Question 1

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.
Difficulty: 3 Hard
Topic: Future Value of an Annuity
Learning Objective: B-P4 Apply future value concepts to an annuity by using interest tables.
Bloom's: Apply
AACSB/Accessibility: Communication / Keyboard Navigation
AICPA: BB Industry; FN Decision Making
Present Value of 1
 
$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \
\hline 3 & 0.9151 & 0.8890 & 0.8638 & 0.8396 & 0.8163 & 0.7938 & 0.7722 & 0.7513 & 0.7118 \
\hline 4 & 0.8885 & 0.8548 & 0.8227 & 0.7921 & 0.7629 & 0.7350 & 0.7084 & 0.6830 & 0.6355 \\hline 5 & 0.8626 & 0.8219 & 0.7835 & 0.7473 & 0.7130 & 0.6806 & 0.6499 & 0.6209 & 0.5674 \
\hline 6 & 0.8375 & 0.7903 & 0.7462 & 0.7050 & 0.6663 & 0.6302 & 0.5963 & 0.5645 & 0.5066 \
\hline 7 & 0.8131 & 0.7599 & 0.7107 & 0.6651 & 0.6227 & 0.5835 & 0.5470 & 0.5132 & 0.4523 \\hline 8 & 0.7894 & 0.7307 & 0.6768 & 0.6274 & 0.5820 & 0.5403 & 0.5019 & 0.4665 & 0.4039 \
\hline 9 & 0.7664 & 0.7026 & 0.6446 & 0.5919 & 0.5439 & 0.5002 & 0.4604 & 0.4241 & 0.3606 \
\hline 10 & 0.7441 & 0.6756 & 0.6139 & 0.5584 & 0.5083 & 0.4632 & 0.4224 & 0.3855 & 0.3220 \
\hline
\end{array}$ Future Value of 1

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \
\hline 3 & 1.0927 & 1.1249 & 1.1576 & 1.1910 & 1.2250 & 1.2597 & 1.2950 & 1.3310 & 1.4049 \
\hline 4 & 1.1255 & 1.1699 & 1.2155 & 1.2625 & 1.3108 & 1.3605 & 1.4116 & 1.4641 & 1.5735 \\hline 5 & 1.1593 & 1.2167 & 1.2763 & 1.3382 & 1.4026 & 1.4693 & 1.5386 & 1.6105 & 1.7623 \
\hline 6 & 1.1941 & 1.2653 & 1.3401 & 1.4185 & 1.5007 & 1.5869 & 1.6771 & 1.7716 & 1.9738 \
\hline 7 & 1.2299 & 1.3159 & 1.4071 & 1.5036 & 1.6058 & 1.7138 & 1.8280 & 1.9487 & 2.2107 \
\hline 8 & 1.2668 & 1.3686 & 1.4775 & 1.5938 & 1.7182 & 1.8509 & 1.9926 & 2.1436 & 2.4760 \\hline 9 & 1.3048 & 1.4233 & 1.5513 & 1.6895 & 1.8385 & 1.9990 & 2.1719 & 2.3579 & 2.7731 \
\hline 10 & 1.3439 & 1.4802 & 1.6289 & 1.7908 & 1.9672 & 2.1589 & 2.3674 & 2.5937 & 3.1058 \
\hline
\end{array}$ Present Value of an Annuity of 1

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \
\hline 3 & 2.8286 & 2.7751 & 2.7232 & 2.6730 & 2.6243 & 2.5771 & 2.5313 & 2.4869 & 2.4018 \\hline 4 & 3.7171 & 3.6299 & 3.5460 & 3.4651 & 3.3872 & 3.3121 & 3.2397 & 3.1699 & 3.0373 \
\hline 5 & 4.5797 & 4.4518 & 4.3295 & 4.2124 & 4.1002 & 3.9927 & 3.8897 & 3.7908 & 3.6048 \
\hline 6 & 5.4172 & 5.2421 & 5.0757 & 4.9173 & 4.7665 & 4.6229 & 4.4859 & 4.3553 & 4.1114 \
\hline 7 & 6.2303 & 6.0021 & 5.7864 & 5.5824 & 5.3893 & 5.2064 & 5.0330 & 4.8684 & 4.5638 \\hline 8 & 7.0197 & 6.7327 & 6.4632 & 6.2098 & 5.9713 & 5.7466 & 5.5348 & 5.3349 & 4.9676 \
\hline 9 & 7.7861 & 7.4353 & 7.1078 & 6.8017 & 6.5152 & 6.2469 & 5.9952 & 5.7950 & 5.3282 \
\hline 10 & 8.5302 & 8.1109 & 7.7217 & 7.3601 & 7.0236 & 6.7101 & 6.4177 & 6.1446 & 5.6502 \
\hline
\end{array}$ Future Value of an Annuity of 1

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \
\hline 3 & 3.0909 & 3.1216 & 3.1525 & 3.1836 & 3.2149 & 3.2464 & 3.2781 & 3.3100 & 3.3744 \
\hline 4 & 4.1836 & 4.2465 & 4.3101 & 4.3746 & 4.4399 & 4.5061 & 4.5731 & 4.6410 & 4.7793 \\hline 5 & 5.3091 & 5.4163 & 5.5256 & 5.6371 & 5.7507 & 5.8666 & 5.9847 & 6.1051 & 6.3528 \
\hline 6 & 6.4684 & 6.6330 & 6.8019 & 6.9753 & 7.1533 & 7.3359 & 7.5233 & 7.7156 & 8.1152 \
\hline 7 & 7.6625 & 7.8983 & 8.1420 & 8.3938 & 8.6540 & 8.9228 & 9.2004 & 9.4872 & 10.0890 \\hline 8 & 8.8923 & 9.2142 & 9.5491 & 9.8975 & 10.2598 & 10.6366 & 11.0285 & 11.4359 & 12.2997 \
\hline 9 & 10.1591 & 10.5828 & 11.0266 & 11.4913 & 11.9780 & 12.4876 & 13.0210 & 13.5795 & 14.7757 \
\hline 10 & 11.4639 & 12.0061 & 12.5779 & 13.1808 & 13.8164 & 14.4866 & 15.1929 & 15.9374 & 17.5487 \
\hline
\end{array}$
-A company needs to have $200,000 in 4 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 4 years?

Accepted Answer

The answer of Answer: The future value of an annuity...

Question 2

The Masterson family is setting up a vacation fund, and they plan on depositing $1,000 per quarter in an investment that will pay 12% annual interest. What amount will they have available for their vacation at the end of 2 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $8,000.00
B) $8,960.00
C) $8,892.30
D) $8,240.00
E) $8,487.20

Accepted Answer

Two years = 8 semiannual periods and a 12% annual interest rate = 3% semiannually
The FV factor on the Future Value of an Annuity table when n = 8; i = 3% is 8.8923
Annuity × FV Factor = Future Value of an Annuity
$1,000 × 8.8923 = $8,892.30

Question 3

Explain the concept of the present value of an annuity.

Accepted Answer

The answer of Explain the concept of the present value...

Question 4

Define interest.

Accepted Answer

The answer of Define interest....

Question 5

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

Accepted Answer

The answer of Explain the concept of the future value...

Question 6

A company is considering an investment that will return $22,000 semiannually at the end of each semiannual period for 4 years. If the company requires an annual return of 10%, what is the maximum amount it is willing to pay for this investment? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) Not more than $69,738
B) Not more than $139,476
C) Not more than $88,000
D) Not more than $142,190
E) Not more than $176,000

Accepted Answer

The PV factor on the Present Value of an Annuity table when n = 8 and i = 5% is 6.4632.
Present Value of an Annuity = Annuity × PV Factor
Present Value of an Annuity = $22,000 × 6.4632 = $142,190

Question 7

Chris wants to accumulate $100,000 in 5 years. He plans on making equal semiannual deposits into an investment account that earns 12% semiannually in order to reach his goal. How much must Chris invest every six months? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $24,331.19
B) $10,153.39
C) $13,586.77
D) $10,000.00
E) $7,586.79

Accepted Answer

Future Value of an Annuity = Annuity × Interest Factor
$100,000 = Annuity × Interest Factor Future Value of an Annuity table; i = 6%; n = 10
$100,000 = Annuity × 13.1808
Annuity = $100,000 / 13.1808 = $7,586.79

Question 8

An individual is planning to set-up an education fund for his grandchildren. He plans to invest $10,000 annually at the end of each year. He expects to withdraw money from the fund at the end of 10 years and expects to earn an annual return of 8%. What will be the total value of the fund at the end of 10 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $46,320
B) $67,107
C) $100,000
D) $144,866
E) $215,890

Accepted Answer

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 = $10,000 × 14.4866 = $144,866

Question 9

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

Accepted Answer

The answer of Explain the concept of the present value...

Question 10

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?

Accepted Answer

The answer of Kelsey has a loan that requires a...

Question 11

Marc Lewis expects an investment of $25,000 to return $6,595 annually. His investment is earning 10% per year. How many annual payments will he receive? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) Three payments
B) Five payments
C) Six payments
D) Four payments
E) More than six payments

Accepted Answer

Present Value of an Annuity = Annuity × PV Factor
$25,000 = $6,595 × PV Factor; PV Factor = 3.7908
3.7908 is the PV factor on the Present Value of an Annuity table; i = 10%; n = 5

Question 12

An individual is planning to set-up an education fund for her daughter. She plans to invest $7,000 annually at the end of each year. She expects to withdraw money from the fund at the end of 9 years and expects to earn an annual return of 8%. What will be the total value of the fund at the end of 9 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $87,413
B) $68,040
C) $50,400
D) $126,000
E) $45,360

Accepted Answer

The FV factor on the Future Value of an Annuity table when n = 9 and i = 8% is 12.4876.
Future Value of an Annuity = Annuity × FV Factor
Future Value of an Annuity = $7,000 × 12.4876 = $87,413

Question 13

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.
Difficulty: 3 Hard
Topic: Future Value of an Annuity
Learning Objective: B-P4 Apply future value concepts to an annuity by using interest tables.
Bloom's: Apply
AACSB/Accessibility: Communication / Keyboard Navigation
AICPA: BB Industry; FN Decision Making
Present Value of 1
 
$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \
\hline 3 & 0.9151 & 0.8890 & 0.8638 & 0.8396 & 0.8163 & 0.7938 & 0.7722 & 0.7513 & 0.7118 \
\hline 4 & 0.8885 & 0.8548 & 0.8227 & 0.7921 & 0.7629 & 0.7350 & 0.7084 & 0.6830 & 0.6355 \\hline 5 & 0.8626 & 0.8219 & 0.7835 & 0.7473 & 0.7130 & 0.6806 & 0.6499 & 0.6209 & 0.5674 \
\hline 6 & 0.8375 & 0.7903 & 0.7462 & 0.7050 & 0.6663 & 0.6302 & 0.5963 & 0.5645 & 0.5066 \
\hline 7 & 0.8131 & 0.7599 & 0.7107 & 0.6651 & 0.6227 & 0.5835 & 0.5470 & 0.5132 & 0.4523 \\hline 8 & 0.7894 & 0.7307 & 0.6768 & 0.6274 & 0.5820 & 0.5403 & 0.5019 & 0.4665 & 0.4039 \
\hline 9 & 0.7664 & 0.7026 & 0.6446 & 0.5919 & 0.5439 & 0.5002 & 0.4604 & 0.4241 & 0.3606 \
\hline 10 & 0.7441 & 0.6756 & 0.6139 & 0.5584 & 0.5083 & 0.4632 & 0.4224 & 0.3855 & 0.3220 \
\hline
\end{array}$ Future Value of 1

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \
\hline 3 & 1.0927 & 1.1249 & 1.1576 & 1.1910 & 1.2250 & 1.2597 & 1.2950 & 1.3310 & 1.4049 \
\hline 4 & 1.1255 & 1.1699 & 1.2155 & 1.2625 & 1.3108 & 1.3605 & 1.4116 & 1.4641 & 1.5735 \\hline 5 & 1.1593 & 1.2167 & 1.2763 & 1.3382 & 1.4026 & 1.4693 & 1.5386 & 1.6105 & 1.7623 \
\hline 6 & 1.1941 & 1.2653 & 1.3401 & 1.4185 & 1.5007 & 1.5869 & 1.6771 & 1.7716 & 1.9738 \
\hline 7 & 1.2299 & 1.3159 & 1.4071 & 1.5036 & 1.6058 & 1.7138 & 1.8280 & 1.9487 & 2.2107 \
\hline 8 & 1.2668 & 1.3686 & 1.4775 & 1.5938 & 1.7182 & 1.8509 & 1.9926 & 2.1436 & 2.4760 \\hline 9 & 1.3048 & 1.4233 & 1.5513 & 1.6895 & 1.8385 & 1.9990 & 2.1719 & 2.3579 & 2.7731 \
\hline 10 & 1.3439 & 1.4802 & 1.6289 & 1.7908 & 1.9672 & 2.1589 & 2.3674 & 2.5937 & 3.1058 \
\hline
\end{array}$ Present Value of an Annuity of 1

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \
\hline 3 & 2.8286 & 2.7751 & 2.7232 & 2.6730 & 2.6243 & 2.5771 & 2.5313 & 2.4869 & 2.4018 \\hline 4 & 3.7171 & 3.6299 & 3.5460 & 3.4651 & 3.3872 & 3.3121 & 3.2397 & 3.1699 & 3.0373 \
\hline 5 & 4.5797 & 4.4518 & 4.3295 & 4.2124 & 4.1002 & 3.9927 & 3.8897 & 3.7908 & 3.6048 \
\hline 6 & 5.4172 & 5.2421 & 5.0757 & 4.9173 & 4.7665 & 4.6229 & 4.4859 & 4.3553 & 4.1114 \
\hline 7 & 6.2303 & 6.0021 & 5.7864 & 5.5824 & 5.3893 & 5.2064 & 5.0330 & 4.8684 & 4.5638 \\hline 8 & 7.0197 & 6.7327 & 6.4632 & 6.2098 & 5.9713 & 5.7466 & 5.5348 & 5.3349 & 4.9676 \
\hline 9 & 7.7861 & 7.4353 & 7.1078 & 6.8017 & 6.5152 & 6.2469 & 5.9952 & 5.7950 & 5.3282 \
\hline 10 & 8.5302 & 8.1109 & 7.7217 & 7.3601 & 7.0236 & 6.7101 & 6.4177 & 6.1446 & 5.6502 \
\hline
\end{array}$ Future Value of an Annuity of 1

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \
\hline 3 & 3.0909 & 3.1216 & 3.1525 & 3.1836 & 3.2149 & 3.2464 & 3.2781 & 3.3100 & 3.3744 \
\hline 4 & 4.1836 & 4.2465 & 4.3101 & 4.3746 & 4.4399 & 4.5061 & 4.5731 & 4.6410 & 4.7793 \\hline 5 & 5.3091 & 5.4163 & 5.5256 & 5.6371 & 5.7507 & 5.8666 & 5.9847 & 6.1051 & 6.3528 \
\hline 6 & 6.4684 & 6.6330 & 6.8019 & 6.9753 & 7.1533 & 7.3359 & 7.5233 & 7.7156 & 8.1152 \
\hline 7 & 7.6625 & 7.8983 & 8.1420 & 8.3938 & 8.6540 & 8.9228 & 9.2004 & 9.4872 & 10.0890 \\hline 8 & 8.8923 & 9.2142 & 9.5491 & 9.8975 & 10.2598 & 10.6366 & 11.0285 & 11.4359 & 12.2997 \
\hline 9 & 10.1591 & 10.5828 & 11.0266 & 11.4913 & 11.9780 & 12.4876 & 13.0210 & 13.5795 & 14.7757 \
\hline 10 & 11.4639 & 12.0061 & 12.5779 & 13.1808 & 13.8164 & 14.4866 & 15.1929 & 15.9374 & 17.5487 \
\hline
\end{array}$
-A company needs to have $150,000 in 5 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 5 years?

Accepted Answer

The answer of Answer: The future value of an annuity...

Question 14

Pelcher Company acquires a machine by issuing a note that requires semiannual payments of $4,000 for 3 years. The interest rate on the note is 10% compounded semiannually. What is the cost of the machine? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $17,421.20
B) $20,302.80
C) $10,892.80
D) $ 9.947.41
E) $24,000.00

Accepted Answer

The PV factor on the Present Value of an Annuity table when n = 6 and i = 5% is 5.0757.
Present Value of an Annuity = Annuity × PV Factor
Present Value of an Annuity = $4,000 × 5.0757 = $20,302.80.

Question 15

A company needs to have $150,000 in 5 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 5 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $141,000
B) $112,095
C) $100,000
D) $45,000
E) $105,000

Accepted Answer

The PV factor on the Present Value of 1 table when n = 5 and i = 6% is 0.7473
Present Value = Future Value × PV Factor
Present Value = $150,000 × 0.7473 = $112,095

Question 16

What amount can you borrow if you make seven semiannual payments of $4,000 at an 8% annual rate of interest? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $28,000.00
B) $25,760.00
C) $31,049.00
D) $24,008.40
E) $35,691.20

Accepted Answer

An 8% annual interest rate = 4% semiannually
The PV factor on the Present Value of an Annuity table when n = 7 and i = 4% is 6.0021.
Present Value of an Annuity = Annuity × PV Factor
Present Value of an Annuity = $4,000 × 6.0021 = $24,008.40

Question 17

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.)
A) $16,150
B) $13,600
C) $11,504
D) $13,986
E) $15,343

Accepted Answer

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 = $13,986

Question 18

What amount can you borrow if you make six quarterly payments of $4,000 at a 12% annual rate of interest? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $24,838.00
B) $21,668.80
C) $31,049.00
D) $40,000.00
E) $44,800.00

Accepted Answer

The PV factor on the Present Value of an Annuity table when n = 6 and i = 3% is 5.4172.
Present Value of an Annuity = Annuity × PV Factor
Present Value of an Annuity = $4,000 × 5.4172 = $21,668.80

Question 19

Clara is setting up a retirement fund, and she plans on depositing $5,000 per year in an investment that will pay 7% annual interest. How long will it take her to reach her retirement goal of $69,082? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) 13.816 years
B) 0.072 years
C) 10 years
D) 20 years
E) 5 years

Accepted Answer

Future Value of an Annuity = Annuity × Interest Factor
$69,082 = $5,000 × Interest Factor; Interest Factor = 13.8164
13.8164 is the interest factor on the Future Value of an Annuity table; i = 7%; n = 10

Question 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.)
A) $58,204
B) $47,840
C) $58,075
D) $57,040
E) $62,582

Accepted Answer

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 = $58,204

Quiz 14: Time Value of Money

Explain the concept of the present value of an annuity.

Define interest.

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

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

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?

Marc Lewis expects an investment of $25,000 to return $6,595 annually. His investment is earning 10% per year. How many annual payments will he receive? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

What amount can you borrow if you make seven semiannual payments of $4,000 at an 8% annual rate of interest? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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.)

What amount can you borrow if you make six quarterly payments of $4,000 at a 12% annual rate of interest? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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.)