Present & Future Values | Test Bank – Appendix B – 10e

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Student name:__________

FILL IN THE BLANK. Write the word or phrase that best completes each statement or answers the question.
1) _____________ is a borrower’s payment to the owner of an asset for its use.

2) The interest rate is also called the __________________ rate.

3) To calculate present value of an amount, two factors are required: The __________________ and the___________________.

4) A(n) _____________ is a series of equal payments occurring at equal intervals.

5) The future value of a(n) ________________ annuity is the accumulated value of each annuity payment with interest as of the date of the final payment.

ESSAY. Write your answer in the space provided or on a separate sheet of paper.
6) Define interest.

7) Explain the concept of the present value of a single amount.

8) Explain the concept of the future value of a single amount.

9) Explain the concept of the present value of an annuity.

10) Explain the concept of the future value of an annuity.

11) A company needs to have $200,000 in 4 years and will create a fund to ensure 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 4 years? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

12) A company needs to have $150,000 in 5 years and will create a fund to ensure 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 5 years? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

13) 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

14) 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

15) 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

16) Protocol Company has acquired equipment from a dealer that requires equal payments of $12,000 at the end of each of the next five years. This transaction includes interest at 9%, compounded annually. What is the value of the machine today? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

17) A company is creating a fund today by depositing $65,763. The fund will grow to $90,000 after 8 years. What annual interest rate is the company earning on the fund? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

18) 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

19) 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 8 years? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

20) 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 6 years? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

21) Trey has $105,000 now. He has a loan of $175,000 that he must pay at the end of 5 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 5 years? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

22) 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 1. The deposits will earn 10% interest. How much money will Garcia have accumulated at the end of five years to replace the machine? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

23) A company borrows money from the bank by promising to make 6 annual year-end payments of $27,000 each. How much is the company able to borrow if the interest rate is 9%? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

24) A company borrows money from the bank by promising to make 8 semiannual payments of $9,000 each. How much is the company able to borrow if the interest rate is 10% compounded semiannually? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

25) 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

26) 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

27) Giuliani Company 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

28) 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

29) 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

30) 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? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

31) A company is setting up a sinking fund to pay off $8,654,000 in bonds that are due in 7 years. The fund will earn 7% interest, and the company intends to put away a series of equal year-end amounts for 7 years. What is the amount of the annual deposits that the company must make? ( PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Answer Key

Test name: Appendix B Test Bank (Problem Material)

1) Interest

2) Discount

3) [Interest rate (i) or Discount rate, Number of time periods (n)]

4) Annuity

5) Ordinary

6) Interest represents a borrower’s payment to an owner of an asset in exchange for its use.

7) 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.

8) 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.

9) 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.

10) 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.

11) The PV factor on the Present Value of 1 table when n = 4 and i = 7% is 0.7629
Present Value = Future Value × PV Factor
Present Value = $200,000 × 0.7629 = $152,580

12) $152,580

13) The PV factor on the Present Value of 1 table when n = 3 and i = 5% is 0.8638
Present Value = Future Value × PV Factor
Present Value = $25,000 × 0.8638 = $21,595

14) The PV factor on the Present Value of 1 table when n = 4 and i = 5% is 0.8227
Present Value = Future Value × PV Factor
Present Value = $17,000 × 0.8227 = $13,985.90

15) Five years = 10 semiannual periods at an 8% annual interest rate = 4% semiannually
The PV factor on the Present Value of 1 table when n = 10 and i = 4% is 0.6756
Present Value = Future Value × PV Factor
Present Value = $45,000 × 0.6756 = $30,402

16) The PV factor on the Present Value of an Annuity table when n = 5 and i = 9% is 3.8897
Present Value = Future Value × PV of an Annuity Factor
Present Value = $12,000 × 3.8897 = $46,676.40

17) 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%

18) 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
1.4049 is the FV factor on the Future Value table; n = 3; i = 12%

19) 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%

20) The FV factor on the Future Value of 1 table when n = 6 and i = 4% is 1.2653
Future Value = Present Value × FV Factor
Future Value = $46,000 × 1.2653 = $58,203.80

21) 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 × 2 = 10; i = 10/2 = 5%
Goal of $175,000 − Future Value of $171,034.50 = Shortage of $3,965.50

22) 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

23) Present Value of an Annuity = Annuity × PV Factor
Present Value of an Annuity = $27,000 × 4.4859 = $121,119.30
4.4859 is the PV factor on the Present Value of an Annuity table; n = 6; i = 9%

24) 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%

25) Present Value of an Annuity = Annuity × PV Factor
$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 = 9

26) 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

27) 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

28) The FV factor on the Future Value of an Annuity table when n = 10 and i = 10% is 15.9374.
Future Value of an Annuity = Annuity × Interest Factor
Future Value of an Annuity = $15,000 × 15.9374 = $239,061

29) 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

30) The FV factor on the Future Value of an Annuity table when n = 10 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

31) 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%