APPENDIX B PRESENT AND FUTURE VALUES IN ACCOUNTING Present Value of Periods 10 3% 0.9151 0.8885 0.8626 0.8375 0.8131 0.7894 0.7664 0.7441 4% 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 5% 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768 0.6446 0.6139 6% 0.8396 0.7921 0.7473 0.7050 0.6651 0.6274 0.5919 0.5584 7% 0.8163 0.7629 0.7130 0.6663 0.6227 0.5820 0.5439 0.5083 8% 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 9% 0.7722 0.7084 0.6499 0.5963 0.5470 0.5019 0.4604 0.4224 10% 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 12% 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.3606 0.3220 4% 1.1249 1.1699 1.2167 1.2653 1.3159 1.3686 1.4233 1.4802 5% 1.1576 1.2155 1.2763 1.3401 1.4071 1.4775 1.5513 1.6289 6% 1.1910 1.2625 1.3382 1.4185 1.5036 1.5938 1.6895 1.7908 7% 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 8% 1.2597 1.3605 1.4693 1.5869 1.7138 1.8509 1.9990 2.1589 9% 1.2950 1.4116 1.5386 1.6771 1.8280 1.9926 2.1719 2.3674 10% 1.3310 1.4641 1.6105 1.7716 1.9487 2.1436 2.3579 2.5937 12% 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 Future Value of Periods 10 3% 1.0927 1.1255 1.1593 1.1941 1.2299 1.2668 1.3048 1.3439 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-1 Present Value of an Annuity of Periods 10 3% 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302 4% 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 5% 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217 6% 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7% 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236 8% 2.5771 3.3121 3.9927 4.6229 5.2064 5.7466 6.2469 6.7101 9% 2.5313 3.2397 3.8897 4.4859 5.0330 5.5348 5.9952 6.4177 10% 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7950 6.1446 12% 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 Future Value of an Annuity of Periods 10 3% 3.0909 4.1836 5.3091 6.4684 7.6625 8.8923 4% 3.1216 4.2465 5.4163 6.6330 7.8983 9.2142 5% 3.1525 4.3101 5.5256 6.8019 8.1420 9.5491 6% 3.1836 4.3746 5.6371 6.9753 8.3938 9.8975 10.1591 11.4639 10.5828 12.0061 11.0266 12.5779 11.4913 13.1808 7% 3.2149 4.4399 5.7507 7.1533 8.6540 8% 3.2464 4.5061 5.8666 7.3359 8.9228 9% 3.2781 4.5731 5.9847 7.5233 9.2004 10% 3.3100 4.6410 6.1051 7.7156 9.4872 10.2598 11.9780 13.8164 10.6366 12.4876 14.4866 11.0285 13.0210 15.1929 11.4359 13.5795 15.9374 12% 3.3744 4.7793 6.3528 8.1152 10.0890 12.2997 14.7757 17.5487 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-2 True / False Questions Interest is the borrower’s payment to the owner of an asset for its use Answer: True Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Easy Learning Objective: APPB-C1 Topic: Present and Future Value Concepts From the perspective of an account holder, a savings account is a liability with interest Answer: False Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Easy Learning Objective: APPB-C1 Topic: Present and Future Value Concepts An interest rate is also called a discount rate Answer: True Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Easy Learning Objective: APPB-P1 Topic: Present Value of a Single Amount Present and future value computations enable companies to measure or estimate the interest component of holding assets or liabilities over time Answer: True Blooms: Understand AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Medium Learning Objective: APPB-C1 Topic: Present and Future Value Concepts Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-3 The number of periods in a present value calculation may only be expressed in years Answer: False Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Easy Learning Objective: APPB-P1 Topic: Present Value of a Single Amount The present value factor for determining the present value of $6,300 to be received three years from today at 10% interest compounded semiannually is 0.7462 Answer: True Blooms: Understand AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Medium Learning Objective: APPB-P1 Topic: Present Value of a Single Amount The present value of formula is often useful when a borrowed asset must be repaid in full at a later date and the borrower wants to know the worth of the asset at the future date Answer: False Blooms: Understand AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Medium Learning Objective: APPB-P1 Topic: Present Value of a Single Amount In a present value or future value table, the length of one time period may be interpreted as one year, one month, or any other length of time Answer: True Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Easy Learning Objective: APPB-P1 Learning Objective: APPB-P2 Topic: Present Value of a Single Amount Topic: Future Value of a Single Amount Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-4 The present value of $2,000 to be received nine years from today at 8% interest compounded annually is $1,000 Answer: True Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Measurement Difficulty: Medium Learning Objective: APPB-P1 Topic: Present Value of a Single Amount Feedback: Present Value = Future Value * Interest Factor for years @8% Present Value = $2,000 * 0.5002 = $1,000 10 Sandra has a savings account that has accumulated to $50,000 She started with $28,225, and earned interest at 10% compounded annually It took her five years to accumulate the $50,000 Answer: False Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA BB: Critical Thinking AICPA FN: Measurement Difficulty: Hard Learning Objective: APPB-P1 Topic: Present Value of a Single Amount Feedback: PV Factor = Present Value/Future Value PV Factor = $28,225/$50,000 = 0.5645 0.5645 is the present value of factor, 10%, periods 11 Future value can be found if the interest rate (i), the number of periods (n), and the present value (p) are known Answer: True Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Easy Learning Objective: APPB-P2 Topic: Future Value of a Single Amount Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-5 12 The number of periods in a future value calculation may only be expressed in years Answer: False Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Easy Learning Objective: APPB-P2 Topic: Future Value of a Single Amount 13 The future value of $100 compounded semiannually for years at 12% equals $140.49 Answer: False Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Measurement Difficulty: Medium Learning Objective: APPB-P2 Topic: Future Value of a Single Amount Feedback: Future Value = Present Value * Interest Factor Future Value = $100 * 1.4185 = $141.85 14 At an annual interest rate of 8% compounded annually, $5,300 will accumulate to a total of $7,210.65 in years Answer: False Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Measurement Difficulty: Hard Learning Objective: APPB-P2 Topic: Future Value of a Single Amount Feedback: FV Factor = Future Value/Present Value FV Factor = $7,210.65/$5,300 = 1.3605 1.3605 is the future value of $1 factor, 8%, periods 15 An annuity is a series of equal payments occurring at equal intervals Answer: True Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Easy Learning Objective: APPB-P3 Topic: Present Value of an Annuity Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-6 16 The present value of an annuity table can be used to determine the value today of a series of payments to be received in the future Answer: True Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Easy Learning Objective: APPB-P3 Topic: Present Value of an Annuity 17 A series of equal payments made or received at the end of each period is an ordinary annuity Answer: True Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Easy Learning Objective: APPB-P3 Topic: Present Value of an Annuity 18 The present value of $5,000 per year for three years at 12% compounded annually is $12,009 Answer: True Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P3 Topic: Present Value of an Annuity Feedback: 2.4018 is the PV factor on the Present Value of an Annuity table; n = 3; i = 12% Present Value of an Annuity = Annuity * PV Factor Present Value of an Annuity = $5,000 * 2.4018 = $12,009 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-7 19 With deposits of $5,000 at the end of each year, you will have accumulated $38,578 at the end of the sixth year if the annual rate of interest is 10% Answer: True Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P4 Topic: Future Value of an Annuity Feedback: 7.7156 is the FV factor on the Future Value of an Annuity table; n = 6; i = 10% Future Value of an Annuity = Annuity * FV Factor Future Value of an Annuity = $5,000 * 7.7156 = $38,578 7.7156 is the interest factor on the Future Value of an Annuity table; n = 6; i = 10% 20 The future value of an ordinary annuity is the accumulated value of each annuity payment excluding interest as of the date of the final payment Answer: False Blooms: Understand AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-P4 Topic: Future Value of an Annuity Multiple Choice Questions 21 Interest may be defined as: A Time B A borrower’s payment to the owner of an asset for its use C The future value of a present amount D Always a liability E Always an asset Answer: B Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Easy Learning Objective: APPB-C1 Topic: Present and Future Value Concepts Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-8 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-9 22 If we want to know the value of present-day assets at a future date, we can use: A Present value computations B Annuity computations C Interest computations D Future value computations E Earnings computations Answer: D Blooms: Understand AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-C1 Topic: Present and Future Value Concepts 23 Which interest rate column would you use from a present value or future value table for 8% interest compounded quarterly? A 12% B 6% C 3% D 2% E 1% Answer: D Feedback: An 8% annual interest rate is divided by to find the quarterly rate Blooms: Understand AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-P1 Learning Objective: APPB-P2 Topic: Present Value of a Single Amount Topic: Future Value of a Single Amount Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-10 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-24 45 A company has $46,000 today to invest in a fund that will earn 4% compounded annually How much will the fund contain at the end of years? A $58,204 B $47,840 C $58,075 D $57,040 E $62,582 Answer: A Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-P2 Topic: Future Value of a Single Amount Feedback: The FV factor on the Future Value of table when n = and i = 4% is 1.2653 Future Value = Present Value * FV Factor Future Value = $46,000 *1.2653 = $58,204 Short Essay Questions 46 Define interest Answer: Interest represents a borrower’s payment to an owner of an asset in exchange for its use Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Easy Learning Objective: APPB-C1 Topic: Present and Future Value Concepts 47 Explain the concept of the present value of a single amount Answer: The present value of a single amount is used to find today’s value for an amount to be received at a future date It is equal to the amount that can be invested now at the specified interest rate to yield the future value Blooms: Apply AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P1 Topic: Present Value of a Single Amount Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-25 48 Explain the concept of the future value of a single amount Answer: The future value of a single amount is equal to the present amount that would accumulate at a future date at a specified rate of interest Blooms: Apply AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P2 Topic: Future Value of a Single Amount 49 Explain the concept of the present value of an annuity Answer: The present value of an annuity is the amount that can be invested now at the specified interest rate to yield a future series of equal periodic payments Blooms: Apply AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P3 Topic: Present Value of an Annuity 50 Explain the concept of the future value of an annuity Answer: The future value of an annuity is the amount invested today at a specified rate of interest that would accumulate at the date of the final periodic payment Blooms: Apply AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P4 Topic: Future Value of an Annuity Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-26 Problems 51 A company needs to have $200,000 in years, and will create a fund to insure that the $200,000 will be available If it can earn a 7% return compounded annually, how much must the company invest in the fund today to equal the $200,000 at the end of years? Answer: $152,580 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P1 Topic: Present Value of a Single Amount Feedback: The PV factor on the Present Value of table when n = and i = 7% is 0.7629 Present Value = Future Value * PV Factor Present Value = $200,000 * 0.7629 = $152,580 52 A company needs to have $150,000 in years, and will create a fund to insure that the $150,000 will be available If it can earn a 6% return compounded annually, how much must the company invest in the fund today to equal the $150,000 at the end of years? Answer: $112,095 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-P1 Topic: Present Value of a Single Amount Feedback: The PV factor on the Present Value of table when n = and i = 6% is 0.7473 Present Value = Future Value * PV Factor Present Value = $150,000 * 0.7473 = $112,095 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-27 53 Kelsey has a loan that requires a $25,000 lump sum payment at the end of three years The interest rate on the loan is 5%, compounded annually How much did Kelsey borrow today? Answer: $21,595 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-P1 Topic: Present Value of a Single Amount Feedback: The PV factor on the Present Value of table when n = and i = 5% is 0.8638 Present Value = Future Value * PV Factor Present Value = $25,000 * 0.8638 = $21,595 54 Jackson has a loan that requires a $17,000 lump sum payment at the end of four years The interest rate on the loan is 5%, compounded annually How much did Jackson borrow today? Answer: $13,896 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-P1 Topic: Present Value of a Single Amount Feedback: The PV factor on the Present Value of table when n = and i = 5% is 0.8227 Present Value = Future Value * PV Factor Present Value = $17,000 * 0.8227 = $13,986 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-28 55 Mason Company has acquired a machine from a dealer that requires a payment of $45,000 at the end of five years This transaction includes interest at 8%, compounded semiannually What is the value of the machine today? Answer: $30,402 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P1 Topic: Present Value of a Single Amount Feedback: Five years = 10 semiannual periods at an 8% annual interest rate = 4% semiannually The PV factor on the Present Value of table when n = 10 and i = 4% is 0.6756 Present Value = Future Value * PV Factor Present Value = $45,000 * 0.6756 = $30,402 56 Protocol Company has acquired equipment from a dealer that requires equal payments of $12,000 at the end of the next five years This transaction includes interest at 9%, compounded annually What is the value of the machine today? Answer: $46,676 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P3 Topic: Present Value of an Annuity Feedback: The PV factor on the Present Value of an Annuity table when n = and i = 9% is 3.8897 Present Value = Future Value * PV of an Annuity Factor Present Value = $12,000 * 3.8897 = $46,676 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-29 57 A company is creating a fund today by depositing $65,763 The fund will grow to $90,000 after years What annual interest rate is the company earning on the fund? Answer: 4% Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P1 Learning Objective: APPB-P2 Topic: Present Value of a Single Amount Topic: Future Value of a Single Amount Feedback: Present Value = Future Value * PV Factor $65,763 = $90,000 * PV Factor; PV Factor = 0.7307 0.7307 is the PV factor on the Present Value table; n = 8; i = 4% Or, Alternative Solution: Future Value = Present Value * FV Factor $90,000 = $65,763 * FV Factor; FV Factor = 1.3686 1.3686 is the FV factor on the Future Value table; n = 8; i = 4% 58 A company is setting aside $21,354 today, and wishes to have $30,000 at the end of three years for a down payment on a piece of property What interest rate must the company earn? Answer: 12% Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P1 Learning Objective: APPB-P2 Topic: Present Value of a Single Amount Topic: Future Value of a Single Amount Feedback: Present Value = Future Value * PV Factor $21,354 = $30,000 * PV Factor; PV Factor = 0.7118 0.7118 is the PV factor on the Present Value table; n = 3; i = 12% Or, Alternative Solution: Future Value = Present Value * FV Factor $30,000 = $21,354 * FV Factor; FV Factor = 1.4049 1.3605 is the FV factor on the Future Value table; n = 3; i = 12% Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-30 59 A company has $50,000 today to invest in a fund that will earn 7% How much will the fund contain at the end of years? Answer: $85,910 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P2 Topic: Future Value of a Single Amount Feedback: Future Value = Present Value * FV Factor Future Value = $50,000 *1.7182 = $85,910 1.7182 is the FV factor on the Future Value table; n = 8; i = 7% 60 A company has $46,000 today to invest in a fund that will earn 4% compounded annually How much will the fund contain at the end of years? Answer: $58,204 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-P2 Topic: Future Value of a Single Amount Feedback: The FV factor on the Future Value of table when n = and i = 4% is 1.2653 Future Value = Present Value * FV Factor Future Value = $46,000 *1.2653 = $58,204 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-31 61 Trey has $105,000 now He has a loan of $175,000 that he must pay at the end of years He can invest his $105,000 at 10% interest compounded semiannually Will Trey have enough to pay his loan at the end of the years? Answer: No, Trey will be $3,965.50 short of his goal of $175,000 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P2 Topic: Future Value of a Single Amount Feedback: Future Value = Present Value * Interest Factor Future Value = $105,000 * 1.6289 = $171,034.50 1.6289 is the interest factor on the Future Value table; n =5 * = 10; i = 10/2 = 5% Goal of $175,000 – Future Value of $171,034.50 = Shortage of $3,965.50 62 Garcia Brass Fixtures is planning on replacing one of its machines in five years by making a one-time deposit of $20,000 today and four yearly contributions of $5,000 beginning at the end of year The deposits will earn 10% interest How much money will Garcia have accumulated at the end of five years to replace the machine? Answer: $55,415 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P2 Learning Objective: APPB-P4 Topic: Future Value of a Single Amount Topic: Future Value of an Annuity Feedback: Future Value = Present Value * FV Factor Future Value = $20,000 * 1.6105 = $32,210 1.6105 is the FV factor on the Future Value table; n = 5; i = 10% Future Value of an Annuity = Annuity * FV Factor Future Value of an Annuity = $5,000 * 4.6410 = $23,205 4.6410 is the FV factor on the Future Value of an Annuity table; n = 4; i = 10% Accumulated Funds = $32,210 + $23,205 = $55,415 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-32 63 A company borrows money from the bank by promising to make annual year-end payments of $27,000 each How much is the company able to borrow if the interest rate is 9%? Answer: $121,119 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P3 Topic: Present Value of an Annuity Feedback: Present Value of an Annuity = Annuity * PV Factor Present Value of an Annuity = $27,000 * 4.4859 = $121,119 4.4859 is the PV factor on the Present Value of an Annuity table; n = 6; i = 9% 64 A company borrows money from the bank by promising to make semiannual payments of $9,000 each How much is the company able to borrow if the interest rate is 10% compounded semiannually? Answer: $58,168.80 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-P3 Topic: Present Value of an Annuity Feedback: Present Value of an Annuity = Annuity * PV Factor Present Value of an Annuity = $9,000 * 6.4632 = $58,168.80 6.4632 is the PV factor on the Present Value of an Annuity table; n = 8; i = 10%/2 = 5% 65 When you reach retirement age, you will have one fund of $100,000 from which you are going to make annual withdrawals of $14,702 The fund will earn 6% per year For how many years will you be able to draw an even amount of $14,702? Answer: Nine Years Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P3 Topic: Present Value of an Annuity Feedback: Present Value of an Annuity = Annuity * PV Factor Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-33 $100,000 = $14,702 * PV Factor; PV Factor = 6.8017 6.8017 is the PV factor on the Present Value of an Annuity table; i = 6%; n = 66 City Peewee League borrowed $883,212, and must make annual year-end payments of $120,000 each If City’s interest rate is 6%, how many years will it take to pay off the loan? Answer: Ten Years Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P3 Topic: Present Value of an Annuity Feedback: Present Value of an Annuity = Annuity * Interest Factor $883,212 = $120,000 * Interest Factor; Interest Factor = 7.3601 7.3601 is the interest factor on the Present Value of an Annuity table; i = 6%; n =10 67 Giuliani Co lends $524,210 to Craig Corporation The terms of the loan require that Craig make six semiannual period-end payments of $100,000 each What semiannual interest rate is Craig paying on the loan? Answer: 4% semi-annual rate Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P3 Topic: Present Value of an Annuity Feedback: Present Value of an Annuity = Annuity * Interest Factor $524,210 = $100,000 * Interest Factor; Interest Factor = 5.2421 5.2421 is the interest factor on the Present Value of an Annuity table; n = 6; i = 4% Craig is paying a 4% semi-annual rate or an 8% annual rate of interest Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-34 68 A company is beginning a savings plan It will be saving $15,000 per year for the next 10 years How much will the company have accumulated after the tenth year-end deposit, assuming the fund earns 10% interest? Answer: $239,055 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-4 Topic: Future Value of an Annuity Feedback: The FV factor on the Future Value of an Annuity table when n = 10 and i = 10% is 15.937 Future Value of an Annuity = Annuity * Interest Factor Future Value of an Annuity = $15,000 * 15.937 = $239,055 69 A company is beginning a savings plan to purchase a new building It will be saving $43,000 per year for the next 10 years How much will the company have accumulated after the tenth year-end deposit, assuming the fund earns 9% interest? Answer: $653,294.70 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-4 Topic: Future Value of an Annuity Feedback: The FV factor on the Future Value of an Annuity table when n = 10 and i = 9% is 15.1929 Future Value of an Annuity = Annuity * FV Factor Future Value of an Annuity = $43,000 * 15.1929 = $653,294.70 70 You are little late planning your retirement, but are looking forward to retiring in 10 years You expect to save $6,000 a year at an annual rate of 8% How much will you have accumulated when you retire? Answer: $86,919.60 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-P4 Topic: Future Value of an Annuity Feedback: The FV factor on the Future Value of an Annuity table when n = 10 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-35 and i = 8% is 14.4866 Future Value of an Annuity = Annuity * FV Factor Future Value of an Annuity = $6,000 * 14.4866 = $86,919.60 71 A company is setting up a sinking fund to pay off $8,654,000 in bonds that are due in years The fund will earn 7% interest, and the company intends to put away a series of equal year-end amounts for years What is the amount of the annual deposits that the company must make? Answer: $1,000,000 Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P4 Topic: Future Value of an Annuity Feedback: Future Value of an Annuity = Annuity * Interest Factor $8,654,000 = Annuity * 8.6540; Annuity = $1,000,000 8.6540 is the interest factor on the Future Value of an Annuity table; n = 7; i = 7% Fill-in-the-Blank Questions 72 _ is a borrower’s payment to the owner of an asset for its use Answer: Interest Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Easy Learning Objective: APPB-C1 Topic: Present and Future Value Concepts 73 The interest rate is also called the rate Answer: Discount Blooms: Understand AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Medium Learning Objective: APPB-C1 Topic: Present and Future Value Concepts Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-36 Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-37 74 To calculate present value of an amount, two factors are required: The and the _ Answer: Interest rate (i); Number of time periods (n) Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Easy Learning Objective: APPB-P1 Topic: Present Value of a Single Amount 75 An _ is a series of equal payments occurring at equal intervals Answer: Annuity Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Easy Learning Objective: APPB-P3 Topic: Present Value of an Annuity 76 The future value of an annuity is the accumulated value of each annuity payment with interest as of the date of the final payment Answer: Ordinary Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Decision Making Difficulty: Easy Learning Objective: APPB-P4 Topic: Future Value of an Annuity Copyright © 2016 McGraw-Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw-Hill Education B-38 ... $5,000? A 5% B 8% C 10% D 12% E 15% Answer: B Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P1 Learning Objective: APPB-P2 Topic:... years B years C years D years E 10 years Answer: C Blooms: Apply AACSB: Analytic AICPA BB: Industry AICPA FN: Decision Making Difficulty: Hard Learning Objective: APPB-P1 Learning Objective: APPB-P2... length of time Answer: True Blooms: Remember AACSB: Communication AICPA BB: Industry AICPA FN: Measurement Difficulty: Easy Learning Objective: APPB-P1 Learning Objective: APPB-P2 Topic: Present Value