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Exam 14: Time Value of Money

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Question 41

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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

F) A) and C)
G) A) and B)

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Question 42

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________ is a borrower's payment to the owner of an asset for its use.

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Question 43

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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.)

Russell Company has acquired a building with a loan that requires payments of $20,000 every six months for 5 years. The annual interest rate on the loan is 12%. What is the present value of the building? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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?

Present and future value computations enable companies to measure or estimate the interest component of holding assets or liabilities over time.

A company expects to invest $5,000 today at 12% annual interest and plans to receive $15,529 at the end of the investment period. How many years will elapse before the company accumulates the $15,529? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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

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?

Which interest rate column would you use from a present value or future value table for 8% interest compounded quarterly?

Cody invests $1,800 per year from his summer wages at a 4% annual interest rate. He plans to take a European vacation at the end of 4 years when he graduates from college. How much will he have available to spend on his vacation? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Future Value of an Annuity of 1 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 $\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \\\hline 3 & 2.8286 & 2.7751 & 2.7232 & 2.6730 & 2.6243 & 2.5771 & 2.5313 & 2.4869 & 2.4018 \\\hline 4 & 3.7171 & 3.6299 & 3.5460 & 3.4651 & 3.3872 & 3.3121 & 3.2397 & 3.1699 & 3.0373 \\\hline 5 & 4.5797 & 4.4518 & 4.3295 & 4.2124 & 4.1002 & 3.9927 & 3.8897 & 3.7908 & 3.6048 \\\hline 6 & 5.4172 & 5.2421 & 5.0757 & 4.9173 & 4.7665 & 4.6229 & 4.4859 & 4.3553 & 4.1114 \\\hline 7 & 6.2303 & 6.0021 & 5.7864 & 5.5824 & 5.3893 & 5.2064 & 5.0330 & 4.8684 & 4.5638 \\\hline 8 & 7.0197 & 6.7327 & 6.4632 & 6.2098 & 5.9713 & 5.7466 & 5.5348 & 5.3349 & 4.9676 \\\hline 9 & 7.7861 & 7.4353 & 7.1078 & 6.8017 & 6.5152 & 6.2469 & 5.9952 & 5.7950 & 5.3282 \\\hline 10 & 8.5302 & 8.1109 & 7.7217 & 7.3601 & 7.0236 & 6.7101 & 6.4177 & 6.1446 & 5.6502 \\\hline\end{array}$ $\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \\\hline 3 & 3.0909 & 3.1216 & 3.1525 & 3.1836 & 3.2149 & 3.2464 & 3.2781 & 3.3100 & 3.3744 \\\hline 4 & 4.1836 & 4.2465 & 4.3101 & 4.3746 & 4.4399 & 4.5061 & 4.5731 & 4.6410 & 4.7793 \\\hline 5 & 5.3091 & 5.4163 & 5.5256 & 5.6371 & 5.7507 & 5.8666 & 5.9847 & 6.1051 & 6.3528 \\\hline 6 & 6.4684 & 6.6330 & 6.8019 & 6.9753 & 7.1533 & 7.3359 & 7.5233 & 7.7156 & 8.1152 \\\hline 7 & 7.6625 & 7.8983 & 8.1420 & 8.3938 & 8.6540 & 8.9228 & 9.2004 & 9.4872 & 10.0890 \\\hline 8 & 8.8923 & 9.2142 & 9.5491 & 9.8975 & 10.2598 & 10.6366 & 11.0285 & 11.4359 & 12.2997 \\\hline 9 & 10.1591 & 10.5828 & 11.0266 & 11.4913 & 11.9780 & 12.4876 & 13.0210 & 13.5795 & 14.7757 \\\hline 10 & 11.4639 & 12.0061 & 12.5779 & 13.1808 & 13.8164 & 14.4866 & 15.1929 & 15.9374 & 17.5487 \\\hline\end{array}$ -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.

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?

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

Future Value of an Annuity of 1 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 $\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \\\hline 3 & 2.8286 & 2.7751 & 2.7232 & 2.6730 & 2.6243 & 2.5771 & 2.5313 & 2.4869 & 2.4018 \\\hline 4 & 3.7171 & 3.6299 & 3.5460 & 3.4651 & 3.3872 & 3.3121 & 3.2397 & 3.1699 & 3.0373 \\\hline 5 & 4.5797 & 4.4518 & 4.3295 & 4.2124 & 4.1002 & 3.9927 & 3.8897 & 3.7908 & 3.6048 \\\hline 6 & 5.4172 & 5.2421 & 5.0757 & 4.9173 & 4.7665 & 4.6229 & 4.4859 & 4.3553 & 4.1114 \\\hline 7 & 6.2303 & 6.0021 & 5.7864 & 5.5824 & 5.3893 & 5.2064 & 5.0330 & 4.8684 & 4.5638 \\\hline 8 & 7.0197 & 6.7327 & 6.4632 & 6.2098 & 5.9713 & 5.7466 & 5.5348 & 5.3349 & 4.9676 \\\hline 9 & 7.7861 & 7.4353 & 7.1078 & 6.8017 & 6.5152 & 6.2469 & 5.9952 & 5.7950 & 5.3282 \\\hline 10 & 8.5302 & 8.1109 & 7.7217 & 7.3601 & 7.0236 & 6.7101 & 6.4177 & 6.1446 & 5.6502 \\\hline\end{array}$ $\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline\text { Periods } & 3 \% & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% & 9 \% & 10 \% & 12 \% \\\hline 3 & 3.0909 & 3.1216 & 3.1525 & 3.1836 & 3.2149 & 3.2464 & 3.2781 & 3.3100 & 3.3744 \\\hline 4 & 4.1836 & 4.2465 & 4.3101 & 4.3746 & 4.4399 & 4.5061 & 4.5731 & 4.6410 & 4.7793 \\\hline 5 & 5.3091 & 5.4163 & 5.5256 & 5.6371 & 5.7507 & 5.8666 & 5.9847 & 6.1051 & 6.3528 \\\hline 6 & 6.4684 & 6.6330 & 6.8019 & 6.9753 & 7.1533 & 7.3359 & 7.5233 & 7.7156 & 8.1152 \\\hline 7 & 7.6625 & 7.8983 & 8.1420 & 8.3938 & 8.6540 & 8.9228 & 9.2004 & 9.4872 & 10.0890 \\\hline 8 & 8.8923 & 9.2142 & 9.5491 & 9.8975 & 10.2598 & 10.6366 & 11.0285 & 11.4359 & 12.2997 \\\hline 9 & 10.1591 & 10.5828 & 11.0266 & 11.4913 & 11.9780 & 12.4876 & 13.0210 & 13.5795 & 14.7757 \\\hline 10 & 11.4639 & 12.0061 & 12.5779 & 13.1808 & 13.8164 & 14.4866 & 15.1929 & 15.9374 & 17.5487 \\\hline\end{array}$ -At an annual interest rate of 8% compounded annually, $5,300 will accumulate to a total of $7,210.65 in 5 years. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Keisha has $3,500 now and plans on investing it in a fund that will pay her 12% interest compounded quarterly. How much will Keisha have accumulated after 2 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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?

A series of equal payments made or received at the end of each period is an ordinary annuity.

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.)

The number of periods in a future value calculation may only be expressed in years.