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` Financial Calculator Guide Please feel free to distribute this document, and

` Financial Calculator Guide Please feel free to distribute this document, and also please try to avoid printing out such a long document. The current version is here. Comments or corrections should be sent to Larry Schrenk. Table of Contents Chapter 1–Single Dollar Problems: Future Value and Present Value .............. p. 2 ▪ Future Value Problems ▪ Present Value Problems ▪ Resetting your Calculator Chapter 2–Single Dollar Problems: Interest Rate and Time ............................... p. 9 ▪ Interest Rate Problems ▪ Time Problems ▪ Why Enter Negative Values? (optional) Chapter 3–Annuities: Future Value and Present Value ..................................... p. 12 ▪ Future Value Annuity Problems ▪ Present Value Annuity Problems Chapter 4–Annuities: Interest Rate, Time and Payment .................................... p. 16 ▪ Interest Rate Annuity Problems ▪ Time Annuity Problems ▪ Payment Annuity Problems Time Value of Money Decision Flowchart ........................................................... p. 20 Chapter 5–Non-Annual Compounding and Discounting ................................. p. 21 Chapter 6–Accounting for Inflation: Real versus Nominal Rates ...................... p. 23 ▪ The Effects of Inflation ▪ Inflation-Adjusted Saving ▪ Alternate Method (optional) Appendix–Other Calculators ................................................................................. p. 26 ▪ Hewlett-Packard 10bII ▪ TI-83/84 CALCULATOR REQUIREMENTS: You will need a calculator with financial functions for most finance classes. If you already have a TI-83 or 84 graphing calculator, that will do nicely. If not, you will need to buy a financial calculator. (Unfortunately, 9/1/13 Financial Calculator Guide 2 basic scientific calculators normally do not have financial functions. If in doubt, contact me.) Do not spend a lot of money on a fancy model. A basic financial calculator should cost $30-$40 at many department stores (maybe cheaper if you can get it online or used). A financial calculator has many financial functions (so you won‟t need to memorize a lot of formulae for the exams). The most common models are the Texas Instruments BA II Plus and the Hewlett- Packard 10bII. BEWARE: Do not buy the no-name financial calculator available at some stores for about $7.00–It does not work. Remember, if something appears to be too good to be true, it probably is. Important: I use the Texas Instruments BA II Plus in these instructions, because it seems to be the most popular model. If you have the Hewlett-Packard 10bII or a TI-83/84 graphing calculator, please see the appendix before trying any problems with your calculator. Chapter 1–Single Dollar Problems: Present and Future Value There are three different methods for doing calculations: 1) using a financial calculator, 2) using formulae and a regular calculator and 3) using financial value tables and a regular calculator. We will only use the first (and easiest) method in this class, i.e., a financial calculator, so you may ignore the sections of the textbook that show how to use either formulae or tables. This gives you very little to read in the textbook, which is good because success with a financial calculator depends a lot of practice. This guide will have a few example problems and more will be assigned in individual topics. But first a small bit of theory… THE TIME VALUE OF MONEY: Everyone prefers getting $100 today to getting $100 in five years. But before we do any calculations, we should consider why this is so. We can isolate three separate motives for the time value of money, that is, three distinct reasons why you would prefer $100 today to $100 in five years: 1. Inflation: Prices go up, so if I wait five years I can buy less with the $100. 2. Opportunity Cost: By delaying the payment, I loose the opportunity to spend the $100 for the next five years. 3. Risk: In five years, you may not have the money to pay me, so waiting involves a risk of not getting $100. 9/1/13 Financial Calculator Guide 3 The interest rate is how fast money grows (annually) over time. We get a return (or interest rate) on an investment to compensate us for waiting and accepting these three costs. Terminology: In different contexts, the rate money grows over time may be called the „interest rate‟, the „rate of return on an investment‟ (often shortened to „rate of return‟ or just „return‟), the „compounding rate‟ or the „discounting rate‟. TIME LINES: When you are dealing with payments over time, the easiest way to visualize them is to draw a time line such as the one below. Today is 0. A year from now is 1, two years from now is 2, etc. Until you are comfortable with these problems, always start by drawing a timeline. Future Value Problems How much will you have in your bank account 5 years from now, if you deposit $100 today, earn 10% interest per year and make no additional deposits. (For clarity examples will be underlined.) In this time line X represents the amount in my account in five years: This is a future value problem because I am asking the future value of a single dollar amount today. The amount deposited today is called the present value, and the process of going from the present value to the future value is called compounding. Future value problems often have the general pattern: How much future value (FV) will you have after N years, if you deposit the present value (PV) today and get a I/Y interest rate per year? 0 1 2 3 4 5 Today Time X 100 0 1 2 3 4 … N Today Time 9/1/13 Financial Calculator Guide 4 We will use a financial calculator to solve these problems, but you should see the step by step calculations to understand what is going on. Year 1: If start with $100.00, how much will I have after one year? $100.00 × 1.10 = $110.00 I multiply the $100 by 1 because I still have my $100 deposit and by 10% because that is the interest I receive for one year. We combine these in one calculation by multiplying the $100 by 1.10. Year 2: I start the year with $110.00 in my account. How much will I have after one more year? $110.00 × 1.10 = $121.00 As in the first year, I multiply the starting amount by 1.10. Year 3: I start the year with $121.00 in my account. How much will I have after another year? $121.00 × 1.10 = $133.10 You see that pattern: multiple each year by 1.10. I don‟t need to do this in three different steps; instead, I can find the amount in year 3 from the original deposit: $100.00 × 1.10 × 1.10 × 1.10 = $100.00 × 1.103 = $133.10 This is what our financial calculator will do, but instead of worrying about formulae (yes, this one is easy and you could easily do it with a regular calculator, but the formulae get more complicated later), we just need to enter the data: N = 3 I/Y = 10 PV = $100.00 into a financial calculator. FUTURE VALUE ON YOUR CALCULATOR: Now let‟s use your calculator. Here are the most basic financial keys on the Texas Instruments BA II Plus–later we will add a few more: 9/1/13 Financial Calculator Guide 5 How much do you have after 4 years if you deposit $200 today and the interest rate is 12%? N = 4 I/Y = 12 PV = 200 1. Press 4, press N 2. Press 12, press I/Y 3. Press 200, press +|-, press PV (you get -200) 4. Press CPT, FV to get 314.70, i.e., $314.70 In 4 years, your bank account will have $314.70. 4 12 -200 314.70 Notes:  A number in red indicates a solution.  You can enter the values for N, I/Y, and PV in any order.  On some calculators, the interest rate key is labeled I, instead of I/Y.  As in Excel, you enter 12% as 12 (don‟t enter it as the decimal 0.12, because the calculator will think the interest rate is 0.12%).  The present value must be entered as a negative value. (If you want to know why see Why Enter Negative Values?. Otherwise, just do it.)  HP USERS ONLY: The Hewlett-Packard 10bII does not have a CPT key, just press FV and ignore all future references to a CPT key. If you still do not get the correct answer, you probably did not read the HP appendix. FUTURE VALUE PRACTICE PROBLEMS: 1) How much is $350.00 worth in 5 years if the interest rate is 9%? 9/1/13 Financial Calculator Guide 6 5 9 -350 538.52 2) How much is $400.00 worth in 15 years if the interest rate is 11%? 15 11 -400 1,913.84 3) How much is $1.00 worth in 100 years if the interest rate is 15%? 100 15 -100 1,174,313.45 Present Value Problems I might also ask the reverse question: How much must you deposit today to have $100.00 in a bank account 5 years from now, if you earn 5% per year and make no additional deposits? In this timeline, X is the amount I need to deposit today: uploads/s1/ fin-calc-guide.pdf