Financial Calculator[3]

This is version 1.0 beta of the Financial Calculator tool (last update: 26 March 2000). Emmanuel E. Vert http://members.aol.com/verte/The tools' official page (check it regularly for updates): http://businesstools.org/tools1.html Email address (feedback and mailing list subscription): VertE@aol.com A financial calculator is no longer a professionally-oriented tool but a widely public one, in spite of its apparent complexity. Nowadays for instance, stock markets are becoming increasingly global and transparent. Global in the sense that investing in foreign markets is easily feasible. Global in the other sense that small, individual, investors can manage their own portfolio of securities by themselves as well as access a wealth of information that used to be the exclusivity of a few. A financial calculator is a powerful tool that anyone nowadays can grasp with a basic knowledge of algebra, to improve his/her business or his/her personal finance. This tool aims to get anyone into using financial computations to reach new highs in performance and satisfaction, through numerous practical illustrations and constant guidance. This tool is indeed dedicated to fill a void: the lack of a publicized method to use and understand a financial calculator. This tool can only improve from your experience: Please share your doubts, criticisms, suggestions even business life at the email address posted below. And do subscribe to our mailing list (privacy enforced; 2-3 messages max per year) to know of updates and additional tools: subject "tools", body "subscribe" at that same email address below. Legal stuff in plain English: The free use and distribution of this file is highly encouraged. However, it does not mean you own it: the content as a whole is not public domain and you may not claim it is yours or sell it. Should you adapt the content to fit your own needs, you are not allowed to render such editing public without my authorization. Use this at your very own risk: I must insist on the unachieved and sometimes misleading character of this work. Features and guide. You need only enter data in yellow-colored cells. Words highlighted and underlined in blue are hypertext links: when you click on them, you will be taken to their definition for instance. This only works with Excel 97 and above. The Parameters sheet allows you to change the currency symbol. Beginners and students should first get themselves accustomed to the concepts of Yield and Cash Flows by reading the Tutorial sheet and practicing each alternative of the Cases with self-made bogus examples. Practitioners will directly skip to Cases that fit their needs or the Raw sheet that features a raw financial calculator with a few interactive commentaries. Power users may appreciate the Tests sheet which put Excel functions against Visual Basic functions that mimic scripts used in the interactive online edition of the calculator. These scripts show the inner working of such calculator. Power users will benefit from the Strategies sheet, which features a growing (hopefully) number of theories and practical accounts centered around pricing strategies and economic theories. Going further A few links to related resources are available on the tool's official page (http://businesstools.org/tools1.html).A few links to related resources are available on the tool's official page (http://businesstools.org/tools1.html).widely public one, in spite of its apparent global and transparent. Global in the sense sense that small, individual, investors can access a wealth of information that used to be anyone nowadays can grasp with a basic reach new highs in performance and guidance. This tool is indeed dedicated to doubts, criticisms, suggestions even our mailing list (privacy enforced; 2-3 subject "tools", body "subscribe" at that you click on them, you will be taken to the concepts of Yield and Cash Flows by with self-made bogus examples. sheet that features a raw financial functions against Visual Basic functions that These scripts show the inner working of growing (hopefully) number of theories Tutorial A) Time is money. Because of the rate of inflation and variations in one's purchasing power, the value of money changes over time. Simply put: $100 now are generally worth more than $100 later. A financial calculator integrates this principle, by taking into accounts the compounded interests Here lies the difference between a real yield and a nominal yield: the former shows the interests earned on the interests while the later does not. For instance, suppose you invest $10 now for a year, at a nominal yield of 10% per semester. You will end up with $12.10. Indeed, over two periods, you will have earned 21% on you original investment: 10% each time on the $10 of principal (twice and 10% on the interests earned after the first period ($0.10). Hence, a nominal yield of 20% a year amount to a real yield of 21% over 2 semesters. B) Interest converter. DATA 1) Complete ONE of the fields below right. Nominal yield per period: Nominal yields per year: Also know as APR, or Annual Percentage Rate This tutorial is meant to provide you with a good grasp of the concept of value of money over time, as well as other concepts financial computations. The interest converter allows to play with the concept of compounding. Basically, il will consider three alternatives: 1) No compounding of interests. The interest payments received are not re-invested. In such case, nominal yields and real yields are equal, that the total interest payments received are equal to the sum of the individual interest payments. 2) Periodic compounding. Interest payments are re-invested and, therefore, interests are paid on these reinvestments, from the time payments are made until the end of the original investment. The real yield will depend on the number of interest that are performed each year. 3) Continuous compounding. Interest payments are re-invested and, therefore, interests are paid on these reinvestments, on a continuous Therefore, the real yield does not depend on the number of interest payments that are performed each year.Real yield per period: 1.000% It is the yield that is considered when performing computations with a financial calculator. Real yield per year: 2) Complete the number of interest payments that will be performed each year. Number of payments per year: 12 3) Cross (X) the compounding method. None Periodic x Continuous A financial calculator will consider the real yield per period you enter, and will compound it. The difference between a periodic compounding and a continuous compounding will only effect the translation of the yield from a "per period" basis to a yearly basis. C) Financial calculator basics. The most important principle to remember is: What you pay is NEGATIVE, what you receive is POSITIVE Complete either 4 of the following 5 fields below. The one that will be left blank will be computed. 1) The number of periods (N). The number of periods is the amount of time the loan or investments lasts, ie the number of times interests are paid on an investment or the number of times payments are made to solve a loan. For instance: a) For your savings investment, you want to know how much you will have accumulated after 24 periods (ie, 2 years with 12 periods per year). Enter 24 in this field. b) For your loan, you are trying to find out how long it will take to repay it. Therefore, leave this field blank. 2) The Yield (I) The yield is the rate of interest you earn on an investment or pay on a loan. It is the Real Periodic yield discussed in section For instance, for both a and b, we will consider a rate of 1% per month (enter 1 in the field). Unless the compounding of interests (see section B above) is continuous, this rate corresponds toan Annual Percentage Rate of 12%. 3) The Present Value (PV) The Present Value is a sum you receive or pay at the beginning of a timeline. For instance: a) You invest $1,000 in a savings account: enter -1000 in the field on your right. b) You borrow $1,000: enter 1000 in the field on your right. 4) The Periodic payment (PMT) The Payment is a sum you periodically receive or pay. For instance: a) You save $50 each month that you put on your savings account: enter -50 on your right. b) Each month, you pay $50 to reimburse the loan with the interests: enter -50 in the field on your right. 5) The Future Value (FV) The Future Value is a sum you pay at the end of a typical loan or receive at the end of a typical investment. For instance: a) For your savings investment, this is the information you are looking for: You want to know how much in savings you have accumulated. Therefore, lease this field blank. b) You want to repay your loan periodically, with nothing to owe at the end of the loan. Therefore, enter 0 in this field. Optional: Timing of periodic payments. Cross (x) the timing of the payments: Payments are made at the beginning of each period. Payments are made at the end of each period. In general, payments are considered being made at the end of each period. Optional: Compounding method. Cross (x) the method of compounding chosen. No compounding. Periodic compounding. Continuous compounding. This choice is only useful for you to experiment with. In real life, you will always consider investment alternatives or loan decisions by taking into account the compounding of interests. Note: When checking the no compounding option, calculation will be performed using functions defined as macros. If you disabled macros when opening this spreadsheet, you will not get any result. Periodic paymentsRESULT COMMENTS Typical loan: money is earned now, to be reimbursed periodically. $1, 000 are earned at first. The real yield is 0,01% per period. D) Amortization table. An amortization table distinguishes for each period between, the payment of the principal and, the payment of the interests. This table will be computed in cases of typical loans (Present Value positive, Periodic payments, Future Value = 0). Period Beginning amount 1 1,000.00 2 962.93 3 925.49 4 887.67 5 849.47 6 810.89 Present Value Periodic payments Number of periods7 771.93 8 732.58 9 692.83 10 652.68 11 612.13 12 571.18 13 529.82 14 488.04 15 445.85 16 403.24 17 360.20 18 316.73 19 272.82 20 228.47 21 183.68 22 138.44 23 92.75 24 46.60 purchasing power, the value of money changes over time. compounded interests (interests paid on the interests). : the former shows the interests earned on the interests that were paid, nominal yield of 10% per semester. You will end up with $12.10. original investment: 10% each time on the $10 of principal (twice $1.00), 21% over 2 semesters. OUTCOME 0 1.000% 0 12.000% concept of value of money over time, as well as other concepts attached to compounding. Basically, il will consider three alternatives: such case, nominal yields and real yields are equal, which means sum of the individual interest payments. are paid on these reinvestments, from the time each of these investment. The real yield will depend on the number of interest payments are paid on these reinvestments, on a continuous basis. of interest payments that are performed each year.1 1.000% 0 12.683% 10101 The most important principle to remember is: pay is NEGATIVE, what you receive is POSITIVE will be left blank will be computed. 1) The number of periods (N). investments lasts, ie the number of times payments are made to solve a loan. you will have accumulated after 24 24 repay it. Therefore, leave this field blank. 2) The Yield (I) pay on a loan. It is the Real Periodic yield discussed in section B (interest converter) above. month (enter 1 in the field). Unless the this rate corresponds to 1.000%3) The Present Value (PV) 1,000.00 4) The Periodic payment (PMT) account: enter -50 on your right. interests: enter -50 in the field on your right. 5) The Future Value (FV) or receive at the end of a typical investment. looking for: You want to know how -at the end of the loan. Therefore, Timing of periodic payments. made at the beginning of each period. Payments are made at the end of each period. x Compounding method. No compounding. Periodic compounding. x Continuous compounding. you will always consider investment alternatives or will be performed using functions defined as macros. Periodic paymentsPeriodic payments PMT = 47.07 -Number of periods of interest payments Rate of interest Present Value Periodic payments Typical loan: money is earned now, to be reimbursed periodically. Future Value The real yield is 0,01% per period. The timeline is 24 periods long. Periodic payments are $ 047. The end value is worth $ 000 the payment of the principal and, the payment of the interests. Value positive, Periodic payments, Future Value = 0). Payment Interest Repayment of Principal principal balance (47.07) (10.00) (37.07) 962.93 (47.07) (9.63) (37.44) 925.49 (47.07) (9.25) (37.82) 887.67 (47.07) (8.88) (38.20) 849.47 (47.07) (8.49) (38.58) 810.89 (47.07) (8.11) (38.96) 771.93 Time Future Value Periodic payments Number of periods(47.07) (7.72) (39.35) 732.58 (47.07) (7.33) (39.75) 692.83 (47.07) (6.93) (40.15) 652.68 (47.07) (6.53) (40.55) 612.13 (47.07) (6.12) (40.95) 571.18 (47.07) (5.71) (41.36) 529.82 (47.07) (5.30) (41.78) 488.04 (47.07) (4.88) (42.19) 445.85 (47.07) (4.46) (42.61) 403.24 (47.07) (4.03) (43.04) 360.20 (47.07) (3.60) (43.47) 316.73 (47.07) (3.17) (43.91) 272.82 (47.07) (2.73) (44.35) 228.47 (47.07) (2.28) (44.79) 183.68 (47.07) (1.84) (45.24) 138.44 (47.07) (1.38) (45.69) 92.75 (47.07) (0.93) (46.15) 46.60 (47.07) (0.47) (46.61) (0.01) outcome Real yield per year RA = 0.000% 12.68% INT table Real yield per period INT2 = 100.000% 1.00% condition outcome Nominal yield per year APR = 0.000% 12.00% 0 Nominal yield per period NP = 0.000% 1.00% 00 Numper = 12 1 1 0Compounding: 0 -None 0 x Periodic 1 0.01 -Continuouscondition outcome Data Begint Cmp N 24 24 1 0 0 I 0.01 1.000% 1 1 1 PV 1000 1000 1 0 PMT -47.073472 0 FV 0 0 14 1 1 Numper = 12 Reliability test: 1 Type of payment: -Beginning of a period Errors: x End of a period Compounding: -None Interest rate: no x Periodic -ContinuousDETYIELD table outcome data Condition APR INT2 RA NP 0 0 0 1 0.12 0.01 0.126825 0.01 1 0 0 0001 0.12 0.01 0.126825 0.01Comments condition N I PV PMT FV 0 0 1% 1000 0 0 0 24.0 1000 0 3 0 24.0 1% 0 0 0 24.0 1% 1000 0 0 0 24.0 1% 1000 0 0 1% 1000 0 0 0 24.0 1000 0 0 0 24.0 1% 0 0 1 24.0 1% 1000 -47.07347 0 0 0 24.0 1% 1000 0 24 0.01 1000 -47.07347 0 03Data looked for Periodic payments -47.07347 PMT Periodic payments-47.07347 PMTRaw Optional: Timing of periodic payments (cross (x) one). Beginning of periods. DATA 1) The number of periods (N). Complete either 4 of the following 5 fields. The one that will be left blank will be computed. 2) The Yield (I) Remember: What you pay is NEGATIVE, what you receive is POSITIVE 3) The Present Value (PV) 4) The Periodic payment (PMT) 5) The Future Value (FV) RESULT COMMENTS Typical loan: money is earned now, to be reimbursed periodically. $50, 000 are earned at first. The real yield is 0,01% per period. This Raw sheet allows you to enter data and get the outcome right next to the data, without having to pull the elevator up extensively!Timing of periodic payments (cross (x) one). Beginning of periods. End of periods. x number of periods (N). 1.000% 50,000.00 Periodic payment (PMT) 600.00 --Number of periods of interest payments N = 180.07 Typical loan: money is earned now, to be reimbursed periodically. 000 are earned at first. The real yield is 0,01% per period. The timeline is 180 periods long. Periodic payments are $ 600. The end value is worth $ 000 next to the data, without having to pull the elevator up and down Cases -Loans A loan is a sum of money lent against the payment of interests. Select the information you are looking for by putting a cross against ONE of the following choices. How long will it take to repay the loan? Is it worth to refinance that loan? What is my loan balance? x How much do I have to pay each month? How much do you have to pay each month? Follow the instructions below, completing all five fields but the one corresponding to periodic payments. 1) The number of periods (N). The number of periods is the amount of time the loan lasts, ie the number of times payments are made to solve a loan. Enter the number of payments left until the end of your loan (for instance: 120 for 10 years with 12 payments per year). 2) The Yield (I) The yield is the rate of interest you pay on a loan. It is the Real Periodic yield discussed in section B (interest converter) 3) The Present Value (PV) The Present Value is the loan you benefit from. It must be entered as a POSITIVE. Enter the value of your loan (eg, price of the car minus downpayment). 4) The Periodic payment (PMT) The Payment is the sum you will periodically give to reimburse the loan and pay the interests. It must be entered as a NEGATIVE. This is the information you are looking for. Therefore, leave this field blank. 5) The Future Value (FV)Usually, no sum is due at the end of a loan. Hence, enter 0 in this field. Optional: Timing of periodic payments. Cross (x) the timing of the payments: Payments are made at the beginning of each period. Payments are made at the end of each period. In general, payments are considered being made at the end of each period. RESULT COMMENTS Typical loan: money is earned now, to be reimbursed periodically. $1, 000 are earned at first. The real yield is 0,01% per period. Amortization table. An amortization table distinguishes for each period between, the payment of the principal and, the payment of the interests. Period Beginning amount 1 1,000.00 2 962.93 3 925.49 4 887.67 5 849.47 6 810.89 7 771.93 8 732.58 9 692.83 10 652.68 11 612.13 12 571.18 13 529.82 14 488.04 15 445.85 16 403.24 17 360.20 18 316.73 19 272.82 20 228.47 21 183.68 22 138.44 23 92.75 24 46.60 against ONE of the following choices. How long will it take to repay the loan? Is it worth to refinance that loan? What is my loan balance? How much do I have to pay each month? one corresponding to periodic payments. 1) The number of periods (N). the number of times payments are made to solve a loan. instance: 120 for 10 years with 12 payments per year). 24 2) The Yield (I) Periodic yield discussed in section B (interest converter) of the Tutorial sheet. 1.000% 3) The Present Value (PV) 1,000.00 4) The Periodic payment (PMT) the loan and pay the interests. It must be entered as a NEGATIVE. 5) The Future Value (FV)-Timing of periodic payments. made at the beginning of each period. Payments are made at the end of each period. x Periodic payments PMT = 47.07 -Typical loan: money is earned now, to be reimbursed periodically. The real yield is 0,01% per period. The timeline is 24 periods long. Periodic payments are $ 047. The end value is worth $ 000 the payment of the principal and, the payment of the interests. Payment Interest Repayment of Principal principal balance (47.07) (10.00) (37.07) (47.07) (9.63) (37.44) (47.07) (9.25) (37.82) (47.07) (8.88) (38.20) (47.07) (8.49) (38.58) (47.07) (8.11) (38.96) (47.07) (7.72) (39.35) (47.07) (7.33) (39.75) (47.07) (6.93) (40.15) (47.07) (6.53) (40.55) (47.07) (6.12) (40.95) (47.07) (5.71) (41.36) (47.07) (5.30) (41.78) (47.07) (4.88) (42.19) (47.07) (4.46) (42.61) (47.07) (4.03) (43.04) (47.07) (3.60) (43.47) (47.07) (3.17) (43.91) (47.07) (2.73) (44.35) (47.07) (2.28) (44.79) (47.07) (1.84) (45.24) (47.07) (1.38) (45.69) (47.07) (0.93) (46.15) (47.07) (0.47) (46.61) 962.93 925.49 887.67 849.47 810.89 771.93 732.58 692.83 652.68 612.13 571.18 529.82 488.04 445.85 403.24 360.20 316.73 272.82 228.47 183.68 138.44 92.75 46.60 (0.01) Cases -Investments An investment is a sum of money you put into an asset to earn a return on. Whether you want to purchase a substantial asset (car, household equipment) or put asside enough for your retirement or you need to plan your savings to reach a specific goal. Select the information you are looking for by putting a cross against ONE of the following choices. Assets (car, stereo, apartment…): Retirement: College education: x College education: Periodic savings needed. You want to know how much you should save periodically to face the cost of college education. Follow the instructions below, completing all 5 fields but one. Note that the answer to this question is a two-step process: follow the instructions for step 1, write down the result, then follow 1) The number of periods (N). The number of periods is the amount of time the money will be invested. STEP 1: Enter the number of years of college education expected. STEP 2: Enter the number of years in between now and the time at which you will face the cost of college tuitions. 2) The Yield (I) The yield is the rate of interest you earn on an investment. It is the Real Periodic yield discussed in section B (interest converter) Enter the expected rate of interest that will be earned on your savings, minus the expected rate of increase of college tuitions, which is presently (year 2000) higher than the inflation rate. For instance, you expect to earn 7,50% on your savings and witness college tuitions to increase at a rate of 5,25%. Enter 3) The Present Value (PV) The Present Value is the amount you invested at the very beginning. It must be entered as a NEGATIVE. STEP 1: This is the amount you are looking for to write down prior to performing step 2. It is the amount you need to have Leave this field blank. Make sure the result you get is POSITIVE (it is an initial investment you will need to have). STEP 2: Enter the amount of savings you have put aside so far towards college education. Enter 0 if none. 4) The Periodic payment (PMT) The Payment is the sum you will periodically invest (NEGATIVE) or earn from you investment (POSITIVE).STEP 1: Enter the actual cost of tuitions for a year of college, minus what you expect on being able to pay from revenues you will be earning, as a NEGATIVE. STEP 2: This is the amount you are looking for: The amount to put aside each year for college tuitions. Leave this field blank. Make sure the result you obtain is NEGATIVE (it is a periodic payment). 5) The Future Value (FV) The Future Value is the money your investment will be worth at the end of the investment's timeline. STEP 1: Enter 0 in this field. STEP 2: Enter the amount you obtained from step 1 here, as a POSITIVE. Optional: Timing of periodic payments. Cross (x) the timing of the payments: Payments are made at the beginning of each period. Payments are made at the end of each period. In general, payments are considered being made at the end of each period. RESULT COMMENTS Typical investment (savings), where you invest money periodically. The real yield is 0,02% per period.household equipment) or put asside enough for your retirement or your children's education, against ONE of the following choices. Assets (car, stereo, apartment…): How much to periodically put aside? How long before I can afford it? How much will I have after a while? How much should I put aside? When should I retire? College education: How much should I put aside? face the cost of college education. follow the instructions for step 1, write down the result, then follow the instructions for step 2. 1) The number of periods (N). 10 2) The Yield (I) the Real Periodic yield discussed in section B (interest converter) of the Tutorial sheet. savings, minus the expected rate of increase of 2.250% witness college tuitions to increase at a rate of 5,25%. Enter (7,50 -5,25 =) 2,25%. 3) The Present Value (PV) beginning. It must be entered as a NEGATIVE. prior to performing step 2. It is the amount you need to have aside at the time of the first college tuition. -towards college education. Enter 0 if none. 4) The Periodic payment (PMT) NEGATIVE) or earn from you investment (POSITIVE).minus what you expect on being able put aside each year for college tuitions. NEGATIVE (it is a periodic payment). 5) The Future Value (FV) the end of the investment's timeline. 93,500.00 Timing of periodic payments. made at the beginning of each period. Payments are made at the end of each period. x Periodic payments PMT = 8,441.90 -Typical investment (savings), where you invest money periodically. The real yield is 0,02% per period. The timeline is 10 periods long. Periodic payments are $8, 442. The end value is worth $93, 500PMT PMTCases -Stocks and bonds (securities). Stocks are pieces of property of a company. Bonds are long-term debt instruments held against a company. Select the information you are looking for by putting a cross against ONE of the following choices. Bonds x Stocks Bond -Duration. The duration is another mean to compare investment opportunities by taking into account yield evolution. 1) The number of periods (N). The number of periods is the amount of time the money will be invested. A security is generally valued by discounting expected earnings at an expected rate of return. These expectations can then market as a whole by putting the computed present value against the market value of the security. Stock Valuation. The price of a stock is determined through the law of offer and demand: how much people are willing to pay for a stock or price is to compare that computed price (intrinsic value) with that of the market (market value), in order to decide whether One way of providing an estimate is to discount all the estimated earnings to come at the present date. In other words, it and finding out how much those earnings can be worth today. Bond Valuation. At the time of its issuance, a bond's price should be at par with its principal value (face value), since the coupon rate present time on similar (in terms of risk) bonds. Later, the price of the bond will evolve depending on the actual rate being issued. For instance, for a bond previously issued with 10% coupons, should newly issued bonds with similar caracteristics provide bond's price will rise in such manner that buyers will only earn a 5% return on the price they pay until the bond matures. Such a 5% required yield on its market price, although the coupon rate is still 10% of the face value. It will also be known as being price above the face value). Conversely, should coupon rates of similar newly issued bonds rise above 10%, the bond should Do note that the stock and bond valuations below (present value method) do not allow for irregular cash flows or rates of This is the information you are looking for. Therefore, leave this field blank. 2) The Yield (I) The yield is the rate of interest you earn on an investment. It is the Real Periodic yield discussed in section B (interest converter) Enter the coupon rate being paid on newly issued bonds with similar caracteristics. Add or withdraw your expectation on the coupon rate evolution (do you expect rates to rise or diminish in the years to come?). 3) The Present Value (PV) The Present Value is the amount you invested at the very beginning. It must be entered as a NEGATIVE. Enter the current market price of the bond. 4) The Periodic payment (PMT) The Payment is the sum you will periodically invest (NEGATIVE) or earn from you investment (POSITIVE). Enter the amount of the coupon being regularly paid. 5) The Future Value (FV) The Future Value is the money your investment will be worth at the end of the investment's timeline. Sum the face value of the bond with the last coupon. Optional: Timing of periodic payments. Cross (x) the timing of the payments: Payments are made at the beginning of each period. Payments are made at the end of each period. In general, payments are considered being made at the end of each period. RESULTCOMMENTS $1, 000 are invested at first. The real yield is 0,05% per period.long-term debt instruments held against a company. against ONE of the following choices. How much is a bond worth? Yield to Maturity Duration How much is the intrinsic stock value today? opportunities by taking into account yield evolution. 1) The number of periods (N). at an expected rate of return. These expectations can then be compared with those of the against the market value of the security. demand: how much people are willing to pay for a stock or sell it. The aim of finding out a stock market value), in order to decide whether it is worth buying or selling. earnings to come at the present date. In other words, it involves forecasting future earnings face value), since the coupon rate will reflect the rate being paid at the of the bond will evolve depending on the actual rate being paid on similar bonds being newly should newly issued bonds with similar caracteristics provide a lower return (say 5%), the 5% return on the price they pay until the bond matures. Such bond will be known as providing rate is still 10% of the face value. It will also be known as being sold at a premium (market similar newly issued bonds rise above 10%, the bond should then be sold at a discount. method) do not allow for irregular cash flows or rates of return to be taken into account.2) The Yield (I) the Real Periodic yield discussed in section B (interest converter) of the Tutorial sheet. do you expect rates to rise or 5.186% 3) The Present Value (PV) beginning. It must be entered as a NEGATIVE. 1,000.00 -4) The Periodic payment (PMT) NEGATIVE) or earn from you investment (POSITIVE). 50.00 5) The Future Value (FV) the end of the investment's timeline. 1,050.00 Timing of periodic payments. made at the beginning of each period. Payments are made at the end of each period. x Number of periods of interest paymentsN = 17.27 000 are invested at first. The real yield is 0,05% per period. The timeline is 17 periods long. Periodic revenues are $ 050. The end value is worth $1, 050Currency symbol: $outcome Real yield per year RA = 12.68% INT table Real yield per period INT2 = 1.00% Nominal yield per year APR = 12 12.00% Nominal yield per period NP = 1.00% Numper = 12 Compounding: None X Periodic Continuous scripts Excel formulae Number of periods of interest payments N 16.43 16.430 Rate of interest I 5.20% 5.200% Present Value PV -1000 -1000 -Periodic payments PMT 50 50 1.00 Future Value FV 1050 1050 -Numper = 12 Type of payment: Beginning of a period x End of a period Compounding: None Periodic x ContinuousDETYIELD table outcome condition outcome data Condition APR INT2 RA 0 1 1 0.12 0.01 0.126825 0 0 0 0 1 0 0 0 0 0 0 0 0 1 12 1 0.12 0.01 0.126825 1 0.12 condition Loan or investment Data Begint Cmp condition N 0 0 0 0 1 0 1 1 0 0 0 0 -1 1 0 -1 0 -1 0 -4 1 1 0 1 1 16.4 0 -Reliability test: 1 0 -0 -0 -16.43NP 0.01 0.01 I PV PMT FV 5% -1000 50 1050 -1000 50 1050 5% 50 1050 5% -1000 1050 5% -1000 50 5% -1000 50 1050 -1000 50 1050 5% 50 1050 5% -1000 1050 5% -1000 50 0.052 -1000 50 1050