Financial: Solve for each varaible

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The formula FV = PV(1 + R*T) is most helpful if we have been given the present value, the rate, and the time. For the problem (which changes every time this page is loaded or refreshed):

The reason this works so well is that the problem gave all of the values that appear on the right side of FV = PV(1 + R*T) and it asks us to find the single value given as the left side of that equation, namely, FV. However, we could rearrange the equation in different ways so that we have any of the four variables on the left side and all the other variables on the right side. For example, if we solve the equation for PV we get PV = FV/(1 + R*T) This would be a great form to have if we are given a problem such as:

Altenatively, we could solve the equation for R to get R = ( FV/PV - 1)/T This would be a great form to have if we are given a problem such as:

Finally, we could solve the equation for T to get T = ( FV/PV - 1)/R This would be a great form to have if we are given a problem such as:

There are a two approaches to performing these computations on the calculator. First, we can just remember the desired formul and plug values into the calculator. Figures 1 through 4 below demonstate an example of each kind of problem done on the calculator in this way. A second approach is to capture the required steps for each kind of problem in a program and then just run the program. One variation of this approach is to have a separate program for each kind of problem. A different variation is to put all four types into a single program and then use a menu system to let the user choose the appropriate problem type from the menu. This is the approach used here. The program is called SIMPFIN2. It is shown and demonstated after Figure 04.

Figure 01	Invest, at simple interest, $2210 at 5.7% for 3 years and 4 months. Find the future value of that investment? Use the formula *`FV = PV(1 + RT)`*. On the caluclator we evaluate 2210(1+0.0573.33333), as shown in Figure 01, which gives FV the value $2629.90, rounded to the nearest cent if need be.
Figure 02	What present value is required to end up with $2861.24 if we invest at simple interest at 4.8% for 4 years and 9 months? Use the equation *`PV = FV/(1 + RT)`*. On the calculator evaluate the expression 2861.24/(1+0.0484.75), as shown in Figure 02, which gives PV the value $2330.
Figure 03	What rate is required to end up with $5300.81 if we invest $4250 for 5 years and 9 months? Use the equation `R = (FV/PV - 1)/T` . On the calculator, in Figure 03, evaluate the expression (5300.81/4250-1)/5.75 which gives R the value 0.043 or 4.3%.
Figure 04	What time is required to end up with $1789.32 if we invest $1560 at 2.1%? Use the formula `T = (FV/PV - 1)/R` . On the calculator evaluate (1789.32/1560-1)/0.021, which gives T the value 7.00000 or 7 years.

While the steps shown above are really straight forward implementations of the various versions of our equation, they all require us to remember or look up those versions of the equation. We can capture all of that in a program. Here is a listing of a program that will do this.

This program is available to you to download at SIMPFIN2, which happens to be the name of the program. [Two quick points about the listing. First, line 7 was wrapped around into three lines so that it would fit more easily on the page. Second, the line numbers are not part of the program but are supplied to make it easier to reference particular lines in the text below.]

In our work above we created four different versions of the the equation that relates present value, future value, rate, and time, namely,

FV = PV(1 + R*T)
PV = FV/(1 + R*T)
R = (FV/PV - 1)/T
T = (FV/PV - 1)/R

In the program P is present value, F is future value, R is rate, and Y is time (expressed in years). Then, the fourth equation is captured in line 46, the third equation is captured in line 36, the second in line 26, and the first is done in two lines, 14 and 16.

The following figures demonstrate using the program to solve the same problems.

Figure 05	To run the program, once it is loaded onto your calculator, find and highlight the name in the PRGM menu. Then press to paste the command onto the main screen, shown in Figure 06.
Figure 06	Now that the command is in place press to have the calculator start to rn the program.
Figure 07	In Figure 07 we see the menu that was specified in line 7 of the program. We can select an item of the menu by typing its number or by highlighting the desired item and pressing the key. We will start with the first option, FUTUTRE VALUE to do the first problem (from back in Figure 01) where we need to find the future value.
Figure 08	The program clears the screen and starts to ask for the required values, the first of which is the present value.
Figure 09	Figure 09 shows the status of the screen after we have given the program after all the needed values. Press to continue.
Figure 10	Figure 10 shows the intermediate value, namely the interest, and the desired answer, the future value After reading the answer we press and the program takes us back to the menu, shown again in Figure 11.
Figure 11	The next problem will be the one to find the present value, the second option on the menu.
Figure 12	Figure 12 shows that we entered the same information that we had in Figure 02.
Figure 13	We see the answer in Figure 13. From there we would press , return to the menu screen, and then select the third option to solve the problem given in Figure 03.
Figure 14	Figure 14 shows the data from the problem.
Figure 15	Figure 15 shows the answer. Again, pressing retyurns us to the menu where we choose the fourth option to move to Figure 16.
Figure 16	We enter the required data.
Figure 17	Figure 17 shows the answer.
Figure 18	And, just for completeness, Figure 18 shows the result of choosing option 5: QUIT from the menu.