Exam 14: Time Value of Money

Patricia wants to invest a sum of money today that will yield $10,000 at the end of 6 years. Assuming she can earn an interest rate of 6% compounded annually, how much must she invest today? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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.)

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

An ________ is a series of equal payments occurring at equal intervals.

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 -The present value of $5,000 per year for three years at 12% compounded annually is $12,009. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

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?

The future value of an ________ annuity is the accumulated value of each annuity payment with interest as of the date of the final payment.

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?

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

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 -An annuity is a series of equal payments occurring at equal intervals.

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.)

Explain the concept of the present value of an annuity.

Interest is the borrower's payment to the owner of an asset, for its use.

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 -The present value of four $10,000 semiannual payments invested for 2 years at 12% compounded semiannually is $43,746. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Jessica received a gift of $7,500 at the time of her high school graduation. She invests it in an account that yields 10% compounded semiannually. What will the value of Jessica's investment be 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.)

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 -Hao made a single investment which, after 5 years invested at 12% compounded semiannually, has accumulated to $214,900. How much did Hao invest initially? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

The present value of an annuity table can be used to determine the value today of a series of payments to be received in the future.

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.)

An interest rate is also called a discount rate.

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?