Understanding the Time Value of MoneyCongratulations!!! You have.docx

Understanding the Time Value of MoneyCongratulations!!! You have.docx

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  Understanding the TimeValue of Money Congratulations!!! You have won a cash prize! You have two payment options: A: Receive $10,000 now or B: Receive $10,000 in three years. Which option would you choose? What Is the Time Value of Money? If you're like most people, you would choose to receive the $10,000 now. After all, three years is a long time to wait. Why would any rational person defer payment into the future when he or she could have the same amount of money now? For most of us, taking the money in the present is just plain instinctive. So at the most basic level, the time value of money demonstrates that all things being equal, it seems better to have money now rather than later. But why is this? A $100 bill has the same value as a $100 bill one year from now, doesn't it? Actually, although the bill is the same, you can do much more with the money if you have it now because over time you can earn more interest on your money. Back to our example: By receiving $10,000 today, you are poised to increase the future value of your money by investing and gaining interest over a period of time. For Option B, you don't have time on your side, and the payment received in three years would be your future value. To illustrate, we have provided a timeline: If you are choosing Option A, your future value will be $10,000 plus any interest acquired over the three years. The future value for Option B, on the other hand, would only be $10,000. So how can you calculate exactly how much more Option A is worth, compared to Option B? Let's take a look. Future Value Basics If you choose Option A and invest the total amount at a simple annual rate of 4.5%, the future value of your investment at the end of the first year is $10,450. We arrive at this sum by multiplying the principal amount of $10,000 by the interest rate of 4.5% and then adding the interest gained to the principal
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  amount: $10,000×0.045=$450begin{aligned} &$10,000 times0.045 = $450 end{aligned}$10,000×0.045=$450 $450+$10,000=$10,450begin{aligned} &$450 + $10,000 = $10,450 end{aligned}$450+$10,000=$10,450 You can also calculate the total amount of a one-year investment with a simple manipulation of the above equation: OE=($10,000×0.045)+$10,000=$10,450where:OE=Original equa tionbegin{aligned} &text{OE} = ( $10,000 times 0.045 ) + $10,000 = $10,450 &textbf{where:} &text{OE} = text{Original equation} end{aligned} OE=($10,000×0.045)+$10,000=$10,450where:OE=Original equa tion Manipulation=$10,000×[(1×0.045)+1]=$10,450begin{aligned} &text{Manipulation} = $10,000 times [ ( 1 times 0.045 ) + 1 ] = $10,450 end{aligned} Manipulation=$10,000×[(1×0.045)+1]=$10,450 Final Equation=$10,000×(0.045+1)=$10,450begin{aligned} &text{Final Equation} = $10,000 times ( 0.045 + 1 ) = $10,450 end{aligned} Final Equation=$10,000×(0.045+1)=$10,450 The manipulated equation above is simply a removal of the like- variable $10,000 (the principal amount) by dividing the entire original equation by $10,000. If the $10,450 left in your investment account at the end of the first year is left untouched and you invested it at 4.5% for another year, how much would you have? To calculate this, you would take the $10,450 and multiply it again by 1.045 (0.045 +1). At the end of two years, you would have $10,920.25. Calculating Future Value The above calculation, then, is equivalent to the following equation: Future Value=$10,000×(1+0.045)×(1+0.045)begin{aligned} &text{Future Value} = $10,000 times ( 1 + 0.045 ) times ( 1 + 0.045 ) end{aligned} Future Value=$10,000×(1+0.045)×(1+0.045)
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  Think back tomath class and the rule of exponents, which states that the multiplication of like terms is equivalent to adding their exponents. In the above equation, the two like terms are (1+ 0.045), and the exponent on each is equal to 1. Therefore, the equation can be represented as the following: Future Value=$10,000×(1+0.045)2begin{aligned} &text{Future Value} = $10,000 times ( 1 + 0.045 )^2 end{aligned}Future Value=$10,000×(1+0.045)2 We can see that the exponent is equal to the number of years for which the money is earning interest in an investment. So, the equation for calculating the three-year future value of the investment would look like this: Future Value=$10,000×(1+0.045)3begin{aligned} &text{Future Value} = $10,000 times ( 1 + 0.045 )^3 end{aligned}Future Value=$10,000×(1+0.045)3 However, we don't need to keep on calculating the future value after the first year, then the second year, then the third year, and so on. You can figure it all at once, so to speak. If you know the present amount of money you have in an investment, its rate of return, and how many years you would like to hold that investment, you can calculate the future value (FV) of that amount. It's done with the equation: FV=PV×(1+i)nwhere:FV=Future valuePV=Present value (origin al amount of money)i=Interest rate per periodn=Number of peri odsbegin{aligned} &text{FV} = text{PV} times ( 1 + i )^ n &textbf{where:} &text{FV} = text{Future value} &text{PV} = text{Present value (original amount of money)} &i = text{Interest rate per period} &n = text{Number of periods} end{aligned} FV=PV×(1+i)nwhere:FV=Future valuePV=Present value (origin al amount of money)i=Interest rate per periodn=Number of peri ods Present Value Basics If you received $10,000 today, its present value would, of course, be $10,000 because the present value is what your investment gives you now if you were to spend it today. If you
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  were to receive$10,000 in one year, the present value of the amount would not be $10,000 because you do not have it in your hand now, in the present. To find the present value of the $10,000 you will receive in the future, you need to pretend that the $10,000 is the total future value of an amount that you invested today. In other words, to find the present value of the future $10,000, we need to find out how much we would have to invest today in order to receive that $10,000 in one year. To calculate the present value, or the amount that we would have to invest today, you must subtract the (hypothetical) accumulated interest from the $10,000. To achieve this, we can discount the future payment amount ($10,000) by the interest rate for the period. In essence, all you are doing is rearranging the future value equation above so that you may solve for present value (PV). The above future value equation can be rewritten as follows: PV=FV(1+i)nbegin{aligned} &text{PV} = frac{ text{FV} }{ ( 1 + i )^ n } end{aligned}PV=(1+i)nFV An alternate equation would be: PV=FV×(1+i)−nwhere:PV=Present value (original amount of m oney)FV=Future valuei=Interest rate per periodn=Number of per iodsbegin{aligned} &text{PV} = text{FV} times ( 1 + i )^{- n} &textbf{where:} &text{PV} = text{Present value (original amount of money)} &text{FV} = text{Future value} &i = text{Interest rate per period} &n = text{Number of periods} end{aligned} PV=FV×(1+i)−nwhere:PV=Present value (original amount of m oney)FV=Future valuei=Interest rate per periodn=Number of per iods Calculating Present Value Let's walk backward from the $10,000 offered in Option B. Remember, the $10,000 to be received in three years is really the same as the future value of an investment. If we had one year to go before getting the money, we would discount the payment back one year. Using our present value formula
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  (version 2), atthe current two-year mark, the present value of the $10,000 to be received in one year would be $10,000 x (1 + .045)-1 = $9569.38. Note that if today we were at the one-year mark, the above $9,569.38 would be considered the future value of our investment one year from now. Continuing on, at the end of the first year we would be expecting to receive the payment of $10,000 in two years. At an interest rate of 4.5%, the calculation for the present value of a $10,000 payment expected in two years would be $10,000 x (1 + .045)-2 = $9157.30. Of course, because of the rule of exponents, we don't have to calculate the future value of the investment every year counting back from the $10,000 investment in the third year. We could put the equation more concisely and use the $10,000 as FV. So, here is how you can calculate today's present value of the $10,000 expected from a three-year investment earning 4.5%: $8,762.97=$10,000×(1+.045)−3begin{aligned} &$8,762.97 = $10,000 times ( 1 + .045 )^{-3} end{aligned} $8,762.97=$10,000×(1+.045)−3 So the present value of a future payment of $10,000 is worth $8,762.97 today if interest rates are 4.5% per year. In other words, choosing Option B is like taking $8,762.97 now and then investing it for three years. The equations above illustrate that Option A is better not only because it offers you money right now but because it offers you $1,237.03 ($10,000 - $8,762.97) more in cash! Furthermore, if you invest the $10,000 that you receive from Option A, your choice gives you a future value that is $1,411.66 ($11,411.66 - $10,000) greater than the future value of Option B. Present Value of a Future Payment Let's up the ante on our offer. What if the future payment is more than the amount you'd receive right away? Say you could receive either $15,000 today or $18,000 in four years. The decision is now more difficult. If you choose to receive $15,000 today and invest the entire amount, you may actually end up
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  with an amountof cash in four years that is less than $18,000. How to decide? You could find the future value of $15,000, but since we are always living in the present, let's find the present value of $18,000. This time, we'll assume interest rates are currently 4%. Remember that the equation for present value is the following: PV=FV×(1+i)−nbegin{aligned} &text{PV} = text{FV} times ( 1 + i )^{-n} end{aligned}PV=FV×(1+i)−n In the equation above, all we are doing is discounting the future value of an investment. Using the numbers above, the present value of an $18,000 payment in four years would be calculated as $18,000 x (1 + 0.04)-4 = $15,386.48. From the above calculation, we now know our choice today is between opting for $15,000 or $15,386.48. Of course, we should choose to postpone payment for four years! The Bottom Line These calculations demonstrate that time literally is money—the value of the money you have now is not the same as it will be in the future and vice versa. So, it is important to know how to calculate the time value of money so that you can distinguish between the worth of investments that offer you returns at different times. (For related reading, see "Time Value of Money and the Dollar") Sponsored Hire a Pro: Compare Financial Advisors In Your Area Finding the right financial advisor that fits your needs doesn’t have to be hard. SmartAsset’s free tool matches you with fiduciary financial advisors in your area in 5 minutes. Each advisor has been vetted by SmartAsset and is legally bound to act in your best interests. If you’re ready to be matched with local advisors that will help you achieve your financial goals, get started now. Running head: NURSING WORKFORCE CHANGE 1 NURSING WORKFORCE CHANGE 2
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  Nursing Workforce Change FirstName Last Name Colorado Technical University Nursing Workforce Change Begin writing your paper with a .5” indent and continue the paper with an indent for each new paragraph. Identify and describe a recent change that occurred in your workplace. It could be a change in the levels of staffing; a change in policy, such as time off or tuition reimbursement; a change in use of equipment or supplies; a change in charting or computerized medical records; and so on. Describe the change in 3-4 sentences. 1 of the sentences should address the rationale for the change. Change Issue: Low Census Staffing Policy Currently, when the patient census is low, staff go home based on tenure; the same staff are continually going home, resulting
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  in a lowerpaycheck for these nurses. The proposed change is to rotate all staff to leave when the census is low, regardless of tenure, so the burden of potentially lower pay is shared among the entire staff and not the same few. Place in alphabetical order. The next step requires the development of an annotated bibliography for each of the 6 articles listed in Step 2. This step should be 6 paragraphs total (1 for each article that is summarized and analyzed) and approximately 450–700 words in 2–3 double-spaced pages. Table 1. Change Issue: Low Census Staffing Policy Bibliography Article Author Last Name, First, Initial (Year). Title of Article. Title of Publication, Volume # (Issue #), Pages. 1 2
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  3 4 5 6
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  Annotated Bibliography Aiello, J.(2003). Primary care provider: Who should that be for the ESRD patient? Nephrology Nursing Journal, 30(5), 587–588. Retrieved from http://proquest.umi.com/pqdweb?index=1&did=461916921 Summarize the main points for each of the 6 references (must be from within the last 5 years) from Step 2, each in its own paragraph. Use the MEAL method of writing, where each paragraph contains a minimum of 4 sentences. M is for Main point. E is for Examples and evidence with citation. Analyses refers to what was significant about the article and how the article was related to the change topic you selected. Be sure to include at least 1 analysis sentence about each reference in that paragraph. Link or transition to the main topic. Remember to cite each article appropriately (Author(s) Last Name, Year) and include an APA formatted reference page. (See APA 6th edition). Anderson, E. B. (2002). Patient-centeredness: A new approach. Nephrology News & Issues, 16(12), 80–82. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/12452113 Summarize the main points for each of the 6 references (must be from within the last 5 years) from Step 2, each in its own paragraph. Use the MEAL method of writing, where each paragraph contains a minimum of 4 sentences. M is for Main
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  point. E isfor Examples and evidence with citation. Analyses refers to what was significant about the article and how the article was related to the change topic you selected. Be sure to include at least 1 analysis sentence about each reference in that paragraph. Link or transition to the main topic. Remember to cite each article appropriately (Author(s) Last Name, Year) and include an APA formatted reference page. (See APA 6th edition). References