The table below describes six different kinds of problems and it gives a sample of such a problem. Also, for each problem type, the table identifies the Figures below that deal with that particular style of problem, first from the program perspective and then from the TVM-Solver perspective. The program being used here is the FINANCL program. It will be supplied in class. In order to run all of the features of the FINANCL program the calculator must also have the TOSTR and DOLLAR programs installed.

Description Table
TYPE	Problem Description	Figures showing the program	Figures showing the TVM solver
Getting to the system	Screens to show how to access the program FINANCL or the TVM-Solver	1-2	41-43
COMPOUND Future Value	Given the PRESENT VALUE, the ANNUAL RATE, the Compounding Period (i.e., the number of times per year that we do compounding), and the number of years (from which we can determine the number of compounding periods) find the FUTURE VALUE. This is a straight compound interest problem. Sample Problem: Present Value = 7500, Annual Rate = 3.5% (i.e., 0.035), Compunded monthly (i.e., 12 compunding periods in a year) Number of years = 5 (i.e., 60 compounding periods) Find the Future value.	3-7	44-45
Present Value	Given the FUTURE VALUE, the ANNUAL RATE, the Compounding Period (i.e., the number of times per year that we do compounding), and the number of years (from which we can determine the number of compounding periods) find the PRESENT VALUE. This is the reverse of a normal compound interest problem. Here we know the amount at the end and we want to find the amount at the start. Sample Problem: Future Value = 7500, Annual Rate = 3.5% (i.e., 0.035), Compunded weekly (i.e., 52 compunding periods in a year) Number of years = 6 (i.e., 312 compounding periods) Find the Present value.	8-12	46-47a
Find the Rate	Given the PRESENT VALUE, the FUTURE VALUE, the Compounding Period (i.e., the number of times per year that we do compounding), and the number of years (from which we can determine the number of compounding periods) find the ANNUAL RATE that would be required to make this work. This takes the normal compound interest formula and solves it for the rate. Sample Problem: Present Value = 7500, Future Value = 8500, Compunded daily (i.e., 365 compunding periods in a year) Number of years = 7 (i.e., 2555 compounding periods) Find the required Annual Rate.	13-16	48-49
Effective Rate	The effective rate is the simple interest rate that produces the same annual interest as does a given compound rate. To find the effective rate we need to specify the compound rate and the frequency of compounding. Sample Problem: Annual (compound) rate = 4.75% (i.e., 0.0475) Compunded daily (i.e., 365 compunding periods in a year) Find the Effective Rate.	17-19	50
Annuity	For an annuity we assume that we start with zero in the account and we make regular deposits to an account. The deposits are made with the same frequency as we have for the compounding. Thus, if we make monthly deposits we are assumiong that interest is compounded monthly too. To find the value of the annuity at some point in the future we need to specify the amount of the regular deposit (called the Rent amount), the annual rate, the deposit/compounding period (how many times per year this is done), and the number of years (thus, the number of deposits). In addition, we get two different values if we make the deposit at the end of each period (an ORDINARY annuity) or if we make the deposit at the start of each peiod (an annuity DUE). Sample Problem: Rent amount = 30, Annual Interest Rate = 2.75% (i.e., 0.0275), Deposits/Compounding taking place weekly (i.e., 52 times per year), Time = 10 years (i.e., 520 deposits/compounding periods) Find the Future Value of the annuity for both an Ordinary annuity and for an anuity DUE.	20-22	51-54
Find Rent Amount	This is taking the formula for finding the value of an annuity and solving it for the Rent amount. Thus, we are asking how much do we have to deposit on a regular basis and at a given annual interest rate in order to achieve a particular value after a given number of years. As before, there are two answers, depending upon the timing of our deposits, either at the start or at the end of the compounding period. Sample Problem: Desired Future value = 30,000, Annual Rate = 3% (i.e., 0.03), Depopsit/Compound period daily (i.e., 365 times a year), Time = 8 years (i.e., 2920 times) Find the required RENT for both an Ordinary annuity and for an anuity DUE.	23-25	55-58
Loan Repayment Installments	Loan repayment is really two problems. If you get a loan from a bank for 5 years with payments due every month, then the bank wants to have your deposits, which amount to an annuity, yield the same amount as the bank would have at the end of that period if they had taken the amount of the load and simply invested it at a same annual rate. Sample Problem: Loan amount = 22,000 Annual rate = 3% (i.e., 0.03) Payments monthly (i.e., 12 times per year) Time = 5 years> (i.e., 60 payments) What is the Future value if the amount of the loan is invested at the same rate and same compunding period over the same time period? Then, what rent amount would produce the same Future Value over that time period? That rent amount will be the payment amount needed to satisfy the loan.	26-34	59-62
Ammortization Schedule	In the process of paying off a loan, after each payment, the outstanding balance goes down, the amount of interest owed for the next payment goes down, and the amount of the next payment that goes to reduce the outstanding balance will go up. We want to create a table of all such values. Sample Problem: Loan amount = 22,000 Annual rate = 3% (i.e., 0.03) Payments monthly (i.e., 12 times per year) Time = 5 years (i.e., 60 payments) Create a ammortization chart for the first four payments.	35-40	63-84

Table of Figures and Explanations
Figure 1	We will start solving the problems posed above using the FINANCL program. To do this we need to start the program. We use the key to open the list of programs. The calculator used to generate these particular screens had numerous programs on it. We use the key to move the highlight down to point to the FINANCL program. Once highlighted, we select that program by pressing the key, moving to Figure 2. [Note that since this program has been enumerated by this calcualtor as the 9th program we could have selected it via one keystroke by pressing the key.]
Figure 2	Selecting the program, as we did in Figure 1, does not run the program. Rather, it pasts the name of the program following the special code "prgm" onto the screen, as shown in Figure 2. Now. to run the program we press . Return to description table.
Figure 3	This particular program is menu driven. That is, the program displays a menu and the user needs to choose one of the options available on that menu. Note that the entire menu must fit on the screen. Therefore, there is a limit of 7 choices. If we want more than 7 choices, which we do in this case, we need to create multiple menus. As we will see later, item 7 of this menu takes us to a second menu for more choices. The FUTURE VALUE problem is handled as a simple COMPOUND interest problem. Thus, the choice we want it item number 3.
Figure 4	We use the key to move thee highlight to item 3 and then press the key to actually request that item.
Figure 5	To solve the typical COMPOUND interest problem, the program asks for the PRESENT VALUE.
Figure 6	In Figure 6 we have given the program the value 7500 and then we press the key. The program responds by asking for the ANNUAL RATE, to which we enter .035 (for 3.5%). Then the progarm asks for the number of compounding periods in a year (TIMES / YEAR), and we specify 12 for monthly. Finally the program asks for the NUMber of PERIODS to which we respond 60 (that being 5*12). At this point we have given the program all the information it needs. Once we press the key the program will do the required computations and then display the answer.
Figure 7	The program was nice enough to not only compute the final answer (8932.071219, which we round to 8932.17) but also to compute the amount of interest earned, 1432.071219. The program then waits on this screen so that we can read the answer. [Jump to Figure 45 to see the same answer from the TVM Solver.] In order to continue the program we need to oress the key. Return to description table.
Figure 8	Having finished the previous problem, the program returns to our menu. The next problem is a PRESENT VALUE problem, and we have moved the highlight down to the PRESENT VALUE option. Then we press the key to perform that option.
Figure 9	Screen 9 shows, in its last two lines, the begining of the information exchange related to the PRESENT VALUE problem. In particular, the top 6 lines are left over from our previous calculations. In the last two lines the prograqm has printed the problem type (PRESENT VALUE), and then it has asked us for the FUTURE VALUE.
Figure 10	In Figure 10 we have not only given the FUTURE VALUE as 7500, we have also responded to the prompts for the ANNUAL RATE and the TIMES / YEAR with .035 and 52 (for weekly).
Figure 11	Figure 11 demonstrates that we can supply values as calculations, not just as numbers. Thus, in Figure 11, we have indicated that the number of periods is 52*6 rather than 312, letting the calculator do the computation.
Figure 12	Once we press the key to leave Figure 11 the program computes and displays the result, namely that the PRESENT VALUE is 6079.811316, which we can round to 6079.81. [Jump to Figure 47a to see the same answer from the TVM Solver.] As usual, once we have read the result we press the key to have the program move ahead. In this case that means returning to the menu as shown in Figure13. This is a good place to point out that it would be a simple change to have the program round the answer for us. If we were using this program for an accounting class, that would make perfect sense. Since this is a math class I have left the values showing the full precision of the calculator computations. Return to description table.
Figure 13	The next problem, Find the Rate, does not correspond to any of the choices in the first menu. Thus, we have highlighted the command to jumpt to the second menu. Press the key to perform that option.
Figure 14	We now see the second menu. In this menu we have the RATE FIND option and we select that to move to Figure 15.
Figure 15	Figure 15 has the start of the data input for this problem. We have entered the values of 7500 for Present Value, 8500 for Future Value, and 365 for daily compunding.
Figure 16	Here we finished the data input with 365*7 for the number of days in 7 years. The program responded with the result .017880887 or, approximately, 1.8%. [Jump to Figure 49 to see the same answer from the TVM Solver.] Return to description table.
Figure 17	Having finished in Figure 16, the program returns to the second menu. Our next problem is to find the Effective Rate, but that was on the first menu. We highlight option 5 and press the key to return to the first menu.
Figure 18	Back on the first menu, we have selected the EFFECTIVE RATE option.
Figure 19	For EFFECTIVE RATE we only need two values, the annual rate for the compound interest and the frequency of compounding. Both are supplied in Figure 19 and the program responds with the answer .0486429603 or about 4.86%. [Jump to Figure 50 to see the same answer from the TVM Solver.] Return to description table.
Figure 20	For Figure 20 we have returned to the main menu where we are prepared to select item 2: ANNUITY.
Figure 21	Figure 21 shows that we have entered the first three values, the rent amount, the annual rate, and the frequency of payments (and compounding) in a year.
Figure 22	Here we have supplied the final information, the number of periods. The program then computes and displays the two answers, one for an ORDINARY annuity where payments are made at the end of each period (17950.49334) and the other for an ANNUITY DUE (17959.98639) where payments are made at the start of each period. [Jump to Figure 52 to see the same ORDINARY annuity answer from the TVM Solver.] [Jump to Figure 54 to see the same Annuity DUE answer from the TVM Solver.] Return to description table.
Figure 23	In Figure 23 we have worked out way to the second menu and we have highlighted the RENT FIND option.
Figure 24	This screen shows that we have entered the first three values of the problem: the desired future value, the annual rate, and the number of times per year.
Figure 25	The final bit of data is the number of periods, this corresponding to 8 years with deposits every day of the year. With all of the data the program computes the required rent payment if the deposit is at the end of each day (9.090783876) or if it is made at the start of each day (9.090036749). [Jump to Figure 56 to see the same annuity DUE answer from the TVM Solver.] [Jump to Figure 58 to see the same ORDINARY annuity answer from the TVM Solver.] In short, if you can find someone who will pay 3% on an annuity where you deposit $9.10 each and every day for the next 8 years, that annuity will be worth over $30,000 at the end of that time. Return to description table.
Figure 26	We will do the LOAN AMOUNT (loan payment determination) twice. First we will follow the description given above. We will find the future value of the amount of the loan at the same interest rate and the same compounding period. Figure 26 indicates that we will use the COMPOUND feature to do this.
Figure 27	Most of the data is entered here.
Figure 28	After entering the number of periods the program tells us that the original $22,000 would be worth $25,555.57 after the 6 years of monthly compounding at 3%. [Jump to Figure 60 to see the same intermediate answer from the TVM Solver.] Therefore, the next part of the process must determine the rent one would have to pay on an annuity for 6 years, monthly, at 3% to yield the same future value.
Figure 29	To do that we return to the RENT FIND option on the second menu.
Figure 30	We enter the values. Notice that we have entered the FUTURE VALUE as the rounded $25,555.57.
Figure 31	We finish entering the values and the program gives us the option of two answers, one for an ORDINARY annuity and one for an ANNUITY DUE. Assuming that the loan is to be paid back in the usual method, paying at the end of each month, the required loan payment will be $395.32, from the ORDINARY RENT, which has been rounded up so that the payments are complete with the final payment being reduced so that we do not overpay the loan. [Jump to Figure 62 to see the same answer from the TVM Solver.]
Figure 32	Of course, it seems strange that we have to do one calculation and then enter the results of that, along with re-entering three of the original variables, in order to get an answer. We should be able to have the program do that for us. And, indeed it will do that. The desired option is the LOAN AMOUNT option, #4.
Figure 33	This time we enter the original data.
Figure 34	And the program just produces the final answer, although it assumes the common practice of having payments at the end of each period. Thus, the answer is the same as the value found from an ORDINARY annuity on Figure 31. [Jump to Figure 62g to see the same one step answer from the TVM Solver.] Return to description table.
Figure 35	Finally, the program does the computations for producing an amortization table. The menu option is the first one: AMMORTIZATION.
Figure 36	The program asks for the required values.
Figure 37	Then the program produces the values needed for the first line of the table. Pay NUM Old $ pay $ Interest Retire New $ 1 22000.00 400.00 55.00 345.00 21655.00 The program then waits for us to press either a 0 or a 1 to end the ammortization calcualtion or to produce another line. We press .
Figure 38	The program responds with the data for the second line of the table. Pay NUM Old $ pay $ Interest Retire New $ 1 22000.00 400.00 55.00 345.00 21655.00 2 21655.00 400.00 54.14 345.86 21309.14
Figure 39	And, the third line... Pay NUM Old $ pay $ Interest Retire New $ 1 22000.00 400.00 55.00 345.00 21655.00 2 21655.00 400.00 54.14 345.86 21309.14 3 21309.14 400.00 53.27 346.73 20962.41
Figure 40	And, the fourth line... Pay NUM Old $ pay $ Interest Retire New $ 1 22000.00 400.00 55.00 345.00 21655.00 2 21655.00 400.00 54.14 345.86 21309.14 3 21309.14 400.00 53.27 346.73 20962.41 4 20962.41 400.00 52.41 347.59 20614.82 [Jump to Figure 71 to see the same remaining balance answers from the TVM Solver.] [Jump to Figure 79 to see the same answers, expressed in Lists from the AMMORTLT program.] [Jump to Figure 92 to see the same answers from the TABLE using the Y= functions.] We could keep going and complete the table, but since we only needed to do four rows we can stop here by pessing the key. That will take us back to the menu system and from there we can get to the second menu where we can choose the QUIT option. Return to description table.
Figure 41	In order to get to the screen shown in Figure 41, press the key. The image in this figure was captured from a TI-84 Plus that had lots of applications installed on it. The Finance application is the first one listed. It will be the first on on a TI-83 Plus. We are only interested in the Finance application. Since it is the highlighted appication, press the key to start it.
Figure 42	The main screen of the Finance application is shown in Figure 42. At his point we want to use the TVM Solver. That is the highlighted choice so press the key to start it.
Figure 43	Figure 43 has a blank TVM Solver screen. The meanings of the various fields is given by The idea of the solver is that one places the known values in the right fields, then moves the highlight to the unknown field, and then presses the key sequence. We will see this as we solve the first problem in the next screens. Return to description table.
Figure 44	For the first problem we set the Present Value to be -7500. It is negative because TVM Solver looks at the flow of money with negative values meaning you are giving up the money. If we are investing $7,500 we are giving up control of that money for the duration of the investment. Therefore, we enter it as a negative value. The interest is input as a percent, 3.5; the Payment is left as 0 since we are not making any regular payments. The problem states monthly compounding, therefore we set P/Y to 12 and that will automatically set C/Y to 12. Then we set the number of periods to 60. Finally, we move the cursor to the Futurre Value field since this is the unknown. To have TVM Solver do its work, we press the key sequence. The result is shown in Figure 45.
Figure 45	The result of our actions in Figure 44 is shown here, the future value is 8932.071219, a positive value since this is money coming back to us. The calculator has left a black square next to the Future Value field to indicate that it just solved for that value. [Jump to Figure 7 to see the same answer from the FINANCL program.] Return to description table.
Figure 46	In Figure 46 we are setting up the second problem where we want to find the present value. We have set the future value to be 7500 as given in the problem. We also need to enter the number of compounding periods. We will do this by entering the expression 52*6, letting the calculator do the work.
Figure 47	Note that the calculator converted our expression of 52*6 to the 312 value. We have also moved the cursor to the Present Value field since this is the unknown value for this problem. Again, we press the key sequence.
Figure 47a	The answer, -6079.811316, is displayed. [Jump to Figure 12 to see the same answer from the FINANCL program.] It is negative since this is money that we would have to commit in order to recieve the 7500 at the end of the time period. Return to description table.
Figure 48	The third problem type is to find the interest rate needed to take a given present value and have it produce a given future value over a specific time period with know compounding frequency. In Figure 48 we have set all of the given fields and we have positioned the highlight at the unkown field, I%. Again, note that for the TVM Solver,we enter the present values as a negative because we would be giving up control of that money. The future value is positive because we will be getting that money. We press the key sequence to move to Figure 49.
Figure 49	The answer is 1.788088696%. [Jump to Figure 16 to see the same answer from the FINANCL program.] Return to description table.
Figure 50	The fourth type of problem is to find the effective rate. There is no direct field for effective rate within the TVM Solver. However, we can use the ssystem to get our answer. Figure 50 shows both the setup and the resulot of doing this. We simply create a convenient present value, $100 (thus setting that field to -100). Then we set the given annual rate, the frequency of compounding, and we set the number of periods to correspond to 1 year. Since our example called for daily compounding we have 365 such periods in the year. Then, we solve for the Future Value. In this case that came out as 104.864296. But that really gives us the effective rate since clearly a simple interest rate of 4.864296% would produce the same result. [Jump to Figure 19 to see the same answer from the FINANCL program.] Return to description table.
Figure 51	To do an annuity we set the Present Value to 0. We set the Payment field to -30 representing our deposit of $30 each period. We set the frequency of payments, in this case 52 to represent weeekly deposits (the frequency of compounding periods is set to the same value). We set the number of periods as the number of years times the frequency of periods per year. We are interested in finding the Future Value so we set the highlight on that field. Then we press the key sequence to move to Figure 52.
Figure 52	Figure 52 gives the answer as 17950.49334 (where the cursor happens to be obscuring the leading 1 in the screen image). [Jump to Figure 22 to see the same ORDINARY annuity answer from the FINANCL program.] But this is only half of the answer since this is for an Ordinary Annuity. We know that it is for an Ordinary Annuity becasue the END at the bottom of the screen is highlighted. In order to get the other half of our answer we will have to change the screen so that the BEGIN becomes highlighted and then we will have to ask for a new computation of the Future Value.
Figure 53	To generate the image in Figure 53 we moved the cursor down to the last line and over to the BEGIN. then we pressed press the key to switch the highlight to the BEGIN After that has been done we move the highlight back to the Future Value field. That is the state that generated Figure 53. Then we press the key sequence to move to Figure 54.
Figure 54	Figure 54 gives us the value of the annuity, the Future Value, for an Annuity Due, namely, 17959.98639. [Jump to Figure 22 to see the same annuity DUE answer from the FINANCL program.] Return to description table.
Figure 55	In Figure 55 we have set up the next problem, find the required Rent amount to achieve a given future value. In this case the Future Value is $30,000, the interest is 3%, payments are to be made daily, and we still start (Preesent Value) at 0. The highlight has been placed on the desired value, namely PMT. Then we press the key sequence to move to Figure 56.
Figure 56	The calculator has given us the answer a $9.0900367, but we note that we still have the BEGIN option set at the bottom of the screen. Thus, this the given answer is for a situation where we make deposits at the start of each day. [Jump to Figure 25 to see the same annuity DUE answer from the FINANCL program.]
Figure 57	The only change in Figure 57 is that we have highlighted the END at the bottom of the screen and then returned the highlight to the PMT field. Then we press the key sequence to move to Figure 58.
Figure 58	Now the answer, corresponding to making deposits at the end of each period, is given as $9.0907838. [Jump to Figure 25 to see the same ORDINARY annuity answer from the FINANCL program.] Return to description table.
Figure 59	As we did using the program above, we will do the LOAN AMOUNT (loan payment determination) twice. First we will follow the description given above. We will find the future value of the amount of the loan at the same interest rate and the same compounding period. Figure 59 sets up TVM Solver to find the Future value of us getting $22,00 and holding it for 5 yeears at 3% compounded monthly. We press the key sequence to move to Figure 60.
Figure 60	We see that we would have to pay back an amount of $25,555.56919 for that loan. [Jump to Figure 28 to see the same intermediate answer from the FINANCL program.]
Figure 61	In Figure 61 we have changed the Future Value to be positive and we have set the Present Value to be 0. Now we want to find the PMT amount that will produce this future value. We press the key sequence to move to Figure 62.
Figure 62	Figure 62 shows us that we would have to pay 395.31119 each month to pay off the loan. [Jump to Figure 31 to see the same ORDINARY annuity answer from the FINANCL program.]
Figure 62a	As you might expect, the calculator could have done this all in one step. Figure 62a sets up TVM SOlver to do this. We have the Present Value set at 22000, the Future Value set at 0, and the other values stay as before. We will just search directly for the PMT amount. We press the key sequence to move to Figure 62b.
Figure 62b	Figure 62b shows the same answer, 395.31119 as the payment amount. [Jump to Figure 34 to see the same one step answer from the FINANCL program.] Return to description table.
Figure 63	The actions in Figures 63 through 67, with the exception of changing the PMT amount in Figure 67, are redundant since the values of N, P/Y, PV, and PMT have all be set by the previous use of the TVM Solver. However, just for completeness, we could set these outside of that system. For example, to store 22000 into PV we start by creating the screen in Figure 63.
Figure 64	To get the PV variable we need to get to the Finance application.
Figure 65	Within the Finance application we move to the VARS screen. Here, as shown in Figure 65, the third item is the PV variable. We select that option (either by pressing the key or by using the key to move the highlight to item 3 and then pressing the key.
Figure 66	Either way, the calculator pastes the PV variable at teh end of the command. Then we press the to perform the assingment. In Figure 66 we ccontinue by setting up the command to store 3 into the I% variable. We would have to return to the Finance application, and move to the VARS screen, and select the second item to get that variable.
Figure 67	Figure 67 shows that we have done all of this. In addition we have set 12 into P/Y and, importantly, we have set the payment to be a nice round $400.
Figure 68	Having set those values we can find the remaining balance after n periods by using the built-in function bal(n,d), where n is the number of periods that have completed and d is the number of decimal places to use in our computations. (If d is omitted then the computatiosn are done as per the general calculator settings.) To find the bal( function we return to the main financial application screen and scroll down to item 9, as shown in Figure 68.
Figure 69	Having pasted the bal( symbol onto the screen, we can now complete the command.
Figure 70	In Figure 70 we have completed the command to ask for the balance, without special rounding, after 1 period. The result is the 21655 that we have seen before.
Figure 71	We can recall and repeat the bal( command for other periods of time. Figure 71 shows this having been done for the remaining balance after 2 periods, then again after 2 periods but this time rounding to 2 decimal places, and finally after three periods, again with the 2 decimal place rounding. [Jump to Figure 40 to see the same remaining balance answers from the FINANCL program.] We could, after all, repeat the command for as many periods as we want. We could even build an ammortization table from these results since we know that we are paying $400 each period and by looking at the starting balance for a month and comparing that to the remaining balance at the end of the period, we can see just how much of our $400 went to retire the balance. From that we can compute the amount that went to interest. This becomes a mechanical process for each month so we might code that process into a small program. One such program is AMORTLT and a listing of it si given here: This program merely repeats calls to the bal( function and then does all of the computations explained above, storing the old balance in L3, the new balance in L6, the amount going to retire the balance in L5, and the amount of interest paid in L4.
Figure 72	To run this program, once it is installed on the calculator, we open the list of programs and select AMORTLT.
Figure 73	THis pasts the program name appended to the key phrase prgm onto the screen. Then we run the program.
Figure 74	The program asks for the number of pays, meaning the number of periods to trace. In Figure 60 we entered this as 60. The program does its work and ends, leaving the results in the various built-in lists.
Figure 75	To see those lists we take the small precaution of going to the STATmenu and selecting item 5, SetUpEditor.
Figure 76	The SetUpEditor command was pasted onto the screen and we execute that command. This will make the built-in lists appear in the editor.
Figure 77	We return to the STAT menu, this time selecting Edit...
Figure 78	Figure 78 shows the first three built-in Lists. Of course, of these we are only interested in L3.
Figure 79	We can, however, use the cursors to scroll across to see other lists, as shown in Figure 79. [Jump to Figure 40 to see the same answers from the FINANCL program.]
Figure 80	And here, in Figure 80 we see the remaining balance list, L6.
Figure 81	In Figure 81 we have moved down the list to the last period where we see that had we paid $400 that last period we would have overpaid by $303.10. Therefore, our final payment would have only been for 96.90. This difference is caused because, back in Figure 67, we set the payment to a nice round $400 instead of trying to come closer to the actual, computed, value $395.31119. In reality, we would have had to have payments of $395.31 (in which case we would have the final payment slightly larger than that to make up the difference), or $395.32 (in which case the final payment would be slightly smaller because we had consistently overpaid). Our choice of $400 was just to make the computations a bit easier.
Figure 82	One of the more interesting consequences of having the ammortization table built into the lists is that we can use other functions on them. Here we have moved to the LIST menu, then over to the MATH screen, and then down to item 5, sum(.
Figure 83	In Figure 83 we see the start of the command pasted onto the screen.
Figure 84	We finished the command by placing the list name L4 and the closing parenthesis on the screen. When we execute that command we get the total of the interest paid for the loan.
Figure 85	Your textbook describes yet another way to achieve the same thing. This method uses the Y= screen to define various functions and the the Finance application to specify those functions. Figure 85 shows the MODE screen. It is presented here just because we want to be sure that the FUNC option is set in the fourth line.
Figure 86	Then we move to the Y= screen so that we can define our functions. The first one that we want will hold the interest for a particular period, where the period will be specified by the value of the independent variable X.
Figure 87	To find the desired function we return to the Finance application screen, shown in Figure 87. Our desired function is further on in the list of items on this screen so we will need to scroll down the screen.
Figure 88	Figure 88 shows that we have moved down the screen to item A. That is the function for finding the sum of all interest from a starting period through an ending period. We will use this function, placing the value X in both the starting period and ebnding period position so that we can have the calculator compute the interest for month X.
Figure 89	Figure 89 shows that we have pasted the desired function onto the screen.
Figure 90	Figure 90 not only has the completed statement for the interest function, namely, starting at period X, ending at period X, and rounding results to 2 decimal digits, but also similar functions, also found on the screen in Figure 88, for the amount of the principal retired in period X and the remaining balance at the end of period X.
Figure 91	Once the functions are set up we move to the TBLSET screen were me have the table start at 0 with step size 1.
Figure 92	From there we move to the TABLE screen where all of our values are shown, at least all the one that fit on the screen. [Jump to Figure 40 to see the same answers from the FINANCL program.]
Figure 93	Finally, in Figure 93 we have scrolled over to see more of the values that would go into our amortization table. Return to description table.

©Roger M. Palay
Saline, MI 48176
February, 2012