Test Bank – Appendix - The Time Value of Money A-1
Appendix A
The Time Value of Money
Multiple Choice Questions
1.Flores Company borrowed $10,000 at 10% interest for 5 years. Which statement is true?
- Regardless of when the note is repaid, total interest over the loan period is the same.
- Interest expense is the same regardless of the compounding periods.
- The amount to be repaid is the same regardless of whether the principal is repaid $2,000 per year, or as a sum at the end of five years.
- Interest is less if simple interest is used than if compound interest is used.
Ans: D BT: AP Difficulty: Moderate TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
2.How much is interest revenue for 90 days on an 8%, 180-day note receivable with a face value of $25,000?
a. $1,800
b. $500
c. $300
d. $400
Ans: B BT: AN Difficulty: Easy TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
3.How much is interest revenue for 30 days on an 8%, 90-day note receivable with a face value of $6,000?
a. $40
b. $50
c. $90
d. $60
Ans: A BT: AN Difficulty: Easy TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
4.The following computation took place:
$20,000 divided by the future value of a 12-year, 4% ordinary annuity
What question will this computation answer?
a.How much must be invested now so that equal payments can be withdrawn at the end of each year for 12 years?
b.How much must be invested now so that $20,000 is accumulated by the end of the 12th year?
c.How much will be available at the end of the12th year if a payment of $20,000 is deposted now?
d.How much must be deposited at the end of every year so that $20,000 is available at the end of 12 years?
Ans: D BT: AP Difficulty: Easy TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
5.Interest is compounded annually. What is the total amount of interest on a $7,000 note payable at the end of five years at 8%?
a.$3,000
b.$3,285
c.$7,000
d.$3,791
e.$7,100
Ans: B BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
6. Which timing of payments is true for an ordinary annuity?
a. All payments occur at the beginning of the first year.
b.Payments begin immediately and occur once per year on the last day of each year.
c. Payments occur at the end of each period.
d. Payments occur at the beginning of each period.
Ans: C BT: C Difficulty: Easy TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
7.Interest is compounded quarterly on a $10,000 note payable for 1 year at 12%. How much is total interest on the note?
a.$1,338
b.$1,286
c.$1,255
d.$1,506
Ans: C BT: AN Difficulty: ModerateTOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
8.You need to calculate the present value of an amount at 10% compounded quarterly for 2 years. What interest factor will you use?
a.10% for 4 periods
b.2.5% for 8 periods
c.20% for 2 periods
d.10% for 8 periods
Ans: B BT: AP Difficulty: Easy TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
9.Sierra Capital wants to accumulate $100,000 at the end of 10 years to fund retirement benefits for its accountant. Annual deposits will be made into a special account earning 6%, beginning at the end of year 1. To calculate the amount of the equal deposits, use the
a.future value of a annuity due.
b.present value of a single amount.
c.future value of an ordinary annuity.
d.present value of an annuity.
Ans: C BT: AP Difficulty: Easy TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
10.Malcom Corp. will deposit $10,000 annually at the end of each year for five years. Malcom will earn 6%. How much will be accumulated at the end of the 5 years?
a.$65,321
b.$70,399
c.$50,000
d.$56,371
Ans: D BT: AN Difficulty: ModerateTOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
11.Calculate the future value of equal semiannual payments of $9,000 at 12% compounded semiannually for 4 years. The answer is
a.$43,014.
b.$55,888.
c.$89,077.
d.$114,757.
Ans: C BT: AN Difficulty: ModerateTOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
12.Present value is
a. how much today’s money will be worth in the future.
b. the amount of money that must be invested now to produce a known future value.
c. always larger than the future value.
d. the total cost of interest over several years.
Ans: B BT: C Difficulty: Easy TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
13.How much would you deposit today in a savings account that earns 10%, in order that you can make equal annual withdrawals of $1,200 each at the end of each of the next 15 years?
a.$5,013
b.$9,127
c.$19,800
d. $18,000
e.$38,127
Ans: B BT: AN Difficulty: ModerateTOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
14.Miracle Corporation wants to withdraw $60,000 from a savings account at the end of each year for ten years beginning one year from now. The savings earns 10% and is compounded annually. Which one of the following reflects the correct procedure to determine the required initial investment at the beginning of the first year?
a. $60,000 times the present value of a 10-year, 10% ordinary annuity.
b. $60,000 divided by the future value of a 10-year, 10% ordinary annuity.
c. $60,000 times the future value of a 10-year, 10% ordinary annuity.
d. $6,000 divided by the present value of a 10-year, 10% ordinary annuity.
Ans: A BT: AP Difficulty: ModerateTOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
15.An annuity due and an ordinary annuity have equal payments, the same interest rates, and the amount of time between the payments is equal. Which statement is true?
a. The present value of the annuity due is less than the present value of the ordinary annuity.
b. The future value of the annuity due is less than the future value of the ordinary annuity.
c. The future value of the annuity due is equal to the future value of the ordinary annuity.
d. The present value of the annuity due is greater than the present value of the ordinary annuity.
Ans: D BT: AP Difficulty: ModerateTOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
16.An amount is deposited for five years at 6% and is compounded semi-annually. Which interest rate and periods will be used to determine the present value?
a. 8% for 5 periods
b. 3% for 10 periods
c. 3% for 2.5 periods
d.8% for 10 periods
Ans: B BT: AP Difficulty: Easy TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
17.To determine how much must be deposited in the bank today so that you can withdraw 6 annual payments beginning one year from now, which interest factor will you need?
a. Future value of an ordinary annuity of 1
b. Future value of an annuity due of 1
c. Present value of an ordinary annuity of 1
d. Present value of an annuity due of 1
Ans: C BT: AP Difficulty: Easy TOT: 1 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
18.This morning Roseland Inc. purchased a land for a new manufacturing facility at a price of $750,000. However, the seller is financing the transaction and equal quarterly payments will be made starting today, July 1, 2005. The last semi-annual payment will be made on December 31, 2024. The applicable interest rate is 8%. How much is each semi-annual payment?
- $35,365
- $36,435
- $37,893
- None of the above
Ans: B BT: AN Difficulty: ModerateTOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
Calculations:n = 40; I = 4% [$750,000/20.58448 (table 6)] = $36,435
19.Carter Holding Co. intends to purchase a new accounting system, including hardware, software and a complete package of services needed to get the new system up and running. Carter has for options for paying for the new system. Which of the four options is the least costly if the applicable interest rate is 12%?
- Make a lump sum payment of $100,000 today
- Make 10 annual payments of $16,000, starting today
- Make 40 quarterly payments of $4,000, starting today
- Make one lump sum payment of $150,000 four years from today
Ans: C BT: AN Difficulty: ModerateTOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
Calculations:a.(no calculations required) $100,000
b.n = 10; I = 12% [$16,000 * 6.32825 (table 6)] = $101,252
c.n = 40; I = 3% [$4,000 * 23.80822 (table 6)] = $95,233
d.n = 4; I = 12% [$150,000 * .63552 (table 4)] = $95,328
20.Jim Hall invested $12,000 at 8% annual interest and left the money invested without withdrawing any of the interest for 15 years. At the end of the 15 years, Jim withdrew the accumulated amount of money. What amount did Jim withdraw, assuming the investment earns simple interest?
- $14,400
- $26,400
- $22,500
- $13,200
Ans: B BT: AN Difficulty: ModerateTOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
21.Karla Simpson Carson invested $12,000 at 8% annual interest and left the money invested without withdrawing any of the interest for 15 years. At the end of the 15 years, Karla decided to withdraw the accumulated amount of money. Karla has found the following values in various tables related to the time value of money.
Present Value of 1 for 15 periods at 8% 0.31524
Future Value of 1 for 15 periods at 8% 3.17217
Present Value of an Annuity of 1 for 15 periods at 8% 8.55948
Future Value of an Annuity of 1 for 15 periods at 8%27.15211
Which factor would she use to compute the amount she would withdraw, assuming that the investment earns interest compounded annually?
- 0.31524
- 3.17217
- 8.55948
- 27.15211
Ans: B BT: AN Difficulty: ModerateTOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
22.Thomas Young invested $12,000 at 8% annual interest and left the money invested without withdrawing any of the interest for 15 years. At the end of the 15 years, Thomas decided to withdraw the accumulated amount of money. Thomas has found the following values in various tables related to the time value of money.
Present Value of 1 for 15 periods at 8% 0.31524
Future Value of 1 for 15 periods at 8% 3.17217
Present Value of an Annuity of 1 for 15 periods at 8% 8.55948
Future Value of an Annuity of 1 for 15 periods at 8%27.15211
To the closest dollar, which amount would he withdraw, assuming that the investment earns interest compounded annually?
a. $32,583
b. $102,714
c. $15,783
d. $38,066
Ans: D BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
23.Rowan and Lisa Sharp invested $10,000 in a savings account paying 5% annual interest when their son, Jeremy, was born. They also deposited $500 on each of his birthdays until he was 20 (including his 20th birthday). Rowan and Lisa have obtained the following values related to the time value of money to help them with their planning process for their compounded interest decisions.
Present Value of 1 for 20 periods at 5% 0.37689
Future Value of 1 for 20 periods at 5% 2.65330
Present Value of an Annuity of 1 for 20 periods at 5% 12.46221
Future Value of an Annuity of 1 for 20 periods at 5%33.06595
To the closest dollar, how much was in the savings account on his 20th birthday (after the last deposit)?
- $53,066
- $43,066
- $30,000
- $26,533
Ans: B BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
24. Harrison Marshall borrowed $65,000 on June 1, 2009. This amount plus accrued interest at 8% compounded annually is to be repaid on June 1, 2022. Harrison has obtained the following values related to the time value of money to help him with his financing process and compounded interest decisions.
Present Value of 1 for 13 periods at 8% 0.36770
Future Value of 1 for 13 periods at 8% 2.71962
Present Value of an Annuity of 1 for 13 periods at 8% 7.90378
Future Value of an Annuity of 1 for 13 periods at 8%21.49530
To the closest dollar, how much will Harrison have to repay on June 1, 2022?
a. $132,600
b. $310,707
c. $116,375
d. $176,775
Ans: D BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
25. Stranton Company is considering investing in an annuity contract that will return $40,000 annually at the end of each year for 12 years. Stranton has obtained the following values related to the time value of money to help in its planning process and compounded interest decisions.
Present Value of 1 for 12 periods at 9% 0.35554
Future Value of 1 for 12 periods at 9% 2.81267
Present Value of an Annuity of 1 for 12 periods at 9% 7.16073
Future Value of an Annuity of 1 for 12 periods at 9%20.14072
To the closest dollar, what amount should Stranton Company pay for this investment if it earns a 9% return?
a. $497,066
b. $592,507
c. $805,629
d. $286,429
Ans: D BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
26.Morgan Company earns 11% on an investment that pays back $220,000 at the end of each of the next 5 years. Morgan’s finance department has the following values related to the time value of money to help in its planning process and compounded interest decisions.
Present Value of 1 for 5 periods at 11% 0.59345
Future Value of 1 for 5 periods at 11% 1.68506
Present Value of an Annuity of 1 for 5 periods at 11% 3.69590
Future Value of an Annuity of 1 for 5 periods at 11% 6.22780
To the closest dollar, what is the amount Nathan invested to earn the 11% rate of return?
a. $370,713
b. $130,559
c. $59,525
d. $141,935
Ans: B BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
27.Everett Corporation issues a 8%, 9-year mortgage note on January 1, 2009, to obtain financing for new equipment. Land is used as collateral for the note. The terms provide for semiannual installment payments of $131,600. The following values related to the time value of money were available to Everett to help them with their planning process and compounded interest decisions.
Present Value of 1 for 9 periods at 8% 0.50025
Present Value of 1 for 18 periods at 4% 0.49363
Future Value of 1 for 9 periods at 8% 1.99900
Future Value of 1 for 18 periods at 4% 2.02582
Present Value of an Annuity of 1 for 9 periods at 8% 6.24689
Present Value of an Annuity of 1 for 18 periods at 4% 12.65930
Future Value of an Annuity of 1 for 9 periods at 8%12.48756
Future Value of an Annuity of 1 for 18 periods at 4%25.64541
To the closest dollar, what were the cash proceeds received from the issuance of the note?
a. $822,091
b. $947,520
c. $1,665,964
d. $1,643,363
Ans: C BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
28.Gaynor Company is considering purchasing equipment. The equipment will produce the following cash flows: Year 1, $25,000; Year 2, $45,000; Year 3, $60,000. Below is some of the time value of money information that Gaynor has compiled that might help them in their planning and compounded interest decisions.
1 period, 11% / 2 periods, 11% / 3 periods, 11%Present Value of 1 / 0.90090 / 0.81162 / 0.73119
Future Value of 1 / 1.11000 / 1.23210 / 1.36763
Present Value of an Annuity of 1 / 0.90090 / 1.71252 / 2.44371
Future Value of an Annuity of 1 / 1.00000 / 2.12000 / 3.37440
Gaynor requires a minimum rate of return of 11%. To the closest dollar, what is the maximum price Gaynor should pay for the equipment?
a. $317,682
b. $102,917
c. $165,253
d. $246,209
Ans: B BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
29.Clarkson Corporation earns 12% on an investment that will return $900,000, 7 years from now. Below is some of the time value of money information that Clarkson has compiled that might help in planning compounded interest decisions.
Present Value of 1 for 7 periods at 12% 0.45235
Future Value of 1 for 7 periods at 12% 2.21068
Present Value of an Annuity of 1 for 7 periods at 12% 4.56376
Future Value of an Annuity of 1 for 7 periods at 12%10.08901
To the closest dollar, what is the amount Clarkson should invest now to earn this rate of return?
a. $198,961
b. $407,115
c. $756,000
d. $410,738
Ans: B BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
30.Turner Company is considering an investment, which will return a lump sum of $450,000 four years from now. Below is some of the time value of money information that Turner has compiled that might help in planning compounded interest decisions.
Present Value of 1 for 4 periods at 10% 0.68301
Future Value of 1 for 4 periods at 10% 1.46410
Present Value of an Annuity of 1 for 4 periods at 10% 3.16986
Future Value of an Annuity of 1 for 4 periods at 10% 4.64100
To the closest dollar, what amount should Turner Company pay for this investment to earn a 10% return?
a. $270,000
b. $180,000
c. $307,355
d. $356,609
Ans: C BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
31.Mitch has been offered three different contracts for a service he provides.
Contract 1: $9,000 received at the beginning of each year for ten years, compounded at a 6 percent annual rate.
Contract 2: $9,000 received today and $20,000 received ten years from today. The relevant interest rate is 12 percent.
Contract 3: $9,000 received at the end of Years 4, 5, and 6. The relevant annual interest rate is 10 percent.
What is the present value of Contract 1?
a. $66,240.81
b. $118,627.11
c. $70,215.21
d. $125,744.76
Solution: C
Contract 1
Present value= $9,000 Present value factor for an annuity due for i = 6% and n = 10
= $9,000 7.80169 (from Table 6)
= $70,215.21
Ans: C BT: AN Difficulty: ModerateTOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
32.Mitch has been offered three different contracts for a service he provides.
Contract 1: $9,000 received at the beginning of each year for ten years, compounded at a 6 percent annual rate.
Contract 2: $9,000 received today and $20,000 received ten years from today. The relevant interest rate is 12 percent.
Contract 3: $9,000 received at the end of Years 4, 5, and 6. The relevant annual interest rate is 10 percent.
What is the present value of Contract 2?
a. $9,337.13
b. $71,117.00
c. $29,000.00
d.$15,439.40
Solution: D
Contract 2
Present value= $9,000 + ($20,000 Present value factor for i = 12% and n = 10)
=$9,000 + ($20,000 0.32197 from Table 4)
=$15,439.40
Ans: D BT: AN Difficulty: Difficult TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
33.Mitch has been offered three different contracts for a service he provides.
Contract 1: $9,000 received at the beginning of each year for ten years, compounded at a 6 percent annual rate.
Contract 2: $9,000 received today and $20,000 received ten years from today. The relevant interest rate is 12 percent.
Contract 3: $9,000 received at the end of Years 4, 5, and 6. The relevant annual interest rate is 10 percent.
What is the present value of Contract 3?
a. $18,497.15
b.$16,815.56
c. $24,619.68
d. $22,381.52
Solution: B
Contract 3
Present value = ($9,000 Present value factor for an ordinary annuity for i = 10% and n = 3)
Present value factor for i = 10% and n = 3
=($9,000 2.48685 from Table 5) 0.75131 from Table 4
=$16,815.56
Ans: B BT: AN Difficulty: Difficult TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
34.Morgan is considering entering into a contract to sell a building on January 1 in exchange for a note. The note pays a lump sum payment of $300,000 in ten years and ten annual payments of $2,500 beginning on the date of sale (January 1). If the annual interest rate is 10 percent, what is the total present value of the contract?
a. $159,489.92
b. $132,559.55
c. $131,023.42
d. $155,505.55
Solution: B
(1)Present value of annual receipts:
Value=$2,500 Present value factor for an annuity due for i = 10% and n = 10
=$2,500 6.75902 (from Table 6)=$16,897.55
(2)Present value of lump-sum receipt:
Value=$300,000 Present value factor for i =10% and n = 10
=$300,000 0.38554 (from Table 4)=$115,662.00
(3)Total present value:
Value=$16,897.55 + $115,662.00=$132,559.55
Ans: B BT: AN Difficulty: Moderate TOT: 2 min. AACSB: Analytic
AICPA BB: Critical Thinking AICPA FN: Measurement
35.Kaitlin is contemplating investing in Cocoa Beach Tans. She estimates that the company will pay the following dividends per share at the end of the next four years and that the current price of the company’s common stock, which is $100 per share, will remain unchanged.
Dividends / Year 1 / Year 2 / Year 3 / Year 4$6 / $7 / $8 / $9
If Kaitlin wants to earn 12 percent on her investment and plans to sell the investment at the end of the fourth year, how much would she be willing to pay for one share of common stock? (Round all calculations to the nearest cent.)
a. $130.00
b. $119.07
c. $85.90
d. $82.00
Solution: C
Present value= Present value of dividends + Present value of proceeds
=[($60.89286 from Table 4) + ($70.79719 from Table 4) + ($80.71178 from Table 4) + ($90.63552 from Table 4)] + ($100 0.63552 from Table 4)
=$5.36 + $5.58 + $5.69 + $5.72 + $63.55=$85.90