Deck 12: Compound Interest and Present Value

Question 1

The number of periods in compounding is found by multiplying the number of years times the number of times compounded per year.

Answer 1

True

Question 2

The rate for a table lookup on a $4,000, 12% investment compounded quarterly for four years is 4%.

Answer 2

False

Question 3

Compounding results in earning higher interest than simple interest.

Answer 3

True

Question 4

Interest calculated on a balance every three months is said to be compounded quarterly.

Question 5

The interest on $3,000 at 8% compounded semiannually for six years by using the table lookup (use table in handbook)is $1,803.

Question 6

A compound table factor of 1.2950 means that $1 at a certain rate of interest for a certain period of time will increase in value to approximately $1.30.

Question 7

Compounding always requires the use of tables.

Question 8

The nominal rate is really the true rate.

Question 9

The table for the compound value of $1 has only table factors over $1.00.

Question 10

Compounding always reduces the principal.

Question 11

Compounding looks into the present when we know what we have in the future.

Question 12

The effective rate (APY)can be calculated by the interest for one year divided by the principal.

Question 13

The number of periods for a table lookup on $5,000 at 12% compounded semiannually for 10 years is 10 periods.

Question 14

Effective rates can be seen in the compounding table for one dollar.

Question 15

The annual rate a bank advertises is the same as the effective rate.

Question 16

Annual means compounded once a year.

Question 17

Compound value = $ amount divided by table factor.

Question 18

Interest = principal × rate divided by the time.

Question 19

The rate used in compounding is found by taking the annual rate divided by the number of times compounded per day.

Question 20

Using the table in the handbook, the table factor for compounding $4,000 at 9% compounded annually for one year is 1.0900.

Question 21

$100,000 for 20 years compounded at 4% annually results in a rate per period of:

A)3%
B)5%
C)4%
D)1%
E)None of these

Question 22

Using the interest for daily compounding (in your handbook), $700 would grow to $790 at the end of three years at 8% interest.

Question 23

The interest on $6,000 at 6% compounded semiannually for eight years is (use table in the handbook):

A)$3,628.20
B)$3,682.02
C)$362.82
D)$13,628.20
E)None of these

Question 24

Effective rate (APY)is:

A)Never related to compound table
B)Interest for one year divided by annual rate
C)Interest for one year divided by principal for two years
D)Interest for one year divided by principal
E)None of these

Question 25

Present value does not:

A)Know future amount
B)Know the present dollar amount
C)Find present dollar amount
D)Use tables
E)None of these

Question 26

Compounding interest daily is seldom used in comparison to compounding once a year.

Question 27

A table factor of 0.7312 from the present value table in this chapter means that a certain rate of interest for a certain period of time will equal:

A)$1
B)Over $1
C)Less than $1
D)Never equal
E)None of these

Question 28

The rate used in the table for calculating compound interest is found by:

A)Annual rate × number of periods
B)Annual rate × number of times compounded per year
C)Annual rate divided by number of times compounded per year
D)Annual rate divided semiannually
E)None of these

Question 29

$14,182 is the present value of $21,000 that earns at a bank 12% compounded quarterly for four years. (Use table in handbook.)

Question 30

Using the table in the handbook, the present value of $12,000 for six years compounded at 6% semiannually is:

A)$12,814.08
B)$8,461.08
C)$8,416.80
D)$8,614.80
E)None of these

Question 31

$20,000 for 14 years compounded at 8% semiannually results in how many periods?

A)64
B)28
C)12
D)14
E)None of these

Question 32

The effective rate (APY)is:

A)The nominal rate
B)The stated rate
C)The true semiannual rate
D)The true annual rate
E)None of these

Question 33

A table factor of 0.7513 from a present value table means that if $.75 is invested at a certain rate of interest for a certain number of periods, it would be worth $1 in the past.

Question 34

Compounding:

A)Calculates interest periodically
B)Looks into the present when the future is known
C)Is done only on an annual basis
D)Results in less interest than simple interest
E)None of these

Question 35

The compound table can be used to prove a present value calculation.

Question 36

In the table of present value of one dollar, all table factors are less than $1.

Question 37

Using the table in handbook, the value of $60 deposited in a bank for six years at a rate of 10% compounded annually is:

A)$96.63
B)$96.36
C)$106.30
D)$106.03
E)None of these

Question 38

In tables for calculating compound interest, the number of periods is equal to:

A)Number of years divided by rate
B)Number of years × rate
C)Number of years × number of times compounded per year
D)Number of years divided by number of times compounded per year
E)None of these

Question 39

Using the table in your handbook, $6,000 for six years at 8½% compounded daily will grow to:

A)$8,991.02
B)$8,950.10
C)$9,991.20
D)$9,990.02
E)None of these

Question 40

Present value starts with the future and tries to calculate its worth in the present.

Question 41

Match the following terms with their definitions.

-Compound

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 42

Anne Katz, the owner of Katz Sport Shop, lends $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Anne at the end of eight years with interest compounded semiannually at 8%. At the end of eight years, Anne will receive (use the tables in the handbook):

A)$14,984
B)$16,857
C)$16,587
D)$14,484
E)None of these

Question 43

Trisha Long wants to buy a boat in five years. She estimates the boat will cost $15,000 at that time. What must Trisha deposit today in an account earning 5% annually to have enough to buy the boat in five years?

A)$12,328.50
B)$11,527.50
C)$11,752.50
D)$11,077.50
E)None of these

Question 44

Interest on $2,630 at 3% compounded semiannually for five years is:

A)$304.90
B)$414.49
C)$511.96
D)$422.12
E)None of these

Question 45

Jim Moore opens a new savings account. He deposits $12,000 at 12% compounded semiannually. At the start of the fourth year, Jim deposits an additional $50,000 that is also compounded semiannually at 12%. At the end of six years, the balance in Jim Moore's account is (use the tables in the handbook):

A)$66,081.20
B)$50,000.00
C)$16,081.20
D)$88,555.42
E)None of these

Question 46

Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that is also compounded semiannually at 10%. At the end of six years, the balance in Merle's account is (use the tables in the handbook):

A)$73,604.00
B)$53,604.00
C)$80,406.00
D)$98,636.72
E)None of these

Question 47

Al Miler, the owner of Al's Garage, estimates that he will need $29,000 for new equipment in 15 years. Al decides that he will put aside the money now so that in 15 years the $29,000 will be available. His bank offers him 10% interest compounded semiannually. (Use the tables in the handbook.)Al must invest today:

A)$6,710.60
B)$6,942.60
C)$6,701.60
D)$125,335.10
E)None of these

Question 48

Gracie Shay wants to buy a new Hummer in six years. Gracie estimates the cost of the Hummer will be $35,000. If she invests $22,000 now at a rate of 6% compounded quarterly, she:

A)Will have enough money
B)Will have exactly $32,000
C)Will have $33,450
D)Will have $31,449
E)None of these

Question 49

Ellen deposits $6,773 into an account earning 1% annually. After seven years what will Ellen's balance have grown to, including interest?

A)$7,516.68
B)$7,516.88
C)$7,261.33
D)$6,836.78
E)None of these

Question 50

Match the following terms with their definitions.

-Rate

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 51

Earl Miller deposited $25,000 at Y Bank at an interest rate of 12% compounded quarterly. (Use the tables in the handbook.)The effective rate (APY)is: (round to the nearest hundredth percent, if applicable)

A)12%
B)12.55%
C)12.15%
D)13.2%
E)None of these

Question 52

Lisa Richter deposited $5,000 at 4% compounded semiannually for three years. At the beginning of the fourth year, Lisa deposited $2,500. What would her balance be at the end of five years assuming she is still earning 4% compounded semiannually?

A)$5,131
B)$8,131
C)$8,800
D)$8,800.99
E)None of these

Question 53

Katie Hector wants to purchase a condo in Oxford, MS, in 20 years. The cost of the condo is expected to be $180,000. Assuming she can earn 6% annually, what should Katie deposit today?

A)$126,900
B)$56,124
C)$89,400
D)$180,000
E)None of these

Question 54

Match the following terms with their definitions.

-Nominal rate

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 55

Match the following terms with their definitions.

-Quarterly

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 56

Mia Kaminsky wants to attend Riverside Community College. She will need to have $25,000 six years from today. Mia is wondering what she will have to put in the bank today so that she will have $25,000 six years from now. Her bank pays 6% compounded semiannually. Using the tables in the handbook, the amount Mia will have to deposit is:

A)$18,950
B)$17,625
C)$17,535
D)$33,622
E)None of these

Question 57

Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. (Use the tables in the handbook.)The best deal is:

A)Four Rivers
B)Four Rivers for first two years
C)Mystic
D)Mystic for last two years
E)None of these

Question 58

Sam Monte deposits $21,500 into Legal Bank, which pays 6% interest that is compounded semiannually. Using the table in the handbook, what will Sam have in his account at the end of six years?

A)$29,760.30
B)$30,654.70
C)$30,456.07
D)$29,670.03
E)None of these

Question 59

Match the following terms with their definitions.

-Semiannually

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 60

Burton Bush wants to retire in Arizona when he is 80 years of age. Burton, who is now 55, believes he will need $500,000 to retire comfortably. To date, he has set aside no retirement money. If he gets an interest rate of 6% compounded annually, he will have to invest today (use the tables in the handbook):

A)$92,300
B)$90,500
C)$100,500
D)$116,500
E)None of these

Question 61

Match the following terms with their definitions.

-Monthly

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 62

Match the following terms with their definitions.

-Effective rate (APY)

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 63

Match the following terms with their definitions.

-Periods

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 64

Solve by using compound table:
$$\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Principal } & \text { Time } & \begin{array} { l } \text { Rate of } \\\text { Compound }\end{array} & \begin{array} { l } \text { When } \\\text { Compounded }\end{array} & \begin{array} { l } \text { \# of Periods to be } \\\text { Compounded }\end{array} & \begin{array} { l } \text { Total } \\\text { Amount }\end{array} & \begin{array} { l } \text { Total } \\\text { Interest }\end{array} \\\hline \$ 300 & 1 \text { year } & 6 \% & \text { Quarterly } & \text { A } & \text { B } & \text { C } \\\hline\end{array}$$

Question 65

Jarad Rodriguez deposits $10,000 at 10% compounded semiannually. At the start of year 6, Jarad deposits an additional $5,000 that is compounded at the same rate. At the end of 10 years, what is the balance in Jarad's account?

Question 66

Solve by using compound table:
$$\begin{array} { | l | l | l | l | l | } \hline \text { Principal } & \text { Rate } & \text { Time } & \begin{array} { l } \text { When } \\\text { Compounded }\end{array} & \text { Total Amount } \\\hline \$ 15,000 & 12 \% & \text { 4 years } & \text { Quarterly } & \text { ? } \\\hline\end{array}$$

Question 67

Pete Sist wants to buy a new Chevrolet in five years. He estimates the car will cost $24,000. Assuming Pete invests $15,000 now at 10% interest compounded semiannually, will he have enough money to buy the car at the end of five years?

Question 68

Solve by using compound table:
$$\begin{array} { | l | l | l | l | l | } \hline \text { Principal } & \text { Rate } & \text { Time } & \begin{array} { l } \text { When } \\\text { Compounded }\end{array} & \text { Total Amount } \\\hline \$ 8,000 & 10 \% & 3 \text { years } & \text { Semiannually } & \text { ? } \\\hline\end{array}$$

Question 69

Molly Scupper wants to attend Clarke University. She will need $90,000 eight years from today. Assume Molly's bank pays 6% interest compounded semiannually. What must Molly deposit today to have $90,000 in eight years? Verify your answer.

Question 70

Use the present value table to complete:
$$\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Future } & & & & & & \\\text { Amount } & \text { Length of } & \text { Rate } & \text { Table } & \text { Rate } & \text { P.V. } & \text { P.V. } \\ \text { Desired } & \text { Time } & \text { Compounded } & \text { Period } & \text { Used } & \text { Factor } & \text { Amount } \\\hline \$ 11,000 & 6 \text { yrs } & 12 \% \text { quarterly } & \text { A } & \text { B } & \text { C } & \text { D } \\\hline\end{array}$$

Question 71

Find effective rate (APY)and show work: (round answer to the nearest hundredth)
$$\begin{array} { | l | l | l | l | } \hline \text { Principal } & \text { Rate } & \begin{array} { l } \text { When } \\\text { Compounded }\end{array} & \begin{array} { l } \text { Effective Rate } \\\text { (APY) }\end{array} \\\hline \$ 5,000 & 10 \% & \text { Semiannually } & \text { ? } \\\hline\end{array}$$

Question 72

Kathy Crag, the owner of The Fabric Corner, lent $15,000 to Dani Flynn to open her own card shop. Dani plans to repay Kathy at the end of 7 years with 8% interest compounded quarterly. How much will Kathy receive at the end of 12 years?

Question 73

John Riviera deposits $14,000 in National Bank at 8% compounded quarterly. What is the effective rate (APY)of interest? (round answer to nearest hundredth)

Question 74

Match the following terms with their definitions.

-Present value

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 75

Use the present value table to complete:
$\begin{array}{|l|l|l|l|l|l|l|}\hline \begin{array}{l}\text { Future } \\\text { Amount }\end{array} & \text { Length of } & \text { Rate } & \text { Table } & \text { Rate } & \text { P.V. } & \text { P.V. } \\\text { Desired } & \text { Time } & \text { Compounded } & \text { Period } & \text { Used } & \text { Factor } & \text { Amount } \\\hline \$ 9,000 & 20 \mathrm{yrs} & \begin{array}{l}10 \% \\\text { semiannually }\end{array} & \text { A } & \text { B } & \text { C } & \text { D } \\\hline\end{array}$

Question 76

Jim Smith believes that in 30 years he will need $80,000 to buy a retirement cottage. Assuming he gets an interest rate of 9% compounded annually, how much will he have to invest today to reach his retirement goal?

Question 77

Match the following terms with their definitions.

-Interest

A)Year times number of times compounded in one year
B)Twice a year
C)Stated rate
D)True rate of interest
E)Amount calculated on adjusted principal
F)Periodically interest is calculated and added to principal
G)Rate divided by number of times compounded per year
H)Know future amount looking for present
I)Four times per year
J)Twelve times per year

Question 78

Complete without using tables. (Show work.)
$$\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Principal } & \text { Time } & \begin{array} { l } \text { Rate of } \\\text { Compound }\end{array} & \begin{array} { l } \text { When } \\\text { Compounded }\end{array} & \begin{array} { l } \text { \# of Periods to be } \\\text { Compounded }\end{array} & \begin{array} { l } \text { Total } \\\text { Amount }\end{array} & \begin{array} { l } \text { Total } \\\text { Interest }\end{array} \\\hline \$ 300 & 1 \text { year } & 6 \% & \text { Quarterly } & \text { A } & \text { B } & \text { C } \\\hline\end{array}$$

Question 79

Moxie Fox deposited $30,000 in a savings account at 6% interest compounded semiannually. At the beginning of year 4, Moxie deposits an additional $60,000 at 6% interest compounded semiannually. At the end of six years, what is the balance in Moxie's account?

Question 80

Juanita Finn deposits $12,000 into Valley Bank, which pays interest of 8% compounded annually for four years. How much will Juanita have in her account?