Deck 23: Time Value of Money Module

Question 1

The present value of an annuity is the present value of a series of equal cash flows that occur in the future.

Answer 1

True

Question 2

The formula to compute the present value of a dollar is PV = FV x . $\frac { 1 } { ( 1 + i ) ^ { n } }$

Answer 2

True

Question 3

FASB's Statement of Financial Accounting Concepts No. 7 does not address recognition issues and therefore does not address when fair value should be based on present value, but it does provide general principles governing the use of present value and the objectives of present value accounting measurements.

Answer 3

True

Question 4

An ordinary annuity is if the cash flows occur on the first day of each period.

Question 5

The formula to calculate a present value of a deferred annuity is:
PV_deferred = C x (Converted Factor for Present Value of Deferred Annuity of 1)

Question 6

The formula for the future value of an ordinary annuity of any amount is: $$F V _ { o } = C \times \left[ \frac { ( 1 + n ) ^ { i } - 1 } { i } \right]$$

Question 7

An annuity is a series of equal cash flows occurring at irregular intervals with interest compounded at a specific rate.

Question 8

Present value measurements involve estimation of future cash flows, the timing, amount, and the risk of those cash flows which create a relevant accounting measurement.

Question 9

The future value of an ordinary annuity is determined immediately after the last cash flow in the series occurs.

Question 10

The future value of an annuity due is determined one period after the first cash flow in the series.

Question 11

To calculate the present value of four annual installments of $1,000 at an 8% interest rate beginning on January 1, 2013 and payments due on December 31 of each year, one would use the present value of an ordinary annuity table.

Question 12

The future value of a single sum is the original principal amount plus the compound interest stated as of a specific future date.

Question 13

The formula to compute the future value of a single sum is: FV = PV x (1 - i)ⁿ.

Question 14

Compounding is the conversion of future cash flow amounts to their present value.

Question 15

The interest that accrues on both the principal and the past unpaid accrued interest is called compound interest.

Question 16

The present value of an annuity due is determined on the date of the last cash flow in the series.

Question 17

The present value of a deferred annuity is determined on today's date, because the annuity payments begin some period after today's date.

Question 18

The formula to calculate the present value of an ordinary annuity is: $$p V o = C \times \left[ \frac { 1 - \frac { 1 } { ( 1 + i ) ^ { n } } } { i } \right]$$

Question 19

To calculate the present value of an annuity due the formula is: $$P V _ { D } = C \times \left[ \frac { 1 - \frac { 1 } { ( 1 + i ) ^ { n + 1 } } } { i } + 1 \right]$$

Question 20

Discounting is the process of converting a future cash flow to a present value.

Question 21

On April 1, 2014, Meyers Company purchased a bulldozer. Payment, totaling $70,000, is not due until April 1, 2016. Assuming interest at a 12% annual rate, Meyers should debit Machinery on April 1, 2014, in the amount of

A) $70,000
B) $62,500
C) $61,600
D) $55,804

Question 22

The formula for the present value of a single sum at compound interest is

A) $\frac { P V } { ( 1 + i ) ^ { n } }$
B) FV x (1 + i)ⁿ
C) FV x $\frac { 1 } { ( 1 + i ) ^ { n } }$
D) PV x $\frac { 1 } { ( 1 + i ) ^ { n } }$

Question 23

If $100,000 is invested on December 31, 2014 to earn compound interest semiannually, and if the future value on December 31, 2020, is $225,219 what is the semiannual interest rate on the investment?

A) 7%
B) 6%
C) 5%
D) 8%

Question 24

The method of converting a future dollar amount into its present dollar value by removing the time value of money is called

A) discounting
B) compounding
C) amortizing
D) interpolation

Question 25

Mildred desires to have $7,049 on deposit five years from today. If she has $4,000 to deposit, what rate of interest, compounded annually, must be obtained to accumulate the desired $7,049 in five years?

A) 12%
B) 10%
C) 9%
D) 8%

Question 26

Simple interest on a $1,250,000, 9%, 15-month note is

A) $112,500
B) $ 9,375
C) $140,625
D) none of these

Question 27

The future value of $50,000 deposited today and compounded quarterly at an 8% annual interest rate for seven years is

A) $57,434
B) $87,051
C) $85,691
D) $78,000

Question 28

To compare the value of amounts received at different times in the future, dollar amounts

A) may be restated to their present value through discounting or restated to their future value by compounding
B) must be converted to a single sum
C) must be restated to their future value by adding the compound interest to date
D) must be restated to their present value by removing the interest from the amount to be received in the future

Question 29

Simple interest on a $25,000, 8%, 18-month note is

A) $22,000
B) $23,000
C) $3,000
D) $2,000

Question 30

The present value of $500,000 received at the end of five years discounted at 10% is

A) $805,255
B) $310,461
C) $306,957
D) none of these

Question 31

Interest calculated on the original principal regardless of the number of time periods that have passed or the amount of interest that has been paid or accrued in the past is

A) compound interest
B) simple interest
C) present value of future cash flows
D) future value of a single sum

Question 32

The formula for the future value of a single amount at compound interest is

A) $\frac { 1 } { ( 1 + i ) ^ { n } }$
B) PV x (1 + i)ⁿ
C) $\frac { ( 1 + i ) ^ { n - 1 } } { i }$
D)

Question 33

Interest compounded quarterly on a $100,000 principal amount at 12% for one year is

A) $ 9,273
B) $12,551
C) $12,000
D) none of these

Question 34

Interest compounded monthly on a $10,000 principal amount at 18% for two years is

A) $1,800
B) $3,600
C) $3,924
D) $4,295

Question 35

The future value of $7,000 deposited today and compounded quarterly at a 16% annual interest rate for five years is

A) $14,724
B) $14,702
C) $ 8,517
D) $15,338

Question 36

The present value of $175,000 received at the end of six years discounted at 12% is

A) $89,523
B) $88,660
C) $82,544
D) $126,000

Question 37

Margaret will receive an insurance settlement of $3,000,000 in five years. Randall is willing to give her a lump sum today in return for the payment in five years. If current interest rates are 12% per year, how much will Margaret receive today?

A) $960,637
B) $1,702,281
C) $1,116,790
D) $1,800,000

Question 38

Compound interest is

A) calculated by multiplying the principal times the rate times the period of time
B) interest on the original principal plus any past unpaid accrued interest to date
C) interest on the original principal paid or received
D) interest on any past unpaid interest accrued to date

Question 39

The future value of $7,000 deposited today and compounded semiannually at an 9% annual interest rate for four years is

A) $9,955
B) $9,520
C) $8,100
D) $7,920

Question 40

Maxine has $1,000 to invest today. How much will her money be worth in 15 years if she earns 9% compounded semiannually on her money?

A) $ 3,745
B) $13,268
C) $ 3,642
D) $ 1,935

Question 41

Jeff desires to accumulate $13,603.83 by December 1, 2016. To accumulate that sum, he will make six equal semiannual deposits of $2,000, beginning on June 1, 2014, into a fund that earns interest compounded semiannually. What annual rate of interest must the fund provide to yield the desired sum?

A) 5%
B) 6%
C) 10%
D) 12%

Question 42

An annuity is a series of

A) equal payments with interest compounded annually
B) payments made at regular intervals in the future with interest compounded yearly
C) payments made at points in the future earning simple interest on a regular basis
D) equal payments made at regular intervals in the future with interest compounded at the end of each time period

Question 43

In order to measure the carrying value of investments in bonds, which of the following time value of money concepts is used?

A) the present value of an ordinary annuity
B) the future value of a single sum
C) the future valuet of an ordinary annuity
D) all of these

Question 44

Jessie's Dry Cleaner began making $2,000 equal, annual deposits in a fund starting on January 2, 2014. The fund earns 10% compounded annually, and the last deposit is made on January 2, 2018. How much will be in the fund on January 2, 2019, one year after the final deposit?

A) $15,000
B) $13,431
C) $12,105
D) $10,641

Question 45

Stephen Michaels wants to know how much he must deposit today at 12% interest to provide three equal annual withdrawals of $10,000, beginning one year from now. This is an example of the present value of

A) an ordinary annuity
B) an annuity due
C) a single sum
D) a deferred annuity

Question 46

All of the following are conditions for an annuity except

A) periodic cash flows must be equal in amount
B) the time periods between the cash flows are the same length
C) the interest rate is constant for each time period
D) the interest rate is compounded in the middle of each time period

Question 47

Abby wants to have $20,000 available in August 2019 to make a college tuition payment. To be able to have this amount available, Abby will have to make equal annual deposits in an investment earning 12% annually in August 2015, 2016, 2017, 2018, and 2019 in the amount of

A) $5,548
B) $4,954
C) $4,000
D) $3,148

Question 48

What is the formula for the present value of an ordinary annuity of 1?

A) $\frac { ( 1 + i ) ^ { n - 1 } } { i }$
B) $\frac { 1 } { ( 1 + i ) ^ { n } }$
C) (1 + i)ⁿ
D) $\frac { 1 - \left[ 1 / ( 1 + i ) ^ { n } \right] } { i }$

Question 49

Tessa won the lottery for $2,500,000 but due to a change in state laws she will not be able to collect it for three years. Ralph is willing to give her a lump sum today in return for the payment in three years. If current interest rates are 14% per year, how much will Tessa receive today?

A) $1,687,430
B) $5,804,080
C) $2,500,000
D) $3,703,860

Question 50

You would like to deposit a sum of money today that would enable you to withdraw $2,000 a year for ten years. If the interest paid on the amount deposited is 10% compounded annually and if the first withdrawal is made one year from today, the formula you would use to determine the amount of the initial deposit is the

A) present value of a deferred annuity
B) present value of an annuity due
C) present value of an ordinary annuity
D) future value of an ordinary annuity

Question 51

Each of the following compound interest factors has the same number of periods (n) at the same interest rate (i). Which one is the table factor for the present value of a single sum?

A) 1.500730
B) 7.153291
C) 0.666342
D) 4.766540

Question 52

At the beginning of 2015, Laura Company issued 10-year bonds with a face value of $4,000,000 due on December 31, 2020. The company will accumulate a fund to retire these bonds at maturity. It will make ten annual deposits to the fund beginning on December 31, 2015. How much must the company deposit each year, assuming that it will earn 12% interest compounded annually?

A) $363,636.36
B) $227,936.65
C) $226,008.92
D) $203,514.87

Question 53

The formula for the future value of an ordinary annuity is

A)

B) $\frac { C \times \left\{ 1 - \left[ 1 / ( 1 - i ) ^ { n } \right] \right\} } { i }$
C)

D)

Question 54

Using the table approach, the future amount of an annuity due may be calculated by finding the table factor for the future amount of an ordinary annuity of

A) n + 1 and then subtract 1
B) n + 1 and then add 1
C) n - 1 and then add 1
D) n - 1 and then subtract 1

Question 55

Jacob Sawyer will deposit $3,000 into a special account each year beginning December 31, 2014, with the last deposit being made on December 31, 2018. Jacob wants to know how much will be in his account on December 31, 2018, immediately after the final deposit, if the account earns 10% compounded annually. To solve the problem, Jacob must find the future value of

A) a single sum
B) a deferred annuity
C) an ordinary annuity
D) an annuity due

Question 56

Table factors for present values

A) decrease as the interest rate decreases
B) decrease as the number of periods increases
C) increase as the interest rate increases
D) increase as the number of periods increases

Question 57

On January 2, 2014, Christopher inherited a trust fund that he could use for college tuition. Christopher hopes to make five equal withdrawals of $40,000 from the fund that will earn 10% compounded annually. The first withdrawal will be made on January 2, 2015. How much does he need to have invested in the fund on January 2, 2014, to be able to withdraw the needed amounts each year?

A) $151,631
B) $200,000
C) $244,204
D) $268,624

Question 58

Georgia deposits $4,000 every three months for five years. The first deposit is made on March 31, 2014, and the last deposit is made on December 31, 2018. The fund earns 16% and interest is compounded quarterly. How much money will Georgia have on December 31, 2018, immediately after her last deposit? Factors for future value of an annuity of $1 are

For Values of n and i
$\begin{array} { l l } \hline = 20 ; I = 4 \% & n = 5 ; i = 16 \% \\7978079 & 6.87135\end{array}$

A) $123,876
B) $119,112
C) $110,034
D) $107,508

Question 59

Jackie's parents loaned her $80,000 to fund her college education. Her parents are not charging interest. They desire to be paid one lump sum of $80,000 when Jackie can accumulate that amount. Jackie established a savings plan that earns 8% compounded annually. Her new job promises to pay an annual holiday bonus that will enable her to make equal annual, year-end deposits of $6,400. Approximately how many years will it take Jackie to accumulate the $80,000?

A) 8 years
B) 8.5 years
C) 9 years
D) 12.5 years

Question 60

The future amount of an annuity due is determined one period

A) after the last cash flow in the series
B) before the next cash flow in the series
C) before the last cash flow in the series
D) after the next cash flow in the series

Question 61

In the present value of an annuity table, the factors

A) increase as the interest rates increase
B) decrease as the periods increase
C) remain the same as the periods increase
D) decrease as the interest rates increase

Question 62

On July 7, 2014, Lawrence Company sold some machinery to Johnson Construction Company. The sales contract requires Johnson to pay five equal annual payments of $75,000 each, beginning on July 7, 2014. What present value concept is appropriate for this situation?

A) present value of an annuity due of $1 for five periods
B) present value of an ordinary annuity of $1 for five periods
C) future value of an annuity of $1 for five periods
D) future value of $1 for five periods

Question 63

Marcus Jones wants to invest $10,000 on January 1, 2014, so that he may withdraw 10 annual payments of equal amounts beginning January 1, 2029. If the fund earn 10% annual interest over its life, what will be the amount of each of the withdrawals?

A) $1,470
B) $10,000
C) $14,709
D) none of these

Question 64

Norah has $2,000,000 in her retirement account. She wants to make 20 equal withdrawals, beginning immediately. The investment plan earns 8%. How much should each withdrawal be to completely deplete the fund after the 20th withdrawal?

A) $188,615
B) $203,704
C) $189,096
D) $43,704

Question 65

Samuel just inherited an annuity. He will receive six equal annual payments of $18,000, beginning today. Assuming a 10% interest rate compounded annually, the present value today of all receipts is

A) $64,886
B) $78,395
C) $86,234
D) $75,058

Question 66

Joshua desires to purchase an annuity on January 1, 2014, that yields him five annual cash flows of $10,000 each, with the first cash flow to be received on January 1, 2017. The interest rate is 10% compounded annually. The cost (present value) of the annuity on January 1, 2014, is

A) $31,328.81
B) $34,461.70
C) $37,907.87
D) $48,684.19

Question 67

On June 1, 2014, Molser Company acquired a new machine by agreeing to pay five equal annual payments of $20,000, beginning on June 1, 2014. Assuming an interest rate of 14% compounded annually, Molser should record the acquisition cost of the machine on June 1, 2014, at

A) $68,661.62
B) $78,274.24
C) $87,719.25
D) $100,000.00

Question 68

The formula for the present value of an annuity due is

A) $C \times \left[ \left( p _ { 0 _ { r _ { 1 } } } \right) \left( p _ { k , t } \right) \right]$

B) $C \times \left[ \frac { 1 - \frac { 1 } { ( 1 + i ) ^ { n } } } { i } \right]$

C) $C \times \left[ \frac { 1 - \frac { 1 } { ( 1 + i ) ^ { n - 1 } } } { i } + 1 \right]$

D) $C \times \left[ \frac { ( 1 + i ) ^ { n } - 1 } { i } \right]$

Question 69

On January 31, 2014, Manning Company acquired a new machine by paying $40,000 cash and agreeing to pay $20,000 annually for four years, beginning on January 31, 2015. Assuming an interest rate of 10%, Manning should record the acquisition cost of the machine on January 31, 2014, at

A) $120,000
B) $109,737
C) $103,397
D) $102,092

Question 70

To determine the converted table factor for the present value of an annuity due, one must find the factor for the present value of an ordinary annuity for

A) n + 1 and then subtract 1
B) n - 1 and then subtract 1
C) n + 1 and then add 1
D) n - 1 and then add 1

Question 71

Stacey has $5,000,000 on deposit in a fund that earns 9% interest compounded annually. How much can Stacey withdraw annually from the fund in ten equal annual withdrawals to completely deplete the fund after the tenth draw, assuming the first withdrawal occurs one year from today?

A) $450,000
B) $714,771
C) $779,100
D) $555,555

Question 72

Charlie's Construction Co. acquired a new $800,000 backhoe on April 1, 2014. Charlie's will make six annual payments based upon 8% interest compounded annually, starting on March 31, 2015. How much will each payment be?

A) $504,136
B) $173,056
C) $160,234
D) $109,052

Question 73

Suppose you borrow money from your parents for college tuition on January 1, 2013. Your parents require four annual payments of $1,000 each, with the first payment due on January 1, 2017. They are charging you 6% annual interest. What is the cost of the college tuition?

A) $2,909.37
B) $1,593.85
C) $4,000.00
D) none of these

Question 74

Which of the following transactions would require the use of the present value of an annuity due concept in order to calculate the present value of an asset acquired or liability assumed?

A) A rental agreement is entered into with the initial payment due immediately.
B) A rental agreement is entered into with the initial payment due one month from the signing of the agreement.
C) A note payable is obtained from a bank requiring monthly payments for six years, beginning at the end of the current month.
D) A machine is acquired by paying $20,000 cash and agreeing to pay equal annual amounts of $10,000 each at the end of the next three years.

Question 75

David Company borrowed $550,000 on December 31, 2014. The loan will be paid with six equal annual payments of $115,388, beginning on December 31, 2015. The rate of interest compounded annually for the loan is

A) 9%
B) 8%
C) 7%
D) 6%

Question 76

Savannah has just won the state lottery. She will receive ten equal annual payments of $15,000, beginning one year from today. Assuming an 8% interest rate compounded annually, the present value of those receipts today is

A) $80,913
B) $100,651
C) $108,703
D) $102,000

Question 77

When the present value of an annuity is calculated as of two or more periods before the payment of the first cash flow, the annuity is

A) an ordinary annuity
B) a deferred ordinary annuity
C) an annuity due
D) a simple annuity

Question 78

Parker Posie wants to determine how much she must deposit today at 14% interest to provide four withdrawals of $26,000 at the end of each year, beginning five years from now. This is an example of the present value of

A) an ordinary annuity
B) an annuity due
C) a single sum
D) a deferred ordinary annuity

Question 79

On September 1, 2014, Watson Company received $44,940 from One Finance Company. To pay off this loan, Watson Company will have to pay One Finance $10,000 each year for ten years. The first payment is due September 1, 2015. Which interest rate compounded annually is Watson paying on this loan?

A) 12%
B) 15%
C) 18%
D) 24%

Question 80

Raymond's Leasing Company signed an agreement to lease an asset that has a fair value of $800,000 on December 31, 2014. The lease will be paid in seven equal annual payments of $138,730, beginning on December 31, 2014. The interest rate included in the lease agreement is

A) 8%
B) 7%
C) 6%
D) 5%