Module 5: Interest concepts of future and present value


 Fay Bennett
 6 years ago
 Views:
Transcription
1 Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities and annuities due. You also become familiar with valuation techniques involving the use of a financial calculator and functions in Excel. Finally, you apply what you have learned by using an Excel spreadsheet to make present value calculations. Test your knowledge Begin your work on this module with a set of testyourknowledge questions designed to help you gauge the depth of study required. Note: In this module, the solutions to numerical computations are demonstrated using the most common format of data entry for financial calculators. The method of input may differ slightly across brands and models of calculators. Always refer to your owner s manual for specific instruction. This module introduces the following abbreviations: PV present value FV future value PMT the amount of the annuity payment I the interest rate per period N the number of periods BGN you need to set your calculator to compute an annuity due PV, FV, PMT, I, or N =? you should solve for the desired variable? = a number the displayed solution Please note that present values (PVs) are typically entered as a negative number, and that when you solve for PVs, the calculator s output will normally display a negative number as well. The underlying logic here is that a PV represents what you would pay today (a cash outflow) to obtain a sum or sums of money in the future (cash inflows). Outflows are entered as negatives; inflows are entered as positives. Caution! Some financial calculators such as the popular Texas Instruments BA II Plus have the added functionality of allowing you to specify how many interest compounding periods there are per year. The default setting for the BA II Plus is 12 compounding periods per year whereas the examples that follow are based on the assumption that you have set the number of compounding periods to 1. Refer to your owner s manual for instructions on how to make this change. There are several reasons why the calculator keystrokes are illustrated in this manner: 1. Conceptually, many people find it easier to think in terms of an interest rate per period and the number of periods to maturity. 2. It is consistent with the format for entering the data into Excel.
2 Page 2 of Many students own financial calculators that do not include the added functionality of being able to set the number of compounding periods per year. While the methodology in the examples that follow is of the "interest rate per period" type, you may use whatever method you feel most comfortable with. Learning objectives 5.1 Describe the concept of the time value of money. (Level 1) 5.2 Describe the concept of interest including simple and compound interest, and effective and nominal rates of interest. (Level 1) 5.3 Compute the present and future value of a single payment, and an annuity (ordinary and due). (Level 1) 5.4 Design a worksheet to perform time value of money analysis. (Level 1) 5.1 Time value of money Learning objective Describe the concept of the time value of money. (Level 1) Required reading present_value_appendix.html Appendix: Interest Concepts of Future and Present Value, (located on the OLC) page 395 "Time value of money" (Level 1) LEVEL 1 Please note that this reading is meant to provide you with information pertaining to present and future value concepts, rather than how to compute present values. The reason for this is that while the illustration of principles is sound, the narrative relies on factor tables which are seldom used in practice. The FA2 module notes focus on the use of a financial calculator, and to a lesser degree Excel. To fine tune your skills, we suggest that you use your financial calculator to solve the examples in this appendix. Keep in mind that results may differ slightly because calculators and spreadsheets are more accurate than tables as they take their calculations to more significant decimal places. The required reading provides an indepth study of the time value of money, including the concept of present value (PV). The computation and interpretation of PVs are of interest to accountants, as accounting standards require us to value many liabilities at the present value of the future payment streams. The extent to which PVs are used in accounting will become very evident when you study FA3. Consider Example At this point, you need not perform any calculations; use logic to decide what the appropriate answer should be. The numerical solutions are provided for you to check after you have mastered the subject matter.
3 Page 3 of 23 Example If $10,000 is deposited in a savings account earning 4% interest compounded annually, will you have more money at the end of 5 years or 10 years? 2. If the interest rate is 4% compounded annually, will you be willing to pay more for a payment of $10,000 to be received in 5 years, or $10,000 to be received in 10 years? 3. If $10,000 is deposited in a savings account, will you have more money at the end of 5 years if the interest rate is 4% compounded annually or 6% compounded annually? 4. Will you be willing to pay more today for a payment of $10,000 to be received in 5 years if the interest rate is 4% or 6%? 5. If you deposit $10,000 in a saving account, will you have more money at the end of 5 years if the nominal interest rate of 4% is compounded semiannually or annually? 6. Will you be willing to pay more today for a payment of $10,000 to be received in 5 years if the interest rate is 4% compounded semiannually or annually? Solution 1. You will have $12,167 at the end of 5 years (PV = 10,000, N = 5, I = 4, FV =? = 12,167) and $14,802 at the end of 10 years (PV = 10,000, N = 10, I = 4, FV =? = 14,802). 2. You will be willing to pay $8,219 now to receive $10,000 at the end of 5 years (FV = 10,000, N = 5, I = 4, PV=? = 8,219) and $6,756 to receive $10,000 at the end of 10 years (FV = 10,000, N = 10, I= 4, PV=? = ). 3. As before, you will have $12,167 at the end of 5 years if you earn 4% interest. If the rate increases to 6%, you will end up with $13,382 (PV = 10,000, N = 5, I = 6, FV =?? = 13,382). 4. As before, you will be willing to pay $8,219 now to receive $10,000 in 5 years if the market rate of interest is 4%. If the rate increases to 6%, you will be willing to pay $7,473 (FV = 10,000, N = 5, I = 6, PV =? = 7,473). 5. As before, you will have $12,167 at the end of 5 years if you receive interest at 4% compounded annually. If interest is compounded semiannually, you will receive $12,190 at the end of 5 years [PV = 10,000, N = 10 (5 2), I = 2 (4/2), FV =? = 12,190] 6. As before, you will be willing to pay $8,219 now to receive $10,000 in 5 years if the market rate of interest is 4% compounded annually. If the interest is compounded semiannually, you will be willing to pay $8,203 [FV = 10,000, N = 10 (5 2), I = 2 4/2, PV =? = 8,203]. These simple examples illustrate the following important points about the time value of money:
4 Page 4 of 23 The nominal rate of interest refers to the annual stated rate. The effective rate of interest is the rate that you actually end up receiving or paying once the effects of compounding are considered. All else being equal: The longer the time to maturity, the greater the maturity value (FV) for a stated PV; conversely, the lesser the PV for a given FV. The higher the rate of interest, the greater the FV for a given PV. Conversely, the lesser the PV for a given FV. The more frequent the compounding of interest, the greater the FV for a stated PV. Conversely, the lesser the PV for a given FV. The relationship between PV and FV, which can be stated as FV = PV(1 + I) n, can be restated as PV = FV/(1 + I) n. These formulas are the basis for the above statements about the time value of money. 5.2 Basic interest concepts Learning objective Describe the concept of interest including simple and compound interest, and effective and nominal rates of interest. (Level 1) Required reading Appendix: Interest Concepts of Future and Present Value, (located on the OLC), pages "Basic interest concepts" (Level 1) LEVEL 1 The required reading distinguishes between simple interest and compound interest. As simple interest is rarely used in business, unless stated otherwise, all interest computations are to be calculated on a compound basis. You should assume that the compounding period is annual, unless there is a specific comment to the contrary. An interest period is the period (for example, a month or a year) in which interest is calculated. The method of calculating interest refers to how often the interest is compounded. It is quite common to see lenders compound interest on a daily, weekly, monthly, semiannually, or annually basis. For computational purposes, accountants are interested in the number of periods (not years) that the investment or loan is to be held and the interest rate per period. This frequently requires converting the nominal interest rate per year into a more appropriate measure. Work through Example to help you understand this concept.
5 Page 5 of 23 Example Wittink Company invests $80,000 for 6 years in an account that pays interest at the rate of 12% per annum. How much money will Wittink receive under each of the following scenarios? Interest is compounded annually Interest is compounded semiannually Interest is compounded quarterly Solution Interest rate per period Determination of the rate per period Number of periods Determination of the number of periods Fund balance Annual compounding 12% 12%/1 compounding period per year = 12% per period n=6 6 1 compounding period per year = 6 PV = 80,000, n = 6, I = 12, FV =? = $157,906 Semiannual compounding 6% 12%/2 compounding periods per year = 6% per period n= compounding periods per year = 12 PV = 80,000, n = 12, I = 6, FV =? = $160,958 Quarterly compounding 3% 12%/4 compounding periods per year = 3% per period n= compounding period per year = 24 PV = 80,000, n = 24 I = 3, FV =? = $162,624 As you can see, the more frequent the compounding period, the greater the future value. Effective interest rates For comparative purposes, it is necessary to ensure that all nominal (quoted) rates of interest are converted to effective (what you actually pay or receive) rates. Note that interest rates are, by convention, quoted in annual terms with the number of compounding periods referred to, for example, 10%, compounded quarterly. The quoted rate is known as a nominal rate; the rate that you actually pay when the effects of compounding are taken into account is the effective rate. Nominal rates can be converted to effective rates using the following equation: Effective rate = [1 + (I n)] n 1, where I = the nominal interest rate and n = the number of compounding periods per year. For example, the effective interest rate for 10% compounded quarterly is:
6 Page 6 of 23 Effective rate = [1 + (I n)] n 1 = (1.025) 4 1 = 10.38% The foregoing equation can be rearranged so as to convert effective rates to nominal rates: Nominal rate = [(1 + I) 1/n 1]n, where I = the effective interest rate and n = the number of compounding periods per year. For example, the 10.38% effective rate derived above is equivalent to a nominal rate of 10% per annum determined as follows: Nominal rate = [(1 + I) 1/n 1]n = [(1.1038) 1/4 1]4 =10% However, an easier method to calculate the effective or nominal rate would be to use the builtin functions of your calculator or a spreadsheet. 5.3 Computing present values Learning objective Compute the present and future value of a single payment, and an annuity (ordinary and due). (Level 1) Required reading Appendix: Interest Concepts of Future and Present Value, (located on the OLC), pages (Level 1) LEVEL 1 The required reading details how to compute both the present and future values of a single payment. Our discussion here will be limited to illustrating various methods of accomplishing this. The most common ways to compute PVs and FVs are to use a financial calculator or spreadsheet program such as Excel. While the required reading does illustrate the computation of both present and future values, this topic limits the balance of the discussion to the calculation of present values, because these are what you are most likely to encounter in your accounting career. However, please note that future values do remain examinable. Spreadsheet method Summary of financial functions in Excel Function Purpose =FV(rate, nper, pmt, pv, type) Calculates the future value of an annuity or a present amount =PV(rate, nper, pmt, fv, type) Calculates the present value of an annuity or a future amount =PMT(rate, nper, pv, fv, type) Calculates the payment per period for an annuity
7 Page 7 of 23 =NPER(rate, pmt, pv, fv, type) Calculates the number of interest periods for an annuity Note that you need to specify the present value in the Excel functions as a negative value. For details about Excel, see CT2. Calculator method You should refer to your owner s manual for specific instructions as to the required steps for performing time value of money calculations. FV = $10,000 N = 4 I = 6 PV=? = $7, Now work through the examples below so as to familiarize yourself with the two methods of computation. Example Present value of a future amount What is the present value of a single payment of $10,000, which is to be received 3 years from now using an interest rate of 10% compounded annually? Your known variables are: Future value $ 10,000 Period interest rate 10% Number of periods 3 Calculator method Enter the following on the calculator: Number of periods (N) 3 Period interest rate (I) 10 Future value (FV) PV =?? = 7, Spreadsheet method Start your spreadsheet program. Open the file FA2M5E1. Click the sheet tab M5E1. This worksheet has labels preentered in column A. Enter appropriate values and formulas in cells B3 to B6. Your completed worksheet should look like this:
8 Page 8 of 23 The formula for the present value amount in cell B6 should be =PV(B4,B5,,B3) A 3 Future value $10, Annual interest rate 10.00% 5 Number of years 3 6 Present value $7, Save this worksheet. If you do not obtain the result shown, click the sheet tab for M5E1S and review the formula in cell B6. B Example Present value of an ordinary annuity You are purchasing an investment that will pay you $2,500 semiannually for 6 years (a total of 12 payments). The first payment will be received 6 months from now. How much should you pay for this investment if the interest rate is 8%, compounded semiannually? Calculator method First, confirm that you are in financial mode and that you have fully cleared all the mode registers. Then enter the following data: Number of periods: (N) 12 Payment amount: (PMT) 2500 Interest rate: (I) 4 PV =?? = 23, Spreadsheet method Continue with the M5E1 worksheet. This worksheet has labels preentered in column A. Enter appropriate values and formulas in cells B8 to B11. Your completed worksheet should look like this: A 8 Periodic payment $2, Periodic interest rate 4.00% 10 Number of periods Present value of annuity $23, B
9 Page 9 of 23 The formula for the present value in cell B11 should be =PV(B9,B10,B8) Compare your result with that shown. If necessary, click the solution sheet tab M5E1S to compare results. Using time lines to calculate annuity due The difference between an ordinary annuity and an annuity due is the timing of the payment. For an ordinary annuity, the payment comes at the end of each interest period, whereas for an annuity due, the payment comes at the beginning of each interest period. You can see this difference by comparing the time line of an ordinary annuity with three annual payments to the time line of an annuity due with three annual payments, as shown in Exhibit Exhibit Comparison of an ordinary annuity and an annuity due In the time lines, you can see that the cash flow for an ordinary annuity is made up of three payments starting one period from the initial loan or investment date. In the case of an annuity due, the payments start one period ahead of the ordinary annuity, beginning with the first payment at the initial loan or investment date. The relationship can be expressed as: PV of an annuity due = PV of an ordinary annuity [1 + I] where I = the interest rate per period. Present value of annuity due Example Present value of an annuity due Suppose that you wish to calculate the PV of the investment in the previous example assuming that the first
10 Page 10 of 23 payment will be received immediately. Calculator method Clear the financial mode registers, then enter the following data on the calculator: Mode BGN Number of periods: [N] Payment amount: [PMT] 2500 Interest rate per period: [I] 8% 2 4% PV =?? = 24, Spreadsheet method Continue with the M5E1 worksheet. Add the following model to the worksheet to calculate the present value of the annuity due. The formula in cell B16 should be =PV(B14,B15,B13,,1) A 13 Periodic payment $2, Periodic interest rate 4.00% 15 Number of periods Present value of annuity $24, B 5.4 Computer illustration 5.41: Value of equipment Learning objective Design a worksheet to perform time value of money analysis. (Level 1) LEVEL 1 In this computer illustration, you use present value calculations to assist in determining the value of equipment to be recorded in the company s books. Material provided A file, FA2M5P1, containing a blank formatted worksheet M5P1 and a solution worksheet M5P1S.
11 Page 11 of 23 Description Suppose you want to buy a new piece of equipment from the manufacturer. The terms and conditions of the purchase plan are as follows: down payment of $10, monthly payments of $1,500, first payment to be made at the end of the first month a final payment of $4,000 to be made at the end of the 36th month, with the last monthly payment The going interest rate for this type of lease plan is 12% per year compounded monthly. Required Construct a worksheet to calculate the equipment s value to be recorded in the accounting records. Procedure You must calculate the present value of the equipment. There are three components in the purchase plan: the initial down payment, which is a present value the 36 ordinary annuity payments, which you will discount to present values the final payment at the end of the 36th month, which you will discount to present value Make sure to use the same interest rate and compounding periods for both the annuity and final payment computations. The following is a possible layout of your worksheet: Purchase plan Down payment Final payment Monthly payment Annual interest rate Monthly interest rate Number of payments Present value of monthly payments Present value of final payment Present value of equipment Save the completed worksheet under your own initials. If you construct your formulas correctly, the present value of the equipment should be $57, To compare your result with the suggested solution, click the sheet tab M5P1S.
12 Page 12 of 23 Module 5 selftest Question 1 Computer question Trunet Company has $55,000 in excess cash that it wishes to invest for a fiveyear period. After analyzing several investment options, Trunet narrowed its choice to three GICs (Guaranteed Investment Certificates). As a CGA, you were asked to help the management of Trunet determine which of the investment options yields the best result. The options are GIC A: 5.5% annual interest rate, compounded annually GIC B: 5.25% annual interest rate, compounded semiannually GIC C: 5% annual interest rate, compounded monthly Required Use the partially completed worksheet in the file stest05q01.xls to determine which of the GICs has the highest maturity value (future value). a. Analyze the results from your completed worksheet and identify which GIC has the highest maturity value. What is the value of that GIC? Show the spreadsheet formula used to calculate it. b. Explain the results by discussing the effect of interest compounding. Calculate the effective interest rate of each GIC. Procedure 1. Open the file stest05q01.xls. Note that the worksheet contains three sections dealing with each of the three GICs. 2. For GIC A, move to cell B12 and enter a formula to calculate the interest rate per period. 3. In cell B13, enter the number of interest periods. 4. In cell B14, build a formula that will calculate the future value of the investment based on the amount of the initial investment found in cell B4, and on the interest rate per period and the number of periods calculated in cells B12 and B13, respectively. The formula should make use of absolute cell references where necessary to enable copying to other cells. 5. In cell B15, calculate the effective interest rate. 6. Repeat steps 2 to 5 for GICs B and C, copying formulas from the section for GIC A whenever possible.
13 Page 13 of Save your worksheet, and print your results. 8. Display and print the formulas. 9. Answer parts (a) and (b). Solution Question 2 Multiple choice a. Which of the following statements best describes the relationship between an annuity due and an ordinary annuity? 1. The payments will be the same in both situations in order to accumulate $10,000 in three years. 2. The payment for the ordinary annuity will be equal to the payment for the annuity due plus one period of interest. 3. The interest paid on a purchase would be the same if the amount of purchase is paid with an annuity due as it would be with an ordinary annuity. 4. The principal outstanding will be the same after the same number of payments in each case. b. What is the best definition of the present value? 1. The value of a sum of money today 2. The value of a sum of money at the beginning of the period of a money transaction 3. The accumulation of principal and interest over time 4. The value of goods that can be bought today after considering inflation c. If the interest rates are changed from 8% compounded annually to 8% compounded monthly, which of the following would be true? 1. The future value of a series of dollar values would decrease. 2. The present value of a single dollar figure would increase. 3. The present value of a series of dollar figures would decrease. 4. The present value of an annuity of equal payments would increase. d. Which of the following would provide the greatest growth rate for an investment? 1. 8% compounded monthly % compounded annually % compounded quarterly % compounded semiannually e. A piece of equipment can be leased over five years. Which statement describes how the asset and liability should be valued for this lease? 1. The total of all the payments to be made on the lease 2. The price of the same asset as found in the local store 3. The present value of all the payments discounted at the rate of interest as stated in the lease agreement
14 Page 14 of The present value of all the future payments, but excluding the first payment, made at the time of signing the lease f. Which of the following statements would best describe a deferred annuity? 1. An annuity that is to be received some time in the future and is reported on the balance sheet as deferred revenue 2. A series of equal payments that start immediately 3. A series of equal payments that have been deposited in an account in the past and are being left to accumulate more interest 4. A series of equal payments to pay off a debt where the first payment does not take place for several periods g. When the interest compounding period does not coincide with the payment frequency in an annuity, an adjustment has to be made before the present and future value formulae or tables can be used. Which of the following adjustments must be made? 1. The total of the payments in a year must be divided up in the same frequency as the interest conversion. 2. The given interest rate must be converted into the equivalent interest rate compounded at the same frequency as the payments are made. 3. The payments made in a year must be totalled and at the same time the interest should be converted to the equivalent annual rate. 4. The given annual nominal rate must be divided by the number of payments per year. h. Which will grow to the largest amount in five years time? 1. A single deposit of $5,000 at the rate of interest of 7.5% compounded quarterly 2. A deposit of $2,000 immediately and a further $3,000 in two years time, both earning 8.5% compounded monthly 3. A quarterly deposit of $300 at the end of each quarter at 7.5% compounded quarterly 4. $1100 at the beginning of each year at 8.2% compounded annually i. How long would it take a deposit of $2,000 to reach $5,000 if it could earn interest at 9% compounded annually? years years years years j. What interest rate compounded quarterly is equivalent to 8.5% compounded semiannually? % % % % k. A loan of $20,000 has to be repaid by monthly payments for a period of four years. If interest charged is 12% compounded monthly, what will be the monthly payments? 1. $ $470.83
15 Page 15 of $ $ l. An asset can be obtained with a capital lease for 4 years with quarterly payments of $4,000 starting immediately. The interest included in the lease is 14% compounded quarterly. What value should be placed on the asset? 1. $36, $48, $50, $64, m. What rate of interest compounded quarterly was earned on an investment of $6,000 that earned interest of $1, over a twoyear period? 1. 2% 2. 8% % 4. 9% n. Over the last 20 years, at the end of each month you have been saving $100 in a special savings account that has paid a fixed rate of 6% compounded monthly. You have just made the last deposit and are now considering withdrawing monthly amounts of $800 at the end of each month. If the interest remains at 6% compounded monthly, how long will it be before the account is exhausted? 1. 2 years and 6 month 2. 5 years and 1 months 3. 5 years and 9 months 4. 6 years and 1 month o. What is the present value of $3,000 in two years time and $5,000 in four years time if money is worth 10% compounded quarterly? 1. $5, $5, $6, $8, p. Twenty years ago, you made a single deposit of $30,000 to a savings account. The balance in your account today is $70,000. If interest was compounded quarterly, what was the effective annual rate of interest that you earned on the account? % % % % q. You have made a deposit of $6,000 to a savings account semiannually for the past five years. The first deposit was made on January 1, It is now January 1, 2007 and the balance in your account is $85,000. If interest was compounded semiannually, what was the effective annual rate of interest that you earned on the account? %
16 Page 16 of 23 Solution Question % % % In terms of the time value of money, explain what is meant by a. Future value b. Present value c. Compounding Solution Question 4 a. The market value of a bond is calculated as the present value of the future benefits. If a $10,000 bond pays interest of $500 every six months and returns the $10,000 in 10 years time, what is the market value if interest required on such an investment is 9% compounded semiannually? b. John has just won a lottery in which he can receive $250,000 now or $2,000 at the end of each month for the next 25 years. If John can invest the lump sum at 9% compounded monthly, which option should he take? c. Company XYZ is planning on a large expansion which requires $20 million. This can be funded by issuing bonds that carry interest of 10% payable annually and also by depositing into a sinking fund (a savings account) to earn 6% effective, sufficient monies at the end of every year for 20 years, accumulating $20 million in 20 years time. How much altogether does company XYZ have to pay out each year for this money? d. What is the effective interest rate charged on a loan of $50,000 that requires payments of $7,791 every year for 10 years? Solution Question 5 A company is having a cash flow problem and is due to make a payment of $500,000 today, January 1, 20X2. They wish to renegotiate the payment to delay the payment for two years and then make three annual payments starting in three years time on January 1, 20X5. The lender does not wish to wait for two years before getting any money, so the lender requests $50,000 immediately and $50,000 in one year s time. The rest can be repaid according to the company s wishes. Required a. If the interest to be charged is 12% effective, calculate the annual payments under each alternative. b. Prepare a debt amortization schedule for each alternative.
17 Page 17 of 23 c. Give the journal entries for each alternative up to and including the January 20X5 payment. Assume that the company s reporting year end is December 31. Solution Question 6 A loan negotiated with the bank for $400,000 is to be repaid by quarterly payments starting in three months time and finishing in five years time. If the interest rate being charged is 9% compounded quarterly, how much will those payments be? Solution Question 7 A car that costs $22,000 can be purchased for $2,000 down on January 1, 20X1, with monthly payments of $500 starting one month after the purchase. Interest being charged is 6% compounded monthly. Required a. How long will it be before the purchaser actually owns the car? b. How much will the final payment be? Hint: The last partial payment will be made exactly one month after the last payment of $500. Solution Selftest  Content Links Selftest 5 Question 1 Computer solution a. Of the three GICs, GIC A (5.5%, compounded annually) has the highest maturity value of $71,
Module 5: Interest concepts of future and present value
file:///f /Courses/201011/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present
More informationFoundation review. Introduction. Learning objectives
Foundation review: Introduction Foundation review Introduction Throughout FN1, you will be expected to apply techniques and concepts that you learned in prerequisite courses. The purpose of this foundation
More informationCorporate Finance Fundamentals [FN1]
Page 1 of 32 Foundation review Introduction Throughout FN1, you encounter important techniques and concepts that you learned in previous courses in the CGA program of professional studies. The purpose
More informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
More informationStatistical Models for Forecasting and Planning
Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information
More informationModule 8: Current and longterm liabilities
Module 8: Current and longterm liabilities Module 8: Current and longterm liabilities Overview In previous modules, you learned how to account for assets. Assets are what a business uses or sells to
More informationIntroduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations
Introduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the HewlettPackard
More informationAPPENDIX. Interest Concepts of Future and Present Value. Concept of Interest TIME VALUE OF MONEY BASIC INTEREST CONCEPTS
CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists
More information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationMAT116 Project 2 Chapters 8 & 9
MAT116 Project 2 Chapters 8 & 9 1 81: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the
More informationCALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
More informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
More informationDiscounted Cash Flow Valuation
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
More informationPractice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.
PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor
More informationHow To Read The Book \"Financial Planning\"
Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value
More informationThe Time Value of Money
The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time
More informationKey Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued
6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationTime Value of Money. Background
Time Value of Money (Text reference: Chapter 4) Topics Background One period case  single cash flow Multiperiod case  single cash flow Multiperiod case  compounding periods Multiperiod case  multiple
More informationAppendix C 1. Time Value of Money. Appendix C 2. Financial Accounting, Fifth Edition
C 1 Time Value of Money C 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationPowerPoint. to accompany. Chapter 5. Interest Rates
PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When
More informationChapter F: Finance. Section F.1F.4
Chapter F: Finance Section F.1F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given
More informationThe Time Value of Money C H A P T E R N I N E
The Time Value of Money C H A P T E R N I N E Figure 91 Relationship of present value and future value PPT 91 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure
More informationTexas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e
Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,
More informationChapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS 41 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
More informationTime Value of Money. If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in
Time Value of Money Future value Present value Rates of return 1 If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.
More informationThis is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1).
This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons byncsa 3.0 (http://creativecommons.org/licenses/byncsa/
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More information2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.
2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical definedcontribution
More informationUSING THE SHARP EL 738 FINANCIAL CALCULATOR
USING THE SHARP EL 738 FINANCIAL CALCULATOR Basic financial examples with financial calculator steps Prepared by Colin C Smith 2010 Some important things to consider 1. These notes cover basic financial
More informationThe Institute of Chartered Accountants of India
CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The
More informationUsing Financial Calculators
Chapter 4 Discounted Cash Flow Valuation 4B1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your HewlettPackard or Texas Instruments BA II Plus financial calculator
More informationCompound Interest Formula
Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt $100 At
More informationFIN 3000. Chapter 6. Annuities. Liuren Wu
FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate
More informationOrdinary Annuities Chapter 10
Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate
More informationTime Value of Money. Nature of Interest. appendix. study objectives
2918T_appC_C01C20.qxd 8/28/08 9:57 PM Page C1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use
More informationFinQuiz Notes 2 0 1 4
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
More informationCalculating Loan Payments
IN THIS CHAPTER Calculating Loan Payments...............1 Calculating Principal Payments...........4 Working with Future Value...............7 Using the Present Value Function..........9 Calculating Interest
More informationIng. Tomáš Rábek, PhD Department of finance
Ing. Tomáš Rábek, PhD Department of finance For financial managers to have a clear understanding of the time value of money and its impact on stock prices. These concepts are discussed in this lesson,
More information2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?
CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equalsized
More informationAppendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C 1
C Time Value of Money C 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.
More informationCourse FM / Exam 2. Calculator advice
Course FM / Exam 2 Introduction It wasn t very long ago that the square root key was the most advanced function of the only calculator approved by the SOA/CAS for use during an actuarial exam. Now students
More informationTIME VALUE OF MONEY (TVM)
TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate
More informationFinance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization
CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need
More informationThe Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL733A Calculator Reference is made to the Appendix Tables A1 to A4 in the course textbook Investments:
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More informationChapter 2 Applying Time Value Concepts
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More information300 Chapter 5 Finance
300 Chapter 5 Finance 17. House Mortgage A couple wish to purchase a house for $200,000 with a down payment of $40,000. They can amortize the balance either at 8% for 20 years or at 9% for 25 years. Which
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More informationTVM Applications Chapter
Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (longterm receivables) 7 Longterm assets 10
More informationThe Time Value of Money
CHAPTER 7 The Time Value of Money After studying this chapter, you should be able to: 1. Explain the concept of the time value of money. 2. Calculate the present value and future value of a stream of cash
More informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in
More informationThe Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL738 Calculator Reference is made to the Appendix Tables A1 to A4 in the course textbook Investments:
More informationImportant Financial Concepts
Part 2 Important Financial Concepts Chapter 4 Time Value of Money Chapter 5 Risk and Return Chapter 6 Interest Rates and Bond Valuation Chapter 7 Stock Valuation 130 LG1 LG2 LG3 LG4 LG5 LG6 Chapter 4 Time
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More informationMain TVM functions of a BAII Plus Financial Calculator
Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there
More informationPV Tutorial Using Excel
EYK 153 PV Tutorial Using Excel TABLE OF CONTENTS Introduction Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise 8: Exercise 9: Exercise 10: Exercise 11: Exercise
More informationContinue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not.
Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
More information9. Time Value of Money 1: Present and Future Value
9. Time Value of Money 1: Present and Future Value Introduction The language of finance has unique terms and concepts that are based on mathematics. It is critical that you understand this language, because
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 42 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
More informationCHAPTER 9 Time Value Analysis
Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 91 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams
More informationThe Time Value of Money
C H A P T E R6 The Time Value of Money When plumbers or carpenters tackle a job, they begin by opening their toolboxes, which hold a variety of specialized tools to help them perform their jobs. The financial
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction...2 2. Interest Rates: Interpretation...2 3. The Future Value of a Single Cash Flow...4 4. The
More informationThe time value of money: Part II
The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods
More information6: Financial Calculations
: Financial Calculations The Time Value of Money Growth of Money I Growth of Money II The FV Function Amortisation of a Loan Annuity Calculation Comparing Investments Worked examples Other Financial Functions
More informationBasic financial arithmetic
2 Basic financial arithmetic Simple interest Compound interest Nominal and effective rates Continuous discounting Conversions and comparisons Exercise Summary File: MFME2_02.xls 13 This chapter deals
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: Allendof chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
More informationTime Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology
Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationEXCEL PREREQUISITES SOLVING TIME VALUE OF MONEY PROBLEMS IN EXCEL
CHAPTER 3 Smart Excel Appendix Use the Smart Excel spreadsheets and animated tutorials at the Smart Finance section of http://www.cengage.co.uk/megginson. Appendix Contents Excel prerequisites Creating
More informationKey Concepts and Skills
McGrawHill/Irwin Copyright 2014 by the McGrawHill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash
More informationsubstantially more powerful. The internal rate of return feature is one of the most useful of the additions. Using the TI BA II Plus
for Actuarial Finance Calculations Introduction. This manual is being written to help actuarial students become more efficient problem solvers for the Part II examination of the Casualty Actuarial Society
More informationThe explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.
USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas
More informationDick Schwanke Finite Math 111 Harford Community College Fall 2013
Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of
More informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for
More informationHewlettPackard 10BII Tutorial
This tutorial has been developed to be used in conjunction with Brigham and Houston s Fundamentals of Financial Management 11 th edition and Fundamentals of Financial Management: Concise Edition. In particular,
More information5. Time value of money
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More informationEXAM 2 OVERVIEW. Binay Adhikari
EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 7
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17 2. Use of
More informationDeterminants of Valuation
2 Determinants of Valuation Part Two 4 Time Value of Money 5 FixedIncome Securities: Characteristics and Valuation 6 Common Shares: Characteristics and Valuation 7 Analysis of Risk and Return The primary
More informationExcel Financial Functions
Excel Financial Functions PV() Effect() Nominal() FV() PMT() Payment Amortization Table Payment Array Table NPer() Rate() NPV() IRR() MIRR() Yield() Price() Accrint() Future Value How much will your money
More informationIntegrated Case. 542 First National Bank Time Value of Money Analysis
Integrated Case 542 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money
More informationIntroduction to Real Estate Investment Appraisal
Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has
More informationUNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed. Time Value Analysis
This is a sample of the instructor resources for Understanding Healthcare Financial Management, Fifth Edition, by Louis Gapenski. This sample contains the chapter models, endofchapter problems, and endofchapter
More informationHow To Use Excel To Compute Compound Interest
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
More information1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000
D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of
More informationTIME VALUE OF MONEY. In following we will introduce one of the most important and powerful concepts you will learn in your study of finance;
In following we will introduce one of the most important and powerful concepts you will learn in your study of finance; the time value of money. It is generally acknowledged that money has a time value.
More informationChapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationFuture Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr.
Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM0905. April 28, 2014: Question and solutions 61 were added. January 14, 2014:
More information