1 / 54

Boundless Lecture Slides

Boundless Lecture Slides. Available on the Boundless Teaching Platform. Free to share, print, make copies and changes. Get yours at www.boundless.com. Using Boundless Presentations. Boundless Teaching Platform

race
Download Presentation

Boundless Lecture Slides

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Boundless Lecture Slides Available on the Boundless Teaching Platform Free to share, print, make copies and changes. Get yours at www.boundless.com

  2. Using Boundless Presentations Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: • The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. http://boundless.com/teaching-platform • Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. If you have any questions or problems please email: educators@boundless.com Free to share, print, make copies and changes. Get yours at www.boundless.com

  3. About Boundless • Boundless is an innovative technology company making education more affordable and accessible for students everywhere. The company creates the world’s best open educational content in 20+ subjects that align to more than 1,000 popular college textbooks. Boundless integrates learning technology into all its premium books to help students study more efficiently at a fraction of the cost of traditional textbooks. The company also empowers educators to engage their students more effectively through customizable books and intuitive teaching tools as part of the Boundless Teaching Platform. More than 2 million learners access Boundless free and premium content each month across the company’s wide distribution platforms, including its website, iOS apps, Kindle books, and iBooks. To get started learning or teaching with Boundless, visit boundless.com. Free to share, print, make copies and changes. Get yours at www.boundless.com

  4. Introduction to the Time Value of Money The Time Value of Money Future Value, Single Amount Present Value, Single Amount Annuities ] Valuing Multiple Cash Flows The Time Value of Money Free to share, print, make copies and changes. Get yours at www.boundless.com

  5. Additional Detail on Present and Future Values The Time Value of Money(continued) Yield ] The Time Value of Money Free to share, print, make copies and changes. Get yours at www.boundless.com

  6. The Time Value of Money > Introduction to the Time Value of Money Introduction to the Time Value of Money • Defining the Time Value of Money • Importance of the Time Value of Money 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/introduction-to-the-time-value-of-money-54/

  7. The Time Value of Money > Future Value, Single Amount Future Value, Single Amount • Single-Period Investment • Multi-Period Investment • Calculating Future Value • Approaches to Calculating Future Value 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/future-value-single-amount-55/

  8. The Time Value of Money > Present Value, Single Amount Present Value, Single Amount • Single-Period Investment • Multi-Period Investment • The Discount Rate • Number of Periods • Calculating Present Value 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/present-value-single-amount-56/

  9. The Time Value of Money > Annuities Annuities • Annuities • Future Value of Annuity • Present Value of Annuity • 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/

  10. The Time Value of Money > Valuing Multiple Cash Flows Valuing Multiple Cash Flows • Future Value, Multiple Flows • Present Value, Multiple Flows 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/valuing-multiple-cash-flows-58/

  11. The Time Value of Money > Additional Detail on Present and Future Values Additional Detail on Present and Future Values • The Relationship Between Present and Future Value • Calculating Perpetuities • Calculating Values for Different Durations of Compounding Periods • Comparing Interest Rates • Calculating Values for Fractional Time Periods • Loans and Loan Amortization 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/additional-detail-on-present-and-future-values-59/

  12. The Time Value of Money > Yield Yield • Calculating the Yield of a Single-Period Investment • Calculating the Yield of an 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/yield-60/

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

  14. The Time Value of Money Key terms • accrueTo add, or grow. • amortizationThis is the process of scheduling intervals of payment over time to pay back an existing debt, taking into account the time value of money. • annuityA right to receive amounts of money regularly over a certain fixed period in repayment of a loan or investment (or perpetually, in the case of a perpetuity). • annuityA specified income payable at stated intervals for a fixed or a contingent period, often for the recipient's life, in consideration of a stipulated premium paid either in prior installment payments or in a single payment. For example, a retirement annuity paid to a public officer following his or her retirement. • annuity-dueAn investment with fixed-payments that occur at regular intervals, paid at the beginning of each period. • annuity-duea stream of fixed payments where payments are made at the beginning of each period • capitalizationThe process of finding the future value of a sum by evaluating the present value. • cash flowThe sum of cash revenues and expenditures over a period of time. • compound interestInterest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest. • compound interestInterest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest. • Compound interestAn interest rate applied to multiple applications of interest during the lifetime of the investment. • compounding periodThe length of time between the points at which interest is paid. Free to share, print, make copies and changes. Get yours at www.boundless.com

  15. The Time Value of Money • discountTo find the value of a sum of money at some earlier point in time. To find the present value. • discountto account for the time value of money • discount rateThe interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value. • discountingThe process of finding the present value using the discount rate. • discountingThe process of finding the present value using the discount rate. • discountingThe process of determining how much money paid/received in the future is worth today. You discount future values of cash back to the present using the discount rate. • Effective InterestThe amount of interest accrued per year after accounting for compounding. • effective-interest methodamortizing a debt according to the effective interest rate paid • Future ValueThe value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future, assuming a certain interest rate, or more generally, rate of return, it is the present value multiplied by the accumulation function. • Future Value (FV)The value of the money in the future. • growth rateThe percentage by which the payments grow each period. • incremental cash flowsthe additional money flowing in or out of a business due to a project Free to share, print, make copies and changes. Get yours at www.boundless.com

  16. The Time Value of Money • inflationAn increase in the general level of prices or in the cost of living. • interest rateThe percentage of an amount of money charged for its use per some period of time. It can also be thought of as the cost of not having money for one period, or the amount paid on an investment per year. • interest rateThe percentage of an amount of money charged for its use per some period of time. It can also be thought of as the cost of not having money for one period, or the amount paid on an investment per year. • Interest Rate (i or r)The cost of not having money for one period, or the amount paid on an investment per year. • Internal Rate of Return (IRR)The discount rate that will cause the NPV of an investment to equal 0. • Multi-period investmentAn investment that takes place over more than one periods. • net present valuethe present value of a project or an investment decision determined by summing the discounted incoming and outgoing future cash flows resulting from the decision • Net Present Value (NPV)The present value of a project or an investment decision determined by summing the discounted incoming and outgoing future cash flows resulting from the decision. • Nominal InterestThe amount of interest accrued per year without accounting for compounding. • ordinary annuityAn investment with fixed-payments that occur at regular intervals, paid at the end of each period. • ordinary repairexpense accrued in normal maintenance of an asset • periodThe length of time during which interest accrues. Free to share, print, make copies and changes. Get yours at www.boundless.com

  17. The Time Value of Money • periodThe length of time during which interest accrues. • periodThe length of time during which interest accrues. • Periods (t or n)Units of time. Usually one year. • perpetuityAn annuity in which the periodic payments begin on a fixed date and continue indefinitely. • present valuea future amount of money that has been discounted to reflect its current value, as if it existed today • present valueAlso known as present discounted value, is the value on a given date of a payment or series of payments made at other times. If the payments are in the future, they are discounted to reflect the time value of money and other factors such as investment risk. If they are in the past, their value is correspondingly enhanced to reflect that those payments have been (or could have been) earning interest in the intervening time. Present value calculations are widely used in business and economics to provide a means to compare cash flows at different times on a meaningful "like to like" basis. • Present Value (PV)The value of the money today. • principalThe money originally invested or loaned, on which basis interest and returns are calculated. • quarterA period of three consecutive months (1/4 of a year). • simple interestinterest paid only on the principal. • Single-period investmentAn investment that takes place over one period, usually one year. • time period assumptionbusiness profit or loses are measured on timely basis Free to share, print, make copies and changes. Get yours at www.boundless.com

  18. The Time Value of Money • time value of moneythe value of an asset accounting for a given amount of interest earned or inflation accrued over a given period • yieldIn finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return. Yield applies to various stated rates of return on stocks (common and preferred, and convertible), fixed income instruments (bonds, notes, bills, strips, zero coupon), and some other investment type insurance products Free to share, print, make copies and changes. Get yours at www.boundless.com

  19. The Time Value of Money Compounding Interest The effect of earning 20% annual interest on an initial $1,000 investment at various compounding frequencies. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia.CC BY-SAhttp://upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Compound_Interest_with_Varying_Frequencies.svg/800px-Compound_Interest_with_Varying_Frequencies.svg.pngView on Boundless.com

  20. The Time Value of Money Fisher Equation The nominal interest rate is approximately the sum of the real interest rate and inflation. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Fisher equation."GNU FDLhttp://en.wikipedia.org/wiki/Fisher_equationView on Boundless.com

  21. The Time Value of Money FV of a single payment The PV and FV are directly related. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Time value of money."GNU FDLhttp://en.wikipedia.org/wiki/Time_value_of_moneyView on Boundless.com

  22. The Time Value of Money Percent Change The percent change in value is the change in value from PV to FV (V2 to V1) divided by PV (V1) times 100%. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Percentage change."GNU FDLhttp://en.wikipedia.org/wiki/Percentage_changeView on Boundless.com

  23. The Time Value of Money Present Value Single Payment Finding the PV is a matter of plugging in for the three other variables. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Time value of money."GNU FDLhttp://en.wikipedia.org/wiki/Time_value_of_moneyView on Boundless.com

  24. The Time Value of Money FV of a single payment The PV and FV are directly related. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Time value of money."GNU FDLhttp://en.wikipedia.org/wiki/Time_value_of_moneyView on Boundless.com

  25. The Time Value of Money Car Car loans, mortgages, and student loans all generally have compound interest. Free to share, print, make copies and changes. Get yours at www.boundless.com Open ClipArt."Clipart - American Sport Car."Public domainhttp://openclipart.org/detail/16372/american-sport-car-by-bobocal-16372View on Boundless.com

  26. The Time Value of Money Solving for n This formula allows you to figure out how many periods are needed to achieve a certain future value, given a present value and an interest rate. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Compound interest."GNU FDLhttp://en.wikipedia.org/wiki/Compound_interestView on Boundless.com

  27. The Time Value of Money Calculating the effective annual rate The effective annual rate for interest that compounds more than once per year. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Effective annual rate."GNU FDLhttp://en.wikipedia.org/wiki/Effective_annual_rateView on Boundless.com

  28. The Time Value of Money FV of a single payment The FV of multiple cash flows is the sum of the future values of each cash flow. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Time value of money."GNU FDLhttp://en.wikipedia.org/wiki/Time_value_of_moneyView on Boundless.com

  29. The Time Value of Money Time Value of Money Time value of money requires an understanding of how return rates impact fixed values over time. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."Economics_of_climate_change_chapter3_discounting_curves.png."CC BY-SA 3.0https://upload.wikimedia.org/wikipedia/commons/9/99/Economics_of_climate_change_chapter3_discounting_curves.pngView on Boundless.com

  30. The Time Value of Money Compound Interest Interest is paid at the total amount in the account, which may include interest earned in previous periods. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Future value."GNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com

  31. The Time Value of Money EAR The Effective Annual Rate is the amount of interest actually accrued per year based on the APR. n is the number of compounding periods of APR per year. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Effective APR."GNU FDLhttp://en.wikipedia.org/wiki/Effective_APRView on Boundless.com

  32. The Time Value of Money IRR Example The setup to find the IRR of the investment with cash flows of -4000, 1200, 1410, 1875, and 1050. By setting NPV = 0 and solving for r, you can find the IRR of this investment. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Internal rate of return."GNU FDLhttp://en.wikipedia.org/wiki/Internal_rate_of_returnView on Boundless.com

  33. The Time Value of Money FV of a single payment The FV is related to the PV by being i% more each period. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Time value of money."GNU FDLhttp://en.wikipedia.org/wiki/Time_value_of_moneyView on Boundless.com

  34. The Time Value of Money Sum FV The PV of an investment is the sum of the present values of all its payments. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Time value of money."GNU FDLhttp://en.wikipedia.org/wiki/Time_value_of_moneyView on Boundless.com

  35. The Time Value of Money FV Periodic Compounding Finding the FV (A(t)) given the PV (Ao), nominal interest rate (r), number of compounding periods per year (n), and number of years (t). Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Compound interest."GNU FDLhttp://en.wikipedia.org/wiki/Compound_interestView on Boundless.com

  36. The Time Value of Money Simple Interest Formula Simple interest is when interest is only paid on the amount you originally invested (the principal). You don't earn interest on interest you previously earned. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Future value."GNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com

  37. The Time Value of Money Compound Interest Interest is paid at the total amount in the account, which may include interest earned in previous periods. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Future value."GNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com

  38. The Time Value of Money Simple Interest Formula Simple interest is when interest is only paid on the amount you originally invested (the principal). You don't earn interest on interest you previously earned. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Future value."GNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com

  39. The Time Value of Money Compound Interest Interest is paid at the total amount in the account, which may include interest earned in previous periods. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Future value."GNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com

  40. The Time Value of Money Simple Interest Formula Simple interest is when interest is only paid on the amount you originally invested (the principal). You don't earn interest on interest you previously earned. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Future value."GNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com

  41. The Time Value of Money Compound Interest In this formula, your deposit ($100) is PV, i is the interest rate (5% for Bank 1, 6% for Bank 2), t is time (5 years), and FV is the future value. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Future value."GNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com

  42. The Time Value of Money EAR with Continuous Compounding The effective rate when interest compounds continuously. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Effective annual rate."GNU FDLhttp://en.wikipedia.org/wiki/Effective_annual_rateView on Boundless.com

  43. The Time Value of Money Amortization Schedule Example This shows the first few installments in the example discussed above (i.e. borrowing $100,000 at 8% interest paid monthly over 30 years). Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Amortization_table_%28example%29.gif."CC BY-SA 3.0https://upload.wikimedia.org/wikipedia/commons/a/ac/Amortization_table_%28example%29.gifView on Boundless.com

  44. The Time Value of Money Annuities Equations This table is a useful way to view the calculation of annuities variables from a number of directions. Understanding how to manipulate the formula will underline the relationship between the variables, and provide some conceptual clarity as to what annuities are. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Annuities Equations.JPG."CC BY-SA 3.0https://en.wikipedia.org/wiki/Time_value_of_money#FormulaView on Boundless.com

  45. The Time Value of Money Borrowing and lending Banks like HSBC take such costs into account when determining the terms of a loan for borrowers. Free to share, print, make copies and changes. Get yours at www.boundless.com Geograph."HSBC Bank Acocks Green 40-11-01 (C) Roy Hughes :: Geograph Britain and Ireland."CC BY-SAhttp://www.geograph.org.uk/photo/1107226View on Boundless.com

  46. The Time Value of Money Simple Interest Formula Simple interest is when interest is only paid on the amount you originally invested (the principal). You don't earn interest on interest you previously earned. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Future value."GNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com

  47. The Time Value of Money Simple Interest Formula Simple interest is when interest is only paid on the amount you originally invested (the principal). You don't earn interest on interest you previously earned. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Future value."GNU FDLhttp://en.wikipedia.org/wiki/Future_valueView on Boundless.com

  48. The Time Value of Money Annual Percentage Yield The Annual Percentage Yield is a way or normalizing the nominal interest rate. Basically, it is a way to account for the time factor in order to get a more accurate number for the actual interest rate.inom is the nominal interest rate.N is the number of compounding periods per year. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Annual percentage yield."GNU FDLhttp://en.wikipedia.org/wiki/Annual_percentage_yieldView on Boundless.com

  49. The Time Value of Money Attribution • Wikipedia."Cost of capital."CC BY-SA 3.0http://en.wikipedia.org/wiki/Cost_of_capital • Wiktionary."discount rate."CC BY-SA 3.0http://en.wiktionary.org/wiki/discount_rate • Wikipedia."Discounting."CC BY-SA 3.0http://en.wikipedia.org/wiki/Discounting • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//finance/definition/discounting--2 • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//finance/definition/discount • Wikipedia."Future value."CC BY-SA 3.0http://en.wikipedia.org/wiki/Future_value • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//finance/definition/periods-t-or-n • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//finance/definition/single-period-investment • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//finance/definition/multi-period-investment • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//finance/definition/ordinary-annuity--2 • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//finance/definition/annuity-due--2 • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//accounting/definition/ordinary-repair • OpenStax CNX."Rupinder Sekhon, Mathematics of Finance. September 17, 2013."CC BY 3.0http://cnx.org/content/m18905/latest/ • Wikipedia."Future value."CC BY-SA 3.0http://en.wikipedia.org/wiki/Future_value • Wikipedia."Future value."CC BY-SA 3.0http://en.wikipedia.org/wiki/Future_value • Wiktionary."compound interest."CC BY-SA 3.0http://en.wiktionary.org/wiki/compound_interest • Wikipedia."Present value."CC BY-SA 3.0http://en.wikipedia.org/wiki/Present_value Free to share, print, make copies and changes. Get yours at www.boundless.com

  50. The Time Value of Money • Wiktionary."simple interest."CC BY-SA 3.0http://en.wiktionary.org/wiki/simple_interest • Wiktionary."compound interest."CC BY-SA 3.0http://en.wiktionary.org/wiki/compound_interest • Wikipedia."Cost of capital."CC BY-SA 3.0http://en.wikipedia.org/wiki/Cost_of_capital • Wikipedia."Compound interest."CC BY-SA 3.0http://en.wikipedia.org/wiki/Compound_interest • Wikipedia."Fisher equation."CC BY-SA 3.0http://en.wikipedia.org/wiki/Fisher_equation • Wiktionary."inflation."CC BY-SA 3.0http://en.wiktionary.org/wiki/inflation • Wikipedia."time value of money."CC BY-SA 3.0http://en.wikipedia.org/wiki/time%20value%20of%20money • Wikipedia."Accounting assumptions."CC BY-SA 3.0http://en.wikipedia.org/wiki/Accounting_assumptions • Wikipedia."Compound interest."CC BY-SA 3.0http://en.wikipedia.org/wiki/Compound_interest • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//finance/definition/compounding-period • Wikipedia."Amortization."CC BY-SA 3.0https://en.wikipedia.org/wiki/Amortization • Wikipedia."Amortization (business)."CC BY-SA 3.0https://en.wikipedia.org/wiki/Amortization_(business) • Wikipedia."Loan."CC BY-SA 3.0https://en.wikipedia.org/wiki/Loan • Wikipedia."Amortization calculator."CC BY-SA 3.0https://en.wikipedia.org/wiki/Amortization_calculator • Wikipedia."Amortizing loan."CC BY-SA 3.0https://en.wikipedia.org/wiki/Amortizing_loan • Wikipedia."Future value."CC BY-SA 3.0http://en.wikipedia.org/wiki/Future_value • Wiktionary."principal."CC BY-SA 3.0http://en.wiktionary.org/wiki/principal • Wiktionary."accrue."CC BY-SA 3.0http://en.wiktionary.org/wiki/accrue • Wikipedia."Perpetuity."CC BY-SA 3.0http://en.wikipedia.org/wiki/Perpetuity Free to share, print, make copies and changes. Get yours at www.boundless.com

More Related