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4. Annuities Future Value of Annuity Present Value of Annuity Calculating Annuities Annuities The Time Value of Money > Annuities Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance?campaign_content=book_192_section_57&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. Annuities have payments of a fixed size paid at regular intervals. There are three types of annuities: annuities-due, ordinary annuities, and perpetuities. Annuities help both the creditor and debtor have predictable cash flows, and it spreads payments of the investment out over time. Annuities Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/annuities-57/annuities-265- 8371?campaign_content=book_192_section_57&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com The Time Value of Money > Annuities

6. To find the FV, you need to know the payment amount, the interest rate of the account the payments are deposited in, the number of periods per year, and the time frame in years. The first and last payments of an annuity due both occur one period before they would in an ordinary annuity, so they have different values in the future. There are different formulas for annuities due and ordinary annuities because of when the first and last payments occur. Future Value of Annuity Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/annuities-57/future-value-of-annuity-266- 878?campaign_content=book_192_section_57&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com The Time Value of Money > Annuities

7. The PV for both annuities-due and ordinary annuities can be calculated using the size of the payments, the interest rate, and number of periods. The PV of a perpetuity can be found by dividing the size of the payments by the interest rate. Payment size is represented as p, pmt, or A; interest rate by i or r; and number of periods by n or t. Present Value of Annuity Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/annuities-57/present-value-of-annuity-267- 1545?campaign_content=book_192_section_57&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com The Time Value of Money > Annuities

8. There are five total variables that go into annuity calculations: PV, FV, interest rate (i or r), payment amount (A, m, pmt, or p), and the number of periods (n). The calculations for ordinary annuities and annuities-due differ due to the different times when the first and last payments occur. Perpetuities don't have a FV formula because they continue forever. To find the FV at a point, treat it as an ordinary annuity or annuity-due up to that point. Calculating Annuities Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/annuities-57/calculating-annuities-268- 8372?campaign_content=book_192_section_57&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess PV of a Perpetuity View on Boundless.com The Time Value of Money > Annuities

9. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

10. Key terms annuity-due An investment with fixed-payments that occur at regular intervals, paid at the beginning of each period. annuity-due An annuity where the payments occur at the beginning of each period. annuity-due a stream of fixed payments where payments are made at the beginning of each period ordinary annuity An annuity where the payments occur at the end of each period. ordinary annuity An investment with fixed-payments that occur at regular intervals, paid at the end of each period. ordinary repair expense accrued in normal maintenance of an asset period The length of time during which interest accrues. perpetuity An annuity in which the periodic payments begin on a fixed date and continue indefinitely. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money

11. PV Annuity-due The PV of an annuity with the payments at the beginning of each period Free to share, print, make copies and changes. Get yours at www.boundless.com Math Major. CC BY-SA http://mathmajor.org/accounting-finance-and-investing/annuities-and-perpetuities/ View on Boundless.comCC BY-SAhttp://mathmajor.org/accounting-finance-and-investing/annuities-and-perpetuities/View on Boundless.com The Time Value of Money

12. FV Ordinary Annuity The FV of an annuity with the payments at the end of each period Free to share, print, make copies and changes. Get yours at www.boundless.com http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum. CC BY-SA http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum View on Boundless.comCC BY-SA http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sumView on Boundless.com The Time Value of Money

13. FV Annuity-Due The FV of an annuity with payments at the beginning of each period: m is the amount amount, r is the interest, n is the number of periods per year, and t is the number of years. Free to share, print, make copies and changes. Get yours at www.boundless.com Connexions. "Mathematics of Finance." CC BY 3.0 http://cnx.org/content/m18905/latest/ View on Boundless.comCC BY 3.0http://cnx.org/content/m18905/latest/View on Boundless.com The Time Value of Money

14. PV Ordinary Annuity The PV of an annuity with the payments at the end of each period Free to share, print, make copies and changes. Get yours at www.boundless.com Math Major. CC BY-SA http://mathmajor.org/accounting-finance-and-investing/annuities-and-perpetuities/ View on Boundless.comCC BY-SAhttp://mathmajor.org/accounting-finance-and-investing/annuities-and-perpetuities/View on Boundless.com The Time Value of Money

15. PV of a Perpetuity The PV of a perpetuity is the payment size divided by the interest rate. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Perpetuity." GNU FDL http://en.wikipedia.org/wiki/Perpetuity View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/PerpetuityView on Boundless.com The Time Value of Money

16. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money A security offers to pay the holder $1000 at the end of every month for five years. What type of annuity is this? A) Annuity-due. B) Perpetuity. C) Ordinary annuity. D) Regular annuity.

17. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Time Value of Money A security offers to pay the holder $1000 at the end of every month for five years. What type of annuity is this? A) Annuity-due. B) Perpetuity. C) Ordinary annuity. D) Regular annuity.

18. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money An annuity pays $1500 at the beginning of every month for five years. The interest rate of the annuity is 4%. What is this annuity's future value? A) $99,780 B) $97,948 C) $99,448 D) $101,280

19. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Time Value of Money An annuity pays $1500 at the beginning of every month for five years. The interest rate of the annuity is 4%. What is this annuity's future value? A) $99,780 B) $97,948 C) $99,448 D) $101,280

20. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money A five year annuity pays $1000 at the end of every month for four years. It has an interest rate of 3%. What is its present value? A) $3,717 B) $26,024 C) $25,266 D) $3,828

21. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Time Value of Money A five year annuity pays $1000 at the end of every month for four years. It has an interest rate of 3%. What is its present value? A) $3,717 B) $26,024 C) $25,266 D) $3,828

22. Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money A person purchases a security that pays $1000 a year in perpetuity. The interest rate of that security is 4%. What is the present value of that security? A) $25,000 B) $1040 C) $250,000 D) $4160

23. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Time Value of Money A person purchases a security that pays $1000 a year in perpetuity. The interest rate of that security is 4%. What is the present value of that security? A) $25,000 B) $1040 C) $250,000 D) $4160

24. Attribution Connexions. "Mathematics of Finance." CC BY 3.0 http://cnx.org/content/m18905/latest/CC BY 3.0http://cnx.org/content/m18905/latest/ Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/ordinary-annuity--2CC BY-SA 3.0http://www.boundless.com//finance/definition/ordinary-annuity--2 Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/annuity-due--2CC BY-SA 3.0http://www.boundless.com//finance/definition/annuity-due--2 Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//accounting/definition/ordinary-repairCC BY-SA 3.0http://www.boundless.com//accounting/definition/ordinary-repair Connexions. "Mathematics of Finance." CC BY 3.0 http://cnx.org/content/m18905/latest/CC BY 3.0http://cnx.org/content/m18905/latest/ Wikibooks. "Principles of Finance/Section 1/Chapter 3/Applications of Time Value of Money/Annuities." CC BY-SA 3.0 http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_3/Applications_of_Time_Value_of_Money/AnnuitiesCC BY-SA 3.0 http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_3/Applications_of_Time_Value_of_Money/Annuities Wiktionary. "perpetuity." CC BY-SA 3.0 http://en.wiktionary.org/wiki/perpetuityCC BY-SA 3.0http://en.wiktionary.org/wiki/perpetuity Wikipedia. "Perpetuity." CC BY-SA 3.0 http://en.wikipedia.org/wiki/PerpetuityCC BY-SA 3.0http://en.wikipedia.org/wiki/Perpetuity Connexions. "Mathematics of Finance." CC BY 3.0 http://cnx.org/content/m18905/latest/CC BY 3.0http://cnx.org/content/m18905/latest/ Wikipedia. "Annuity (finance theory)." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Annuity_(finance_theory)CC BY-SA 3.0http://en.wikipedia.org/wiki/Annuity_(finance_theory) Wikipedia. "period." CC BY-SA 3.0 http://en.wikipedia.org/wiki/periodCC BY-SA 3.0http://en.wikipedia.org/wiki/period Wiktionary. "perpetuity." CC BY-SA 3.0 http://en.wiktionary.org/wiki/perpetuityCC BY-SA 3.0http://en.wiktionary.org/wiki/perpetuity Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/ordinary-annuity--2CC BY-SA 3.0http://www.boundless.com//finance/definition/ordinary-annuity--2 Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/annuity-due--2CC BY-SA 3.0http://www.boundless.com//finance/definition/annuity-due--2 http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum. CC BY-SA http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sumCC BY-SA http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum Free to share, print, make copies and changes. Get yours at www.boundless.com The Time Value of Money