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Calculating Time Value of Money on a Calculator

Calculating Time Value of Money on a Calculator. Zachary James. Introduction.

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Calculating Time Value of Money on a Calculator

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  1. Calculating Time Value of Money on a Calculator Zachary James

  2. Introduction • This manual will describe in detail several different calculations of the time value of money (TVM) on a TI 83 Plus calculator. The basic idea of time value of money is that people prefer to consume goods or have money today rather than wait to consumer goods or have money in the future. For example if you have a dollar today, you can invest it and gain value while a dollar in the future is just a dollar. When money grows it compounds. This means that if you gain ten percent interest each year of one dollar you won’t just make ten cents each year. In the first year you will get (1 X .1)= .1 in the second year you will get (1.1 X .1) = .11 and the third year you would get (1.21 x .1)= .121 and so on

  3. Introduction • This process is called compounding and is essential to every time value of money calculation. Finally, some key generalizations can be made about the time value of money. First, the value of a dollar invested at a positive interest rate grows over time, meaning the further in the future you receive that dollar the less it is worth today. Second the trade-off between money today and money in the future is dependent on the rate of interest. Thus with a higher rate of interest people may be more likely to forego consumption to instead invest.

  4. Calculating the Future Value of a Lump Sum • First turn on your calculator by pressing the ‘On’ button in the bottom right hand corner. • Then press the ‘Apps’ button which is blue and towards the middle of calculator keypad. • A list of applications will appear on the calculator screen. The first one is called Finance. Select this option with the arrows and then hit enter.

  5. culating the Future Value of a Lump Sum • A new list of finance applications will show up. You again want to scroll to the first option that says TVM Solver and press enter. • A new screen with 8 different areas to enter in data appear it should look something like this: N= I%= PV= PMT= FV= P/Y= C/Y= • For this problem we will only be using the N, I%, PV, and FV variables. • N is the number of periods of compounding the investment will go through. I% is the interest rate that will be earned on the money. PV is the present value of the investment or how much it is worth at the moment it is invested. FV is the future value of the investment after N periods compounding at an interest rate of of I%.

  6. Example • Suppose you invest $100 for 10 years at an interest rate of 5% what will your investment be worth at the end of the ten years?

  7. Example • First you want to take each available variable from the problem and enter it in the appropriate variable location. • Since the initial investment is $100 you would enter PV= -100 because this is the present value of the investment. The reason you enter it as a negative number is because this money represents an outflow of cash which is always negative and the answer will be an inflow of cash which is always positive. • Since it will compound ten times over ten years you enter N=10.

  8. Example • The investment grows at a five percent interest rate so you enter I%=5. You do not need to convert this number to decimals. • So now your screen should look something like this: N=10 I%=5 PV=-100 PMT=0 FV=? P/Y=1 C/Y=1 • So now the final part is to ask the calculator to analyze these variables and tell you how much the money will be worth after ten years or what is known as the Future Value abbreviated here as the FV variable.

  9. Example • To do this press the arrow until it is in the FV row and then press the yellow ‘2nd’ button and then the green ‘ALPHA’ button. An answer should appear. • If you did this correctly the answer $162.89 should appear. • Note that in this example we are only solving for the FV but if we have 3 of any of the variables it is always possible to calculate the fourth. Thus it is possible, by using this same technique to calculate the interest rate, the number of compounding periods or the present value if you want to.

  10. Rules • The future value of an investment is what the investment will be worth after earning interest for one or more compounding periods of time. • Every TVM calculation has either four or five different variables. You will be given three or four of the other variables and be asked to solve for the fourth or the fifth. To solve these problems you scroll down to the appropriate variable and enter “ALPHA” “Enter”.

  11. Rules • Be sure that any variables that you don’t use are set to zero otherwise you will get incorrect results. • The order that you enter the numbers is up to you but in the following examples we will enter then in order of how they appear on the screen. • Also make sure the P/Y and C/Y variables are set to one. This represents that you will be calculating on the basis of annual compounding.

  12. Rules • When we enter the interest rate enter it as a whole number not a decimal. The calculator will read the number in this row as a percentage. • Enter the number in the Present value column as a negative. You do this because the calculator follows some rules called the Cash Flow Sign Convention. Under this convention, cash inflows are represented as positive numbers and cash outflows are represented as negative numbers. The present value is a cash outflow. Do not change the sign using the minus key, instead be sure to use the negative key.

  13. Rules • You can change any of the values in the equation without having to reenter all of the other data. The data will be saved.

  14. Calculating the Present Value of a Bond • There are several things that are different in calculating for a bond and a lump sum of cash. First, the future value, also in this case known as the par or face value of a bond is always $1000. Second bonds pay semiannual dividends to the bondholder so a new variable, the PMT variable, is used. Finally a bond compounds semiannually so the number of years must be multiplied by two and the interest rate must be divided by two. Lets work through an example to get a better idea of how to calculate the present value of a bond

  15. Example • A bond holder is paid $200 a year in dividends and his bond grows at a rate of 8% annually. Since we know that the bond will pay S1000 at the end of ten years what is the bond worth now?

  16. Example • First turn on your calculator by pressing the ‘On’ button in the bottom right hand corner. • Then press the ‘Apps’ button which is blue and towards the middle of calculator keypad. • A list of applications will appear on the calculator screen. The first one is called Finance. Select this option with the arrows and then hit enter.

  17. A new list of finance applications will show up. You again want to scroll to the first option that says TVM Solver and press enter. • A new screen with 8 different areas to enter in data appear it should look something like this: N= I%= PV= PMT= FV= P/Y= C/Y= • In this case since a bond is compounded semiannually we will multiply the number years by two (10 X2 =20) this will equal N.

  18. Example • Again since the interest is gained over two equal periods throughout the year we must divide the annual interest by two to get the semiannual interest. (8/2=4=I%) • A new variable that we have not used before is the PMT variable. This stands for payment and represents how much the bond pays out to the bond holder. This dividend is paid out twice a year so we must divide the annual amount paid by two to get the semiannual payment. (200/2 = 100) • We know that the future value of any bond is $1000 so we simply enter FV = $1000.

  19. Example • The calculator screen should look like: • N= 10 X 2 = 20 I%= 8/2 = 4 PV=? PMT= 200/2 =100 FV=1000 P/Y=1 C/Y=1 • To find the Present Value scroll to the Present Value row and hit the ‘2nd’ and ‘ALPHA’ button. • If you did this correctly the answer -1815.41 should appear. Again this number is negative because it represents an outflow of cash. Thus the price that you should pay for a bond that pays $200 every year for ten years and grows at 8% is $1815.41. • Note that in this example we are only solving for the PV but if we have 4 of any of the variables it is always possible to calculate the fifth. Thus it is possible, by using this same technique to calculate the interest rate, the number of compounding periods or the annual payments if you want to.

  20. Glossary • Future Value – The sum to which an investment will grow after earning interest • Principal - the amount of the investment • Compounding Interest- Includes simple interest, which is the interest paid on the original investment and remains constant from period to period, and interest earned on the reinvestment of previously earned interest and the interest earned on interest • Present Value- The value today of a future cash flow

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