Exam 14: Time Value of Money

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.)

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

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.)

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

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.)

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: 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 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7118 4 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6355 5 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5674 6 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5066 7 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4523 8 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4039 9 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3606 10 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3220 Future Value of 1 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.4049 4 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735 5 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.7623 6 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.9738 7 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.2107 8 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.4760 9 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.7731 10 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 3.1058 Present Value of an Annuity of 1 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018 4 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.0373 5 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6048 6 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.1114 7 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638 8 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676 9 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7950 5.3282 10 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.6502 Future Value of an Annuity of 1 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744 4 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793 5 5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528 6 6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 8.1152 7 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.0890 8 8.8923 9.2142 9.5491 9.8975 10.2598 10.6366 11.0285 11.4359 12.2997 9 10.1591 10.5828 11.0266 11.4913 11.9780 12.4876 13.0210 13.5795 14.7757 10 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 17.5487 -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?

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

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.)

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

Future Value of an Annuity of 1 Present Value of 1 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7118 4 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6355 5 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5674 6 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5066 7 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4523 8 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4039 9 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3606 10 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3220 Future Value of 1 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.4049 4 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735 5 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.7623 6 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.9738 7 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.2107 8 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.4760 9 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.7731 10 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 3.1058 Present Value of an Annuity of 1 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018 4 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.0373 5 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6048 6 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.1114 7 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638 8 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676 9 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7950 5.3282 10 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.6502 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744 4 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793 5 5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528 6 6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 8.1152 7 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.0890 8 8.8923 9.2142 9.5491 9.8975 10.2598 10.6366 11.0285 11.4359 12.2997 9 10.1591 10.5828 11.0266 11.4913 11.9780 12.4876 13.0210 13.5795 14.7757 10 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 17.5487 -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.)

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

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.)

Future Value of an Annuity of 1 Present Value of 1 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7118 4 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6355 5 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5674 6 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5066 7 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4523 8 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4039 9 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3606 10 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3220 Future Value of 1 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.4049 4 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735 5 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.7623 6 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.9738 7 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.2107 8 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.4760 9 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.7731 10 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 3.1058 Present Value of an Annuity of 1 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018 4 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.0373 5 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6048 6 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.1114 7 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638 8 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676 9 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7950 5.3282 10 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.6502 Periods 3\% 4\% 5\% 6\% 7\% 8\% 9\% 10\% 12\% 3 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744 4 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793 5 5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528 6 6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 8.1152 7 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.0890 8 8.8923 9.2142 9.5491 9.8975 10.2598 10.6366 11.0285 11.4359 12.2997 9 10.1591 10.5828 11.0266 11.4913 11.9780 12.4876 13.0210 13.5795 14.7757 10 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 17.5487 -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.

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.)

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 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?

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.)

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.)

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.)