# Module 5: Interest concepts of future and present value

Size: px
Start display at page:

Transcription

3 file:///f /Courses/ /CGA/FA2/06course/m05t01.htm Note: Solutions in this and subsequent exercises have been rounded to whole numbers, which is consistent with the "traditional" practice of rounding to the nearest dollar for expository purposes. In the real world, though, these amounts would be rounded to the nearest cent. 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=? = 6.756). 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 semi-annually, 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 semi-annually, 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: 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 on an annual basis once the effects of compounding are considered. Unless stated otherwise, all interest rates are quoted on an annual basis. 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. file:///f /Courses/ /CGA/FA2/06course/m05t01.htm (2 of 2) [22/07/2010 9:15:34 AM]

4 file:///f /Courses/ /CGA/FA2/06course/m05t02.htm 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, semi-annual, or annual 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. Example Wittink Company invests \$80,000 for six 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 semi-annually 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 file:///f /Courses/ /CGA/FA2/06course/m05t02.htm (1 of 3) [22/07/2010 9:15:35 AM]

5 file:///f /Courses/ /CGA/FA2/06course/m05t02.htm 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 Semi-annual 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 =? = \$160,976 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 effective rate is the annual rate of interest that includes the effects of compounding. 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: 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 built-in functions of your calculator or a spreadsheet. Equivalent interest rates When the compounding of an interest rate differs from the rate at which the payments occur, the equivalent rate that matches the payment period must be calculated. file:///f /Courses/ /CGA/FA2/06course/m05t02.htm (2 of 3) [22/07/2010 9:15:35 AM]

6 file:///f /Courses/ /CGA/FA2/06course/m05t02.htm Example 1: What rate of interest compounded quarterly is equivalent to a rate of 9% compounded monthly? First, an annual rate of 9% compounded monthly means that the monthly interest rate is 9%/12 = 0.75%. This translates into an effective rate of (1.0075) 12 1 = %, rounded to %. For the effective rate from quarterly compounding to be equivalent to the effective rate from monthly compounding of %, the following relationship must exist: (1 + i/4) 4 1 = (1 + 9%/12) 12 1 Therefore (1 + i/4) 4 1 = % Through rearranging you get (1 + i/4) 4 = (1 + i/4) = ( ) 0.25 i/4 = ( ) i = [( ) ] x 4 i = % Proof: 9%/12 = 0.75%; ( %) 12 1 = % %/4 = %; ( %) 4 1 = %* *Very small difference due to rounding Example 2: What rate compounded quarterly is equivalent to an interest rate of 10% compounded semi-annually? In this example, the unknown interest rate (quarterly) will be compounded twice in the space of a half year. If the unknown rate is "i," then the following relationship exists: (1 + i) 2 = (1 +5%) 1 i = (1 + 5%) ½ 1 = To use this rate in a calculator, you must change it to a percent: % keeping at least five decimals. Never round off these equivalent rates to less than four decimal places because the calculations are very sensitive to the interest rate. file:///f /Courses/ /CGA/FA2/06course/m05t02.htm (3 of 3) [22/07/2010 9:15:35 AM]

7 file:///f /Courses/ /CGA/FA2/06course/m05t03.htm 5.3 Computing present and future 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 =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, Note: 1. The amount of money involved is not negative, but the negative sign represents a "payout" rather than a receipt. That is, you invest (payout) \$7, today (PV) in order to receive \$10,000 (FV) in six periods (in this case, six years time). Not all calculators use the "negative" approach. file:///f /Courses/ /CGA/FA2/06course/m05t03.htm (1 of 5) [22/07/2010 9:15:37 AM]

8 file:///f /Courses/ /CGA/FA2/06course/m05t03.htm 2. Also note that unless the five financial registers (N, I, PV, PMT, and FV) are "zeroed out" before the appropriate amounts are entered, an amount can remain in a register that is not involved in the calculation and the answers may be wrong. To avoid clearing all registers when some numbers are still the same, a "zero" amount should be placed in the register that is not needed in the calculation. In the above case, the PMT does not enter into the calculations (0, PMT). This will ensure that there is no amount in that register. 3. The sequence in which the data is entered into the calculator is irrelevant. Now work through the examples below so as to familiarize yourself with the two methods of computation, but pay particular attention to the use of your calculator. Use your calculator and not someone else's in the examination. Example Present value of a future amount What is the present value of a single payment of \$10,000, which is to be received three years from now using an interest rate of 10% compounded annually? Your known variables are as follows: 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 pre-entered in column A. Enter appropriate values and formulas in cells B3 to B6. Your completed worksheet should look like this: A B 3 Future value \$10, Annual interest rate 10.00% 5 Number of years 3 6 Present value \$7, The formula for the present value amount in cell B6 should be =PV(B4,B5,,B3) file:///f /Courses/ /CGA/FA2/06course/m05t03.htm (2 of 5) [22/07/2010 9:15:37 AM]

9 file:///f /Courses/ /CGA/FA2/06course/m05t03.htm (Note that there is no payment in this calculation which is indicated by the two commas between B5 and B3. In a worksheet the order is important, unlike a calculator.) Save this worksheet. If you do not obtain the result shown, click the sheet tab for M5E1S and review the formula in cell B6. Annuities An annuity is a fixed payment received at regular intervals for a specific amount of time. An ordinary annuity consists of a series of equal payments (or receipts) that occur at the END of EVERY period. If the payments occur at the end of every "interest period," then the annuity is said to be a "simple ordinary" annuity. If the timing of the payments does not correspond to the interest compounding period, the annuity is said to be a complex annuity. For example, an annuity with quarterly payments at the END of EVERY period and interest that is compounded quarterly would be a "simple ordinary" annuity. If the interest were compounded semi-annually but with quarterly payments, then it would be considered a "complex ordinary" annuity. Basic PV and FV formulas used in calculators apply to "simple ordinary" annuities. A common example of a complex annuity is a mortgage where the stated rate is compounded semi-annually but you make payments monthly, biweekly, or weekly. In this situation, the first step is to calculate the equivalent interest rate that compounds at the same frequency as the payments. To solve that type of problem, the interest rate compounded semi-annually must be converted to an equivalent interest rate compounded quarterly, thus turning a complex annuity into a simple annuity. This conversion was demonstrated earlier. Fortunately, most problems involved in business are "simple" annuities and often the period involved is "annual." Example Present value of an ordinary annuity You are purchasing an investment that will pay you \$2,500 semi-annually for six years (a total of 12 payments). The first payment will be received six months from now. How much should you pay for this investment if the interest rate is 8%, compounded semi-annually? In this case, it is a "simple ordinary" annuity the payments come at the end of every six months and the interest is compounded every six months. The interest rate in this situation is 4% every six months. 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) 2,500 Interest rate: (I) 4 PV =?? = 23, Spreadsheet method Continue with the M5E1 worksheet. This worksheet has labels pre-entered 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, B file:///f /Courses/ /CGA/FA2/06course/m05t03.htm (3 of 5) [22/07/2010 9:15:37 AM]

10 file:///f /Courses/ /CGA/FA2/06course/m05t03.htm 9 Periodic interest rate 4.00% 10 Number of periods Present value of annuity \$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. If you wish to invest money to receive back \$2,500 for 12 payments every half year, then you should invest \$23, On the other hand, if you were to borrow money and pay back \$2,500 every six months for 12 payments, you could borrow \$23, 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 file:///f /Courses/ /CGA/FA2/06course/m05t03.htm (4 of 5) [22/07/2010 9:15:37 AM]

11 file:///f /Courses/ /CGA/FA2/06course/m05t03.htm 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 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) 2,500 Interest rate per period: (I) 8% 2 4% PV =?? = 24, Warning: When you use the BGN mode in a calculator, you must be careful to remove it when making "ordinary" annuity calculations. When the BGN mode is engaged, most calculators include "BGN" in the display window, so it is a simple matter to check this. Spreadsheet method Continue with the M5E1 worksheet. Add the following model to the worksheet to calculate the present value of the annuity due. A B 13 Periodic payment \$2, Periodic interest rate 4.00% 15 Number of periods Present value of annuity \$24, The formula in cell B16 should be =PV(B14,B15,B13,,1) file:///f /Courses/ /CGA/FA2/06course/m05t03.htm (5 of 5) [22/07/2010 9:15:37 AM]

12 file:///f /Courses/ /CGA/FA2/06course/m05t04.htm 5.4 Periodic payments required for present value and future value problems Learning objective Compute the required periodic payments for a given present value or future value. (Level 1) LEVEL 1 Ordinary annuities Example: A company wishes to borrow \$50,000 and make annual payments at the end of each year for eight years. If interest being charged on the loan is 10% compounded annually, how much will each annual payment be? Solution: In this problem, the PV is known and it is the PMTs that need to be calculated. First, decide if the annuity is a simple ordinary annuity or not. In this case, it is; the payments are at the END of every year (annually) and the interest is compounded annually. Enter the following in the calculator: Number of periods (N) 8 Period interest rate (I) 10 Present value (PV) 50,000 PMT =?? = 9, Caution: If you do not clear all the registers in your calculator before starting this calculation, you may find that there is an amount residing in the one register that you do not use for this calculation (the FV register), and it will give you the incorrect answer. However, sometimes the information in the other registers doesn't change from a previous calculation, so if you clear all the registers you have to re-enter everything you need. You can overcome this by entering "0" in the register that you will not be using (in the FV register) and that will have the effect of "clearing" the unwanted register. The Excel spreadsheet can also be used; however, practice on your calculator is critical because that will be the tool you are allowed in the examination. Annuity due Example: A piece of equipment that cost \$40,000 is to be leased, instead of purchased, by quarterly payments in advance for a period of six years. Interest charged on the contract is 12% compounded quarterly. What will the quarterly payments be? Solution: Again, you need to determine if this constitutes an ordinary simple annuity. In this case, it is not because the payments are "in advance," meaning that they are made at the beginning of each period. This, then, is an annuity due. It is a simple annuity because the payments and the compounding are both quarterly, so it is a "simple annuity due." To calculate the required payment using the calculator, make sure the various registers have been cleared and enter the following information: Type of annuity BGN file:///f /Courses/ /CGA/FA2/06course/m05t04.htm (1 of 2) [22/07/2010 9:15:37 AM]

13 file:///f /Courses/ /CGA/FA2/06course/m05t04.htm Number of periods (N) 24 Period interest rate (I) 3 Present value (PV) 40,000 PMT =?? = 2, In this case, the PV is positive because you are receiving the benefit of the equipment worth \$40,000. As a result, the payments are entered as a negative representing a cash outflow. file:///f /Courses/ /CGA/FA2/06course/m05t04.htm (2 of 2) [22/07/2010 9:15:37 AM]

14 file:///f /Courses/ /CGA/FA2/06course/m05t05.htm 5.5 Computing the term Learning objective Compute the number of periodic payments and the final payment required to eliminate a debt. (Level 1) LEVEL 1 Example: A company borrowed \$100,000 and agreed to make quarterly payments of \$10,000 starting in three months time. The applicable interest rate is 10% compounded quarterly. How many full payments will be made and how much will the final payment be? The regular payments form a simple ordinary annuity of "N" payments plus a final payment 3 months after the last full payment. Given the PV and the PMT and INT, solve for N using these steps: Enter the following in the calculator: Payment (PMT) 10,000 Period interest rate (I) 2.5 Present value (PV) 100,000 Future value (FV) 0 Number of payments (N) =?? = Entering "0" for the FV removes the necessity of clearing all the registers before entering the new information. There will be 11 full payments and a partial payment made at the end of period 12. To solve for the final payment, the annuity payment and the single payment must be equated with the PV. Most calculators will allow you to calculate a final payment at the same date as the last regular payment, but in this case the last payment will be one period later. Using the calculator, you can calculate the final payment due at point 11 and then add one period of interest to determine what the payment will be at period 12 as follows: Enter the following in the calculator: (This is a situation where the negative sign is important because you have an inflow and an outflow. Whenever there are two or more dollar entries to make, care must be taken as to which amounts are inflows (positive) or outflows (negative) when the calculator uses that concept.) Number of periods (N) 11 Period interest rate (I) 2.5 Present value (PV) 100,000 Payment (PMT) 10,000 Final payment (FV) at 11=?? = 6, To find the payment one period later, add one period of interest: \$6, x ( %) = \$6, file:///f /Courses/ /CGA/FA2/06course/m05t05.htm [22/07/2010 9:15:38 AM]

15 file:///f /Courses/ /CGA/FA2/06course/m05t06.htm 5.6 Computer illustration 5.6-1: 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. 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 file:///f /Courses/ /CGA/FA2/06course/m05t06.htm (1 of 3) [22/07/2010 9:15:39 AM]

16 file:///f /Courses/ /CGA/FA2/06course/m05t06.htm 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. Using the calculator There are two distinct calculations that you can either calculate in two separate steps or in one combined step. The two step method is used here for illustrative purposes only. It is obviously much more efficient to compute this in a single step and you are encouraged to do so. Two-step method Present value of the annuity payments of \$1,500. Enter the following in the calculator: Number of periods (N) 36 Period interest rate (I) 1 Payment (PMT) 1,500 PV =?? = 45, PV of lump sum at the end of three years: Enter the following in the calculator: Number of periods (N) 36 Period interest rate (I) 1 Future value (FV) 4,000 PV =?? = 2, The sum of these two values and the down payment is \$10, , , = \$57, One-step method Number of periods (N) 36 Period interest rate (I) 1 Payment (PMT) 1,500 Future value (FV) 4,000 PV =?? = 47, The computed value plus the down payment is \$10, , = \$57,956.96, which is the same answer arrived at in file:///f /Courses/ /CGA/FA2/06course/m05t06.htm (2 of 3) [22/07/2010 9:15:39 AM]

17 file:///f /Courses/ /CGA/FA2/06course/m05t06.htm the two-step method. file:///f /Courses/ /CGA/FA2/06course/m05t06.htm (3 of 3) [22/07/2010 9:15:39 AM]

18 file:///f /Courses/ /CGA/FA2/06course/m05summary.htm Module 5 summary Interest concepts of future and present value This module explains the fundamental concepts of interest and present and future values. Ordinary and annuities due are explained. Valuation techniques, including the use of a financial calculator and functions in Excel are demonstrated. Describe the concept of the time value of money. A dollar today is worth more than a dollar received tomorrow because today's dollar can be invested to earn interest. Describe the concept of interest including simple and compound interest, and effective and nominal rates of interest. Interest can be thought of as the rent charged for the use of money. Simple interest is calculated based on the principal amount owing only and not on accrued interest. Simple interest is not commonly used. Compound interest is calculated periodically and is based on the principal amount owing plus any unpaid interest. A nominal rate is the stated rate of interest. An effective rate is the annual rate that you actually pay when the effects of compounding are considered. Compute the present and future value of a single payment, and an annuity (ordinary and due). To determine the future and present values of single payments and annuities, you can use either the calculator or formula method. Refer to the owner's manual for your financial calculator for specific instructions about performing time value of money calculations. Compute the regular payment required for an ordinary annuity and an annuity due. Determine the regular payment to extinguish a debt by equal payment due at the end of each interest period. Determine the regular payment required to accumulate a required future amount. Determine the regular payment required, payable in advance, for an acquisition made on credit. Compute the time taken to extinguish a debt by making fixed payments in the future. Determine the number of full payments plus a smaller last payment required to extinguish a debt. file:///f /Courses/ /CGA/FA2/06course/m05summary.htm [22/07/2010 9:15:40 AM]

### Module 5: Interest concepts of future and present value

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

### Corporate 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

### Present 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

### Foundation 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

### Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations

Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the Hewlett-Packard

### Main 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

### Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.

### Module 8: Current and long-term liabilities

Module 8: Current and long-term liabilities Module 8: Current and long-term liabilities Overview In previous modules, you learned how to account for assets. Assets are what a business uses or sells to

### How 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

### Chapter 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

### The 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

### Texas 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,

### In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.

Section 4: Using a Financial Calculator Tab 1: Introduction and Objectives Introduction In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.

### first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest.

ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular

### The 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

### Chapter 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

### Time 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

### Time 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.

### Introduction. Turning the Calculator On and Off

Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction

### Chapter 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

### This 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 by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/

### DISCOUNTED 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

### PV Tutorial Using Excel

EYK 15-3 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

### CALCULATOR 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

### Statistical 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

### Key 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

### Integrated Case. 5-42 First National Bank Time Value of Money Analysis

Integrated Case 5-42 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

### 5. 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

### Ing. 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,

### TVM 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 (long-term receivables) 7 Long-term assets 10

### TIME 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

### CHAPTER 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

### The 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 EL-733A Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

### The 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 EL-738 Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

### Basic 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

### Calculating 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

### Chapter F: Finance. Section F.1-F.4

Chapter F: Finance Section F.1-F.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

### APPENDIX. 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

### Ordinary 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

### Finance Unit 8. Success Criteria. 1 U n i t 8 11U Date: Name: Tentative TEST date

1 U n i t 8 11U Date: Name: Finance Unit 8 Tentative TEST date Big idea/learning Goals In this unit you will study the applications of linear and exponential relations within financing. You will understand

### Discounted 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

### Dick 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

### Time 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

### Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value

Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations

### Key Concepts and Skills

McGraw-Hill/Irwin Copyright 2014 by the McGraw-Hill 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

### Purpose EL-773A HP-10B BA-II PLUS Clear memory 0 n registers

D-How to Use a Financial Calculator* Most personal finance decisions involve calculations of the time value of money. Three methods are used to compute this value: time value of money tables (such as those

### MAT116 Project 2 Chapters 8 & 9

MAT116 Project 2 Chapters 8 & 9 1 8-1: 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

### Time Value of Money. Nature of Interest. appendix. study objectives

2918T_appC_C01-C20.qxd 8/28/08 9:57 PM Page C-1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.

### BEST INTEREST RATE. To convert a nominal rate to an effective rate, press

FINANCIAL COMPUTATIONS George A. Jahn Chairman, Dept. of Mathematics Palm Beach Community College Palm Beach Gardens Location http://www.pbcc.edu/faculty/jahng/ The TI-83 Plus and TI-84 Plus have a wonderful

### CHAPTER 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

### Time-Value-of-Money and Amortization Worksheets

2 Time-Value-of-Money and Amortization Worksheets The Time-Value-of-Money and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or

### Appendix 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

### Important 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

### CHAPTER 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

### TIME 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.

### Appendix. 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.

### Practice 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

### Excel 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

### Chapter 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

### The 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

### CHAPTER 9 Time Value Analysis

Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 9-1 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams

### Using Financial Calculators

Chapter 4 Discounted Cash Flow Valuation 4B-1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your Hewlett-Packard or Texas Instruments BA II Plus financial calculator

### Ch. Ch. 5 Discounted Cash Flows & Valuation In Chapter 5,

Ch. 5 Discounted Cash Flows & Valuation In Chapter 5, we found the PV & FV of single cash flows--either payments or receipts. In this chapter, we will do the same for multiple cash flows. 2 Multiple Cash

### Discounted Cash Flow Valuation

6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

### Chapter The Time Value of Money

Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest

### Hewlett-Packard 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,

### Course 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

### rate nper pmt pv Interest Number of Payment Present Future Rate Periods Amount Value Value 12.00% 1 0 \$100.00 \$112.00

In Excel language, if the initial cash flow is an inflow (positive), then the future value must be an outflow (negative). Therefore you must add a negative sign before the FV (and PV) function. The inputs

### 3. Time value of money. We will review some tools for discounting cash flows.

1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned

### Calculating interest rates

Calculating interest rates A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction 2. Annual percentage rate 3. Effective annual rate 1. Introduction The basis of the time value of money

### Present Value (PV) Tutorial

EYK 15-1 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,

### Continue 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

### The 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

### 300 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

### Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS

Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS 7-1 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 \$10,000(1.10) 5 \$10,000(FVIF 10%, 5 ) \$10,000(1.6105) \$16,105. Alternatively, with a financial calculator enter the

### Chapter 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

### Compounding Quarterly, Monthly, and Daily

126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,

### NPV calculation. Academic Resource Center

NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year

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

### Chapter 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

### TIME VALUE OF MONEY. Hewlett-Packard HP-12C Calculator

SECTION 1, CHAPTER 6 TIME VALUE OF MONEY CHAPTER OUTLINE Clues, Hints, and Tips Present Value Future Value Texas Instruments BA II+ Calculator Hewlett-Packard HP-12C Calculator CLUES, HINTS, AND TIPS Present

### Ehrhardt Chapter 8 Page 1

Chapter 2 Time Value of Money 1 Time Value Topics Future value Present value Rates of return Amortization 2 Time lines show timing of cash flows. 0 1 2 3 I% CF 0 CF 1 CF 2 CF 3 Tick marks at ends of periods,

### Chapter 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest \$1,000 at 6% simple interest for 3 years.

6-1 Chapter 6 Time Value of Money Concepts 6-2 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

### PowerPoint. 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

### Time 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

### CHAPTER 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

### CHAPTER 4 DISCOUNTED CASH FLOW VALUATION

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability

### USING 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

### FinQuiz 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.

### Chapter 8. 48 Financial Planning Handbook PDP

Chapter 8 48 Financial Planning Handbook PDP The Financial Planner's Toolkit As a financial planner, you will be doing a lot of mathematical calculations for your clients. Doing these calculations for

### UNDERSTANDING 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, end-of-chapter problems, and end-of-chapter

### substantially 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

### USING FINANCIAL CALCULATORS

lwww.wiley.com/col APPEDIX C USIG FIACIAL CALCULATORS OBJECTIVE 1 Use a financial calculator to solve time value of money problems. Illustration C-1 Financial Calculator Keys Business professionals, once

### How 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

### 2. 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 equal-sized

### 6: 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

### Introduction 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

### CHAPTER 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