Deck 24: Time Value of Money Module

Question 1

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

Answer 1

B

Question 2

Milton desires to have $6, 442 on deposit five years from today.If he has $4, 000 to deposit, what rate of interest, compounded annually, must be obtained to accumulate the desired $6, 442 in five years?

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

Answer 2

B

Question 3

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

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

Answer 3

D

Question 4

Molly will receive an insurance settlement of $2, 000, 000 in six years.Randal is willing to give her a lump sum today in return for the payment in six years.If current interest rates are 12% per year, how much will Molly receive today?

A)$ 960, 637
B)$1, 013, 262
C)$1, 116, 790
D)$1, 186, 903

Question 5

Lori Miller deposits $2, 000 each year into a savings account beginning January 1, 2010.The last payment will be made on January 1, 2019, after which the total amount will be withdrawn to purchase a yacht.To find the amount available on January 1, 2014, after the last payment, Lori must determine

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

Question 6

The future amount of $6, 000 deposited today and compounded semiannually at an 8% annual interest rate for four years would be

A)$8, 211
B)$8, 163
C)$8, 100
D)$7, 920

Question 7

Each of the following compound interest factors has the same number of time periods and/or rents (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 8

The present value of $75, 000 received at the end of eight years discounted at 12% is

A)$ 29, 523
B)$ 30, 291
C)$ 32, 544
D)$185, 697

Question 9

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 10

Simple interest on a $20, 000, 8%, 15-month note payable would total

A)$22, 000
B)$21, 600
C)$ 2, 000
D)$ 1, 600

Question 11

Compound interest is

A)calculated by multiplying the principal times the rate times the time period
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 12

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 13

An annuity is a

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

Question 14

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 or rents increases

Question 15

On April 1, 2010, the Resendez Company purchased a bulldozer.Payment, totaling $70, 000, is not due until April 1, 2012.Assuming interest at a 12% annual rate, Resendez should debit Machinery on April 1, 2010, in the amount of

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

Question 16

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

A)p(1 + i)ⁿ
B)f(1 + i)ⁿ
C)f[1/(1 + i)ⁿ]
D)p[1/(1 + i)ⁿ]

Question 17

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 at the middle of each time period

Question 18

Kevin Nathan will deposit $1, 000 into a special account each year beginning December 31, 2010, with the last deposit being made on December 31, 2014.Kevin wants to know how much will be in his account on December 31, 2014, immediately after the final deposit, if the account earns 12% compounded annually.To solve the problem, Kevin must find the

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

Question 19

If $10, 000 is invested on December 31, 2008, to earn compound interest semiannually, and if the future value on December 31, 2018, is $38, 697, what is the semiannual interest rate on the investment?

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

Question 20

On January 2, 2010, Claudia Company inherited a trust fund that she could use for college tuition.Claudia 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, 2011.How much does she need to have invested in the fund on January 2, 2010, to be able to withdraw the needed amounts each year?

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

Question 21

Millie Company borrowed $550, 000 on December 31, 2010.The loan will be paid with six equal annual payments of $115, 388, beginning on December 31, 2011.The rate of interest compounded annually for the loan is

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

Question 22

Glenda deposits $4, 000 every three months for five years.The first deposit is made on March 31, 2010, and the last deposit is made on December 31, 2014.The fund earns 16%, and interest is compounded quarterly.How much money will Glenda have on December 31, 2014, immediately after her last deposit? Factors for future value of an annuity of $1 are $\text { For Values of } n \text { and } i$
$\begin{array}{ll}n=5 ; i=16 \% & n=20 ; I=4 \% \\6.8771 & 29.7781\end{array}$

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

Question 23

You would like to deposit a sum of money today that would enable you to withdraw $1, 000 a year for five 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

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

Question 24

On January 31, 2010, Richie Company acquired a new machine by paying $40, 000 cash and agreeing to pay $20, 000 annually for three years, beginning on January 31, 2011.Assuming an interest rate of 10%, Richie should record the acquisition cost of the machine on January 31, 2010, at

A)$100, 000
B)$ 94, 712
C)$ 89, 738
D)$ 62, 092

Question 25

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 26

Abby wants to have $20, 000 available in August 2015 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 2011, 2012, 2013, 2014, and 2015 in the amount of

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

Question 27

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

Question 28

Sol's Laundry began depositing $1, 000 equal annual deposits in a fund beginning on January 2, 2010.The fund earns 10% compounded annually, and the last deposit is made on January 2, 2014.How much will be in the fund on January 2, 2015, one year after the final deposit?

A)$7, 500
B)$6, 716
C)$6, 105
D)$5, 641

Question 29

John desires to accumulate $13, 603.83 by December 1, 2012.To accumulate that sum, he will make six equal semiannual deposits of $2, 000, beginning on June 1, 2010, 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 30

Georgia has just won the state lottery.She will receive six equal annual amounts of $12, 000, beginning one year from today.Assuming an 8% interest rate compounded annually, the present value of those receipts today is

A)$35, 913
B)$55, 475
C)$59, 913
D)$72, 000

Question 31

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

Question 32

On September 1, 2010, the Baker Company received $44, 940 from 4-Most Finance Company.To pay off this loan, the Baker Company will have to pay 4-Most $10, 000 each year for ten years.The first payment is due September 1, 2011.Which interest rate compounded annually is Baker paying on this loan?

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

Question 33

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 34

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 amount of a single sum
C)the future amount of an ordinary annuity
D)all of these

Question 35

At the beginning of 2011, the Loretta 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, 2011.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 36

Hillary Jones wants to know how much she 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 37

Paul's Painting Co.acquired a new $800, 000 press on April 1, 2010.Paul's will make six equal payments based upon 8% compound interest, starting on March 31, 2011.How much will each payment be?

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

Question 38

The future amount of an annuity due is determined one period

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

Question 39

On July 7, 2010, Luke Company sold some machinery to Jones Construction Company.The sales contract requires Jones to pay five equal annual payments of $70, 000 each, beginning on July 7, 2010.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 amount of an annuity of $1 for five periods
D)future amount of $1 for five periods

Question 40

Nancy's parents loaned her $80, 000 to fund her college education.Her parents are not charging interest.They desire to be paid in one lump sum of $80, 000 when Nancy can accumulate that amount.Nancy 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 Mary to accumulate the desired $80, 000?

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

Question 41

Pricilla is considering buying a lottery ticket.She has to decide whether she wants to receive an immediate lump sum payment based upon $50, 000, 000 or 20 equal annual payments of $2, 500, 000.The annual payments begin the day after the lottery is won.
Below are compound interest amounts for 10% and 20 periods taken from the appropriate tables.
Required:
Compute the present value of the amounts to be received under each alternative plan.

Question 42

Joseph desires to purchase an annuity on January 1, 2010, that yields him five annual rents of $10, 000 each, with the first rent to be received on January 1, 2013.The interest rate is 10% compounded annually.The cost (present value)of the annuity on January 1, 2010, is

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

Question 43

Using the compound interest tables, solve the following questions.
Required:

Question 44

Rose Carter wants to determine how much she must deposit today at 14% interest to provide four withdrawals of $6, 000 at the end of each year, beginning five years from now.This is an example of the present value of a(n)

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

Question 45

Rose deposited $18, 000 in a savings account that provides for interest at the rate of 16% compounded quarterly.
Required:
Compute the balance in the account at the end of seven years.

Question 46

Using the compound interest tables, solve each of the following questions.
Required:

Question 47

The Rogers Leasing Company signed an agreement to lease an asset that has a fair value of $800, 000 on December 31, 2010.The lease will be paid in seven equal annual payments of $138, 730, beginning on December 31, 2010.The interest rate included in the lease agreement is

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

Question 48

Balance sheet values are calculated using compound interest (present value)calculations for all of the following except

A)bonds payable
B)long-term notes receivable
C)long-term lease liabilities
D)undeclared dividends payable

Question 49

Beginning December 31, 2010, ten equal annual withdrawals are to be made.
Required:
Using the appropriate tables, determine the equal annual withdrawals if $140, 000 is invested on January 1, 2010 at an interest rate of 10% compounded annually.

Question 50

On May 1, 2010, Mosier Company acquired a new machine by agreeing to pay five equal annual payments of $20, 000, beginning on May 1, 2010.Assuming an interest rate of 14% compounded annually, Mosier should record the acquisition cost of the machine on May 1, 2010, at

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

Question 51

When the present value of an annuity is calculated as of two or more periods before the payment of the first rent, the annuity is a(n)

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

Question 52

Teresa would like to retire on December 31, 2020, and take a trip around the world.In order to do this, she feels she must accumulate $200, 000 in her retirement account by that date.She is willing to deposit a certain amount each year into her retirement account, which earns 12% interest compounded annually.Teresa will make the first deposit on December 31, 2011, and the last deposit on December 31, 2020.
Required:
Determine the amount Teresa must deposit into her retirement account each year.Clearly label all work.

Question 53

Sally has $3, 000, 000 on deposit in a fund that earns 10% interest compounded annually.How much can Sally 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)$300, 000
B)$443, 851
C)$488, 237
D)$545, 945

Question 54

Using the compound interest tables, solve each of the following questions.
Required:

Question 55

Using an appropriate compound interest table, solve the following question.
Required:
What is the future amount on December 31, 2020, of eleven deposits of $4, 000 each with the first deposit being made on December 31, 2010, and interest at 12% compounded annually?

Question 56

At the beginning of 2010, Lucy Co.issued bonds with a face value of $500, 000 due on December 31, 2016.The company desires to accumulate a fund to retire these bonds at maturity by making equal annual deposits beginning on December 31, 2010.
Required:
Compute the amount that the company must deposit at the end of each year, assuming that the fund will earn 10% interest a year compounded annually and seven deposits are made.

Question 57

FASB financial accounting concepts on using estimated future cash flow information in accounting measurements identified each of the following four principles except

A)the cash flows should consider all relevant future events and uncertainties
B)the assumptions used to select interest rates should be consistent with the assumptions inherent in the estimated cash flow amounts
C)the estimated cash flows and interest rates should be free from bias and unrelated factors
D)the estimated cash flows should reflect a single most likely minimum or maximum possible amount, rather than a range of possible cash flows

Question 58

Using the compound interest tables, solve each of the following questions.
Required:

Question 59

Nola has $1, 000, 000 in her retirement account.She wants to make 20 equal withdrawals, beginning immediately.The investment plan earns 6%.How much should each withdrawal be?

A)$82, 250
B)$84, 005
C)$84, 548
D)$87, 185

Question 60

Sammy has just inherited an annuity.He will receive six equal annual amounts of $8, 000, beginning today.Assuming a 12% interest rate compounded annually, the present value today of all receipts is

A)$30, 535
B)$32, 891
C)$36, 838
D)$48, 000

Question 61

On January 1, 2010, Betty's Produce Market leased some equipment from another company.The lease contract calls for $22, 000 payments for eight years, beginning on December 31, 2010.
Required:
Calculate the present value of the lease payments on January 1, 2010.Assume a 6% interest rate.

Question 62

A beginning accounting student has just been introduced to present and future values analysis and has been told that it is based on compound interest, not simple interest.The student is confused about the differences between the two interest methods.
Required:
Explain the difference between the two methods using a single deposit of $1, 000 for two years at 10% interest.

Question 63

The present values of ordinary annuities, annuities due, and deferred annuities were discussed in the textbook.Discuss the ways these three annuities are similar and dissimilar.

Question 64

Compound interest factors are provided below:
$\begin{array}{lrrrr}&35 \%, n=10&5 \%, n=20&10 \%, n=10&10 \%, n=20\\\hline\text { Future value of a lump sum } & 1.629 & 2.653 & 2.594 & 6.728 \\\text { Future value of an ordinary amuity } & 12.578 & 33.067 & 15.937 & 57.275 \\\text { Present value of a lump sum } & .614 & .377 & .386 & 149 \\\text { Present value of an ordinary amuity } & 7.722 & 12.462 & 6.145 & 8.514 \\\text { Present value of an anmuity due } & 8.108 & 13.089 & 6.759 & 9.365\end{array}$ Required:
Using the above factors, answer each of the following questions.

Question 65

Although most accountants believe that the use of present value creates relevant accounting measurements, there are some reliability questions.Discuss the reasons why present value computations create less reliable measurements.

Question 66

Grandpa Brown has agreed to deposit a lump sum into an account that pays 12% interest compounded annually in order to pay for his granddaughter's college education.The granddaughter estimated that she will need to withdraw $40, 000 at the beginning of each year for four years to pay for room, board, tuition, and books.Grandpa will deposit the lump sum on August 1, 2010, and the granddaughter will make the first withdrawal on September 1, 2016.
Required:
Determine the amount that Grandpa Brown must deposit.Clearly label all work.

Question 67

On January 1, 2010, Steelton Company completed arrangements to purchase a new piece of equipment.The agreement calls for equal annual payments on January 1 of each year for six years.The first payment of $7, 500 is to be made on January 1, 2010.The implied interest rate is 12%.
Required:
Calculate the cost of the equipment to Steelton Company.

Question 68

Match the diagrams with the concepts by writing the identifying letter of the diagram on the blank line to the left of the concept."VAL" represents the value to be calculated.

Question 69

The FASB concepts statement relating to cash flow information introduces the concept of expected cash flows when using present values for accounting measurements.Assume that the Smith Company determined that it has a 40% probability of receiving $10, 000 in one year but a 60% probability of receiving $10, 000 two years from now.
Required:
Using the FASB concepts, calculate the present value of the cash flows assuming a 12% interest rate compounded annually.

Question 70

Maggie Company estimated that it has a 20% probability of receiving $240, 000 one year from now, a 30% probability of receiving $240, 000 two years from now, and a 50% probability of receiving $240, 000 three years from now.
Required:
Using the FASB's concept of "expected cash flows, " calculate the present value of the cash flows assuming a 10% interest rate compounded annually.

Question 71

A beginning accounting student comes to you with the following question, "What is the time value of money and does it relate to interest?"
Required:
Explain the two concepts and how they are related.

Question 72

An accounting student has just been introduced to present value analysis and comes to you with the following question, "How is present value used in the financial statements?"
Required:
Give the student examples of financial statement accounts that are stated at present value and explain the advantages of using present value for certain financial statement items.