Exam 14: Time Value of Money

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.)

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 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: 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 $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?

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 is considering investing in a project that is expected to return $350,000 four years from now. How much is the company willing to pay for this investment if the company requires a 12% return? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

How long will it take an investment of $25,000 at 6% compounded annually to accumulate to a total of $35,462.50? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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?

Paul wants to invest a sum of money today that will accumulate to $50,000 at the end of 4 years. Assuming he can earn an interest rate of 8% compounded semiannually, how much must he invest today? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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 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?

Define interest.

The interest rate is also called the ________ rate.

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?

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 -The present value of $2,000 to be received nine years from today at 8% interest compounded annually is $1,000.40. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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

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?

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?

Future value can be found if the interest rate (i), the number of periods (n), and the present value (p) are known.

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 -The present value of $1 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.

Marshall has received an inheritance and wants to invest a sum of money today that will yield $5,000 at the end of each of the next 10 years. Assuming he can earn an interest rate of 5% compounded annually, how much of his inheritance must he invest today? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)