Using Your Calculator to Find the Future Value of a Single Sum with Annual Compounding 1 Dr. Craig Ruff Department of Finance J. Mack Robinson College of Business Georgia State University © 2014 Craig Ruff

2 Solving with the Calculator - Formula Suppose you have the following example: Calculate the future value of $100 in 5 years at an interest rate of 6%, compounded annually. When using the calculator and the formula for the future value of a single sum with annual compounding: you need to remember your calculator’s order of operations. To do this one, you may need to add parentheses to ensure the calculator is doing what you want it to do, as in… “100 x ( ) = “ and you will get an answer of Another way to do this (and without parentheses) is to first enter the 1.06 raised to the fifth and then multiply by 100, as in… “ x 100 = “ and you will get the answer of Recall ‘PEMDAS’ or ‘Please Excuse My Dear Aunt Sally’ from your school days? © 2014 Craig Ruff

3 Using the time-value-of-money buttons on the calculator is generally a game of putting in four of the five pieces of information and asking the calculator to tell you the fifth. It is helpful to set your calculator out to plenty of decimal places. To set your BA II Plus to 8 decimal places, hit 2 ND decimal place (the ‘.’) 9 ENTER Before starting, I also suggest making sure that your BA II Plus setting are: 2 ND I/Y = ‘ ’ 2 ND PMT = ‘END’ The buttons stand for: PV = present value FV = future value I/Y = compound rate for the period N = number of periods in the future (or the number of payments, if an annuity) PMT = this is for annuity payments; for this problem, we input a ‘0’ as we are dealing with a single sum. Solving with the Calculator – TVM Buttons © 2014 Craig Ruff

4 Using the time-value-of-money buttons, On the calculator, the future value of $100 in 5 years at an interest rate of 6%, compounded annually is solved as: Buttons Numbers to Enter PV-100 FV???? I6 N5 PMT0 Solving with the Calculator – TVM Buttons © 2014 Craig Ruff

5 Using the time-value-of-money buttons, On the calculator, the future value of $100 in 5 years at an interest rate of 6%, compounded annually is solved as: Buttons Numbers to Enter PV-100 FV???? I6 N5 PMT0 Solving with the Calculator – TVM Buttons Be careful: Your calculator uses percent form (6). However, the formula uses the decimal form (.06) as in: © 2014 Craig Ruff

6 Using the time-value-of-money buttons, On the calculator, the future value of $100 in 5 years at an interest rate of 6%, compounded annually is solved as: Buttons Numbers to Enter PV-100 FV???? I6 N5 PMT0 Notice that the PV was entered as Had you entered a positive 100, you would have gotten an answer of In terms of doing an easy problem like this one, entering a positive 100 is no big deal; you know that your really represents an ending balance of However, for some problems you will eventually see, the sign of what you enter into the calculator is very important to the final solution. Thus, it is healthy to get into the habit of having money going out of your pocket (as in a deposit) be a negative and money coming in your pocket (as in withdrawing the money from the bank) be a positive. Solving with the Calculator – TVM Buttons © 2014 Craig Ruff

7 As a word of caution, using the calculator’s TVM buttons can make this topic seem deceptively easy. I suggest that when you see this type of time-value question, you not think in robotic terms of “OK, now I push this button and then this button, and…” Instead, I would suggest that you first cast the question in words that make sense to you, such as: ‘Suppose I place $100 today in a bank account that pays 6% interest per year. At the end of five years, how much money will I have in the bank account?’ Also, it is often helpful to imagine the question graphically on a timeline. Here, we are “pushing” the money out to year 5. Or, we could say that we are moving the money forward in time from t=0 to t=5. Graphically, it would look like: t=0 t=5 $100 Solving with the Calculator – TVM Buttons © 2014 Craig Ruff

8 AB 1Present Value-100 2Years5 3Annual Rate6% 4 5Future Value($133.82) Excel has a lot of built in functions, including future value. The ‘0’ in the parenthesis indicates that the annuity payments are zero (as this is a single sum.) =FV(B3,B2,0,B1) Solving with Excel © 2014 Craig Ruff

9 Examples © 2014 Craig Ruff

10 Let’s say Bill Gates is worth $56 billion. Suppose Bill takes his entire $56 billion and deposits it in the Commerce Bank of Beverly Hills at a rate of 2%, compounded annually. How much interest will Bill earn in the first 10 minutes? I have used a PV of -$5.6 billion, since my calculator doesn’t handle $56 billion. That is no problem. I just need to remember to multiply my answer by 10. (Again, I made this a negative number to indicate money going out of Bill’s pocket to make the deposit.) Since the rate is 2%, compounded annually,, I simply plug in ‘2’. The tricky part is telling the calculator how long. There are 525,600 minutes in a year (365 * 24 *60). Thus, N is equal to 10/ (= ). PV-5,600,000,000 FV???5,600,002,110 IY2 PMT0 N Example: Future Value of a Single Sum: Annual Compounding © 2014 Craig Ruff

11 To see how much Bill has made in the first ten minutes, directly subtract the original 5,600,000,000 from this number. The answer you get on your calculator is $2, Notice that this number is not exactly the 2,110 that the results to the left would suggest. That is because, due to space display constraints, your calculator (on the left) is showing you a slightly rounded number. But underneath the necessary ‘rounding’ by your calculator, your calculator is really carrying the true number of 5,600,002, (and also with lots more decimal places than the three I use). Once you subtract the initial 5,600,000,000, your calculator can show you the accurate number of $2, We are not done yet…. Remember that this answer is only based on $5.6 billion. Bill has $56 billion. So, we need to multiply this answer by 10 to get the answer. Bill would make $21, in interest in the first ten minutes. PV-5,600,000,000 FV???? 5,600,002,110 IY2 -5,600,000,000 PMT0 = 2, N Example: Future Value of a Single Sum: Annual Compounding © 2014 Craig Ruff

12 When doing these problems, do not round your inputs. For instance, when entering the value for N, it may be tempting to simply use instead of The problem is that the error associated with the rounding on an input gets magnified in the problem and can really throw off the final answer. But we actually can take this one step further: using is also rounding. The correct number is Yes, that looks like a ridiculous number to enter into a calculator. The point is that you don’t have to enter the number since the number should have never left your calculator in the first place. As soon as you calculate a number, enter it right away as the TVM button value. In this case, for instance, you would enter something like 10 / ( 365 * 24 * 60 ) = and as soon as you hit the equal sign then hit the N button. Your calculator will place the correct (non-rounded) number into N. If you calculate a number that you are not yet ready to use, then use your STO and RCL buttons to hold onto the number until you are ready to use it. On the BA II, the storage buttons will hold 9 numbers simultaneously. PV-5,600,000,000 FV???? 5,600,002,110 IY2 PMT0 N Example: Future Value of a Single Sum: Annual Compounding © 2014 Craig Ruff

13 As another example, we can turn the basic future value calculation around and solve for other variables. For instance, suppose you invest $1,000 today in a savings account and 10 years later you have $2,000 in your account. What annual compound return have you earned over this period? Using your TVM buttons… PV-1000 FV2000 IY???? PMT 0 N10 Notice that the signs here are very important. The negative on the $1,000 signals money coming out of the pocket and the positive on the $2,000 signals money coming back in the pocket. Indeed, if you were to enter both numbers as positives (or both as negatives), your calculator would ‘blow up.’ Example: Future Value of a Single Sum: Annual Compounding © 2014 Craig Ruff

14 Or, as another example, we can ask something along the lines of... Suppose you invest your money in an account paying 5%, compounded annually. How long will it take to triple your money? Using your TVM buttons… PV-100 FV300 IY5 PMT0 N???? Again, the signs on the FV and PV are very important. Notice also that it would not matter had we used -1 and +3 or -10 and +30, etc., as long as the FV was triple the value of the PV. Example: Future Value of a Single Sum: Annual Compounding © 2014 Craig Ruff

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