nearest cent.
​
$ __________

Question 11

Use a calculator to evaluate the amortization formula for the values of the variables P = $16,000, r = 9%, n = 12, and t = 5 years. ​ ​

A) $330.13
B) $332.13
C) $344.45
D) $333.13
E) $342.79

Question 12

Major Magic Corporation deposits $1,500 at the end of each month into an account paying 19% interest compounded monthly. What is the value of the account at the end of years? ​

A) $282,744.37
B) $282,731.34
C) $282,757.40
D) $337,533.26
E) $320,145.67

Question 13

Consider the 20-year fixed-rate home loan of $186,000 with an interest rate of 7.75%. What is the monthly payment?
​
Please round the answer to the nearest cent.
​
$ __________

Question 14

Consider the 35-year fixed-rate home loan of $184,500 with an interest rate of 7.75%. What is the monthly payment? ​

A) $1,263.51
B) $1,290.61
C) $1,277.06
D) $1,266.56
E) $1,285.88

Question 15

For 6 years, Thompson Cleaners deposits $900 at the end of each quarter into an account paying 10% compounded quarterly. What is the value of the account at the end of 6 years?
​
Please round the answer to the nearest cent.
​
$ __________

Question 16

If $3,000 is compounded annually at 6.5% for 15 years, what is the future value? ​

A) $5,925.00
B) $7,724.02
C) $7,720.47
D) $7,710.57
E) $7,715.52

Question 17

For 7 years, Thompson Cleaners deposits $800 at the end of each quarter into an account paying 8% compounded quarterly. What is the value of the account at the end of 7 years? ​

A) $29,654.32
B) $29,627.62
C) $28,552.97
D) $29,632.97
E) $29,640.97

Question 18

Find the value of a $1,000 certificate in 3 years, if the interest rate is 14% compounded annually.
​
Please round the answer to the nearest cent.
​
$ __________

Question 19

State the type and answer the question. What is the monthly payment for a home costing $125,000 with a 20% down payment and the balance financed for 25 years at 10%?
​
Please round the answer to the nearest cent.
​
The type is __________ (present value, amortization, annuity); the monthly payment equals $__________.

Question 20

Find the value of a $3,000 certificate in 3 years, if the interest rate is 15% compounded annually. ​

A) $4,350.00
B) $4,554.84
C) $4,556.63
D) $4,570.42
E) $4,562.63

Question 21

Find the monthly payment for the loan.
​
Finance $550,000 for an apartment complex with a 14.2% 25-year loan
​
Please round the answer to the nearest cent.
​
$ __________

Question 22

Find the value of the annuity at the end of the indicated number of years. Assume that the interest is compounded with the same frequency as the deposit. ​

A) $77,717.44
B) $76,123.47
C) $76,691.15
D) $78,069.56
E) $57,068.70

Question 23

Find the monthly payment for the loan. ​
Finance $650,000 for an apartment complex with a 9.6% 15-year loan
​

A) $6,703.54
B) $6,813.74
C) $6,776.74
D) $6,826.74
E) $5,200.00

Question 24

As the interest rate increases, determine either the amount increases or decreases. Assume that all other variables remain constant. ​
Monthly value for a sinking fund
​

A) decreases
B) increases
C) remains the same

Question 25

Use a calculator to evaluate an ordinary annuity formula for m = $90, r = 7%, and t = 5 yr. Assume monthly payments. ​ ​

A) $6,210.80
B) $7,821.77
C) $7,011.04
D) $6,443.36
E) $7,469.65

Question 26

Find the monthly payment for the loan.
​
Used-car financing of $3,200 for 33 months at 15%.
​
Please round the answer to the nearest cent.
​
$ __________

Question 27

Find the amount of monthly payment necessary for the deposit to a sinking fund. ​

A) $4,889.15
B) $2,275.01
C) $2,627.13
D) $3,085.74
E) $3,653.42

Question 28

Use a calculator to evaluate the amortization formula for the values of the variables ​P​ = $260,000, ​r​ = 9%, ​n​ = 12, and ​t​ = 15 years.
​ ​
Please round the answer to the nearest cent.
​
$ __________

Question 29

As the interest rate increases, determine whether the amount increases, decreases or remains the same. Assume that all other variables remain constant.
​
Monthly value for a sinking fund __________ (decreases, increases, remains the same).

Question 30

A $500,000 lottery prize pays $25,000 per year for the next 20 years. If the current rate of return is 8.75%, what is the present value of this prize?
​
Please round the answer to the nearest cent.
​
$ __________

Question 31

Use a calculator to evaluate the present value of an annuity formula for the values of the variables ​m ​= $150, ​r​ = 7%, ​n​ = 12, and ​t​ = 5 years.
​ ​
Please round the answer to the nearest cent.
​
$ __________

Question 32

A $300,000 lottery prize pays $30,000 per year for the next 10 years. If the current rate of return is 8.25%, what is the present value of this prize? ​

A) $198,928.92
B) $211,595.49
C) $215,473.92
D) $199,007.12
E) $199,052.12

Question 33

Suppose your gross monthly income is $5,000 and your current monthly payments are $525. If the bank will allow you to pay up to 50% of your gross monthly income (less current monthly payments) for a monthly house payment, what is the maximum loan you can obtain if the rate for a 25-year mortgage is 12%?
​
Please round the answer to the nearest cent.
​
$ __________

Question 34

Use a calculator to evaluate the amortization formula for the values of the variables P = $25,000, r = 8%, n = 12, and t = 15 years. ​ ​

A) $238.91
B) $166.67
C) $236.91
D) $234.91
E) $251.23

Question 35

Find the monthly payment for the loan. ​
Used-car financing of $2,500 for 15 months at 8%
​

A) $176.61
B) $170.81
C) $175.69
D) $182.91
E) $163.37

Question 36

Suppose your gross monthly income is $6,500 and your current monthly payments are $525. If the bank will allow you to pay up to 38% of your gross monthly income (less current monthly payments) for a monthly house payment, what is the maximum loan you can obtain if the rate for a 25-year mortgage is 8.65%? ​

A) $278,588.99
B) $281,481.35
C) $275,178.79
D) $278,465.79
E) $278,454.79

Question 37

Find the value of the annuity at the end of the indicated number of years. Assume that the interest is compounded with the same frequency as the deposit. ​

A) $31,101.10
B) $94,380.67
C) $14,621.19
D) $29,507.13
E) $30,533.42

Question 38

Use a calculator to evaluate the amortization formula for the values of the variables ​P​ = $9,000, ​r​ = 8%, ​n​ = 12, and ​t​ = 27 years.
​ ​
Please round the answer to the nearest cent.
​
$ __________

Question 39

Find the value of the annuity at the end of the indicated number of years. Assume that the interest is compounded with the same frequency as the deposit. ​

A) $133,577.37
B) $10,232.02
C) $11,258.31
D) $11,610.43
E) $9,664.34

Question 40

Find the amount of monthly payment necessary for the deposit to a sinking fund. ​

A) $2,245.94
B) $651.97
C) $591.36
D) $1,219.65
E) $2,598.06

Question 41

Find the value of the annuity at the end of the indicated number of years. Assume that the interest is compounded with the same frequency as the deposit.
​ ​
Please round the answer to the nearest cent.
$ __________

Question 42

A business must raise $41,000 in 7 years. What should be the size of the owners' quarterly payment to a sinking fund paying 4% compounded quarterly?
​
Please round the answer to the nearest cent.
​
$ __________

Question 43

Evaluate the expression. ​ ​

A) 352
B) 564
C) 109
D) 455
E) 91

Question 44

John and Rosamond want to retire in 6 years and can save $190 every three months. They plan to deposit the money at the end of each quarter into an account paying 6.48% compounded quarterly. How much will they have at the end of 6 years? ​

A) $5,519.62
B) $4,951.94
C) $4,126.48
D) $4,141.21
E) $6,545.91

Question 45

Find S ₄ when ​ ​

A) S ₄ = 36
B) S ₄ = 24
C) S ₄ = 6
D) S ₄ = 12
E) S ₄ = 0

Question 46

Evaluate the expression. ​ ​

A) 1
B) 17
C) 0
D) 14
E) 16

Question 47

Use a calculator to evaluate an ordinary annuity formula for , r = , and yr. Assume monthly payments.
​ ​
Please round the answer to the nearest cent.
​
$ __________

Question 48

Evaluate the expression. ​ ​

A) 63
B) 19
C) 21
D) 2
E) 91

Question 49

The owner of Sebastopol Tree Farm deposits $450 at the end of each quarter into an account paying 7% compounded quarterly. What is the value of the account at the end of 6 years? ​

A) $9,925.12
B) $13,279.96
C) $14,306.25
D) $13,847.64
E) $14,658.37

Question 50

Find S ₅ when ​ ​

A) S ₅ = 4
B) S ₅ = 6,168
C) S ₅ = 6,144
D) S ₅ = 8,184
E) S ₅ = 6

Question 51

Find the amount of periodic payment necessary for the deposit to a sinking fund.
​ ​
Please round the answer to the nearest cent.
$ __________

Question 52

You want to retire at age 65. You decide to make a deposit to yourself at the end of each year into an account paying 11%, compounded annually. Assuming you are now 25 and can spare $1,100 per year, how much will you have when you retire at age 65? ​

A) $690,965.35
B) $453,330.26
C) $711,509.63
D) $757,034.96
E) $640,008.67

Question 53

A business must raise $57,000 in 5 years. What should be the size of the owners' quarterly payment to a sinking fund paying 8% compounded quarterly? ​

A) $2,345.93
B) $3,140.32
C) $3,372.22
D) $2,913.61
E) $967.52

Question 54

Find the amount of periodic payment necessary for the deposit to a sinking fund.
​ Please round the answer to the nearest cent.
$ __________

Question 55

Find the value of the annuity at the end of the indicated number of years. Assume that the interest is compounded with the same frequency as the deposit.
​ ​
Please round the answer to the nearest cent.
$ __________

Question 56

John and Rosamond want to retire in 8 years and can save $230 every three months. They plan to deposit the money at the end of each quarter into an account paying 7.42% compounded quarterly. How much will they have at the end of 8 years?
​
Please round the answer to the nearest cent.
​
$ __________

Question 57

If possible, find the sum of the infinite geometric series. ​ ​

A) 240
B) 120
C) 480
D) 60
E) not possible

Question 58

You want to retire at age 65. You decide to make a deposit to yourself at the end of each year into an account paying 11%, compounded annually. Assuming you are now 29 and can spare $1,600 per year, how much will you have when you retire at age 65?
​
Please round the answer to the nearest cent.
​
$ __________

Question 59

The owner of Sebastopol Tree Farm deposits $400 at the end of each quarter into an account paying 5% compounded quarterly. What is the value of the account at the end of 9 years?
​
Please round the answer to the nearest cent.
​
$ __________

Question 60

Find the value of the annuity at the end of the indicated number of years. Assume that the interest is compounded with the same frequency as the deposit.
​ Please round the answer to the nearest cent.
$ __________

Question 61

Find the sum of the infinite geometric series.
​

Question 62

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​
27, 64, 125, 216, ...
​

A) Geometric and a ₅ = 1,728
B) None and a ₅ = 343
C) Geometric and a ₅ = 648
D) Fibonacci and a ₅ = 341
E) Arithmetic and a ₅ = 219

Question 63

Find the sum of the even integers between 51 and 99. ​

A) 1,800
B) 3,675
C) 1,725
D) 3,900
E) 3,600

Question 64

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​
1, 6, 7, 13, ...
​

A) None and a₅ = 97
B) Geometric and a₅ = 78
C) Arithmetic and a₅ = 14
D) Arithmetic and a₅ = 19
E) Fibonacci and a₅ = 20

Question 65

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​
3, 4, 5, 6, ...
​

A) Fibonacci and a₅ = 11
B) Geometric and a₅ = 15
C) None and a₅ = 50
D) Arithmetic and a₅ = 7
E) Geometric and a₅ = 7

Question 66

A tennis ball is dropped from a height of 15 ft. If the ball rebounds of its height on each bounce, how far will the ball travel before coming to rest? ​​

A) 60 ft
B) 75 ft
C) 30 ft
D) 15 ft
E) 45 ft

Question 67

Evaluate the expression
​

Question 68

Find the sum of the first 19 positive integers.

Question 69

The game of pool uses 15 balls numbered from 1 to 15 (see the figure below). In the game of rotation, a player attempts to "sink" a ball in a pocket of the table and receives the number of points on the ball. Suppose we consider a game of "super pool", which has 19 consecutively numbered balls on the table. How many points would a player receive to "run the table"? ​ ​

A) 19
B) 420
C) 210
D) 190
E) 171

Question 70

A tennis ball is dropped from a height of 13 ft. If the ball rebounds of its height on each bounce, how far will the ball travel before coming to rest?
​
__________ ft

Question 71

Evaluate the expression.
​

Question 72

Find ​ when
​ ​ __________

Question 73

Find the sum of the even integers between 49 and 101.

Question 74

Find the first three terms of the sequence whose nth term is given. ​ ​

A) , ,
B) , ,
C) ​ , ,
D) , ,
E) , ,

Question 75

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​
3, 15, 75, 375, ...
​

A) Fibonacci and a₅ = 450
B) None and a₅ = 98
C) Arithmetic and a₅ = 380
D) Geometric and a₅ = 1,125
E) Geometric and a₅ = 1,875

Question 76

Find the first three terms of the sequence whose nth term is given. ​ ​

A) , ,
B) , ,
C) ​ , ,
D) ​ , ,
E) ​ , ,

Question 77

Find when
​ ​ __________

Question 78

The game of pool uses 15 balls numbered from 1 to 15 (see the figure below). In the game of rotation, a player attempts to "sink" a ball in a pocket of the table and receives the number of points on the ball. Suppose we consider a game of "super pool", which has 15 consecutively numbered balls on the table. How many points would a player receive to "run the table"?
​ ​
__________ points

Question 79

Evaluate the expression.
​

Question 80

Find the sum of the first 12 positive integers. ​

A) 156
B) 91
C) 82
D) 74
E) 78