RELEASE DATE:  5/1/06         DATE LAST REVISED:  8/18/09
© 2003 Frank Kizer    NOTE:  See copy restrictions and printing hints at the end of this document.  
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General: 
*  TMV Solver - Unless otherwise indicated,  all calculations will be with the TMV Solver.  To access
   this, press APPS, ENTER, ENTER. 
*  Most of these instructions will be carried out using a problem as an example.  Note that some of the  
   problems could be solved, possibly even easier, without the Finance APP, but this document deals with
   that APP only. 
*  Minus Signs - Note that some answers will have a minus sign before them.  These are there because 
   the calculator  follows the cash-flow sign convention in which cash outflows (investments for example)
   are negative and inflows are positive.  For many problems, you can ignore this sign.  When it's
   important, that will be indicated.
*  Setting N, P/Y, and C/Y - As a general rule, when there are no periodic payments, such as in  
   interest calculations, "N" is set equal to the number of years and P/Y is set at 1.  C/Y will be set to
   the number of compounding periods a year.  Notice that for daily compounding, C/Y will be set at 360
   or possibly 365 for some problems.  For loans, annuities, and other such things with periodic payments,
   P/Y will be set for the number of payments a year, "N"  will be the number of payments, and C/Y will be
   set for the number of compoundings per year.

I.  Simple and Compound Interest.

    1. Simple Interest:
        A student had $5000 which she did not need for 11 months.  If she invested it for 11 months at 8%
        annual interest, how much did she have at the end of the 11 months?
        a)  Enter values so that the display appears as follows:  N=1; I%=8*11/12; PV = 5000; PMT=0;
             P/Y =1; C/Y=1; END.
        b)  Set the cursor on FV and press ALPHA; SOLVE.  Note that SOLVE is the third function of the
             ENTER key. 
        c)  Note that if you want the interest accumulated, then just subtract $5000 from the answer
             obtained in the above operation. 

    2. Compound Interest:
        Ex 1:  Suppose that you invest $5000 for 6.5 years at 5.25% interest compounded quarterly,  
        how much money will you have at the end of the period? 
         a) Press APPS, ENTER, ENTER to display the TMV Solver.
         b)  Enter values so that the following display is completed:  N=6.5; I%=5.25; PV = -5000; PMT=0;
              P/Y =1; C/Y=4; END.
        c)  Set the cursor on FV and press ALPHA; SOLVE.  Note that SOLVE is the third function of the
             ENTER key. Your answer should be 7017.93.
        d)  Note that if you want the interest accumulated, then just subtract $5000 from the answer
             obtained in the above operation. 

       Ex 2:  Suppose that you have $1200 and you need $1800 in 7 years,  at what interest compounded
       quarterly,  will you need to invest the money to earn this amount?
        a)  Enter values so that the following display is completed:  N=7; I%=0; PV = -1200; PMT=0; FV=1800,
             P/Y =1; C/Y=4; END.
        b)  Set the cursor on I%, and press ALPHA; SOLVE.  Note that SOLVE is the third function of the
             ENTER key. Your answer should be 5.835 rounded to 3 decimal places.

        EX 3:  Interest Compounded Continuously:
           Although the formula A=Pe^rt is just about as easy as using the Finance APP, some users have difficulty
           rearranging the formula to obtain time or rate.  So, I will include this example of continuous compounding.
            Let's take the information in Ex 2 above except that we have interest compounded continuously.
            a)  Enter the information exactly as in Ex 2 except that for C/Y, enter 1E9.  Do that by pressing 2, 2ND
                 EE (the comma key), 9, ENTER. 
            b)  Set the cursor on I%, and press ALPHA; SOLVE.  Note that SOLVE is the third function of the
              ENTER key. Your answer should be 5.834 rounded to 3 decimal places.

 3. Effective Interest Rate:
     Suppose that a one bank tells you that it pays 3.9% compounded monthly and another tells you
     that it pays 4% compounded semi-annually.  Which one is the best investment?
     a)  Press APPS, ENTER, move the cursor down  to C:EFF( and press ENTER.  (Alternatively, you
          may press ALPHA C.)  "EFF (" will be pasted to the screen.
     b)  Enter 3.9, 12) and press ENTER.  The effective interest rate will be 3.97%.
     c)  Press 2nd, ENTRY (the second function of ENTER); then edit the entry so that you have
          EFF(4, 2); then press ENTER.  Your answer will be 4.04.  So, this is the best investment.

II. Annuities and Mortgages:

     1. Ordinary Annuities:
         For our purposes, an ordinary annuity will be one in which equal payments are made at equal
         periods of time, the compounding period is the same as the payment period, and the payments
         are made at the end of the period. Note Well:  Because there are payments in an annuity, "N" in
         the TMV Solver must set equal to the number of payment periods.
         Ex. 1:  Suppose that you pay $20,000 each year into an annuity for 7 years.  If the interest is 6%
         compounded annually, how much will you have at the end of the period?
         a) Press APPS, ENTER, ENTER to display the TMV Solver.
         b)  Enter values so that the following display is completed:  N=7; I%=6; PV = 0;PMT=-20000;
              P/Y =1; C/Y=1; END.
         c)  Set the cursor on FV and press ALPHA, SOLVE.  Note that SOLVE is the third function of the
             ENTER key. Your answer should be 167876.75.

     2. Annuities Due:
         Annuities Due have the same setup as ordinary annuities, except that BEGIN is highlighted
         instead of END.
         Ex. 1:  Suppose that you pay $500 each year into an annuity due for 7 years.  If the interest is
         6% compounded annually, how much will you have at the end of the year?
         a) Press APPS, ENTER, ENTER to display the TMV Solver.
         b)  Enter values so that the following display is completed:  N=7; I%=6; PV = 0;PMT=-500;
              P/Y =1; C/Y=1; BEGIN
         c)  Set the cursor on FV and press ALPHA, SOLVE.  Note that SOLVE is the third function of the
             ENTER key. Your answer should be 4196.92, rounded to 2 decimal places.

     3. Sinking Funds:
         Sinking funds have the same characteristics as annuities,  but they are for purposes other than an
         annuity. They may be to accumulate enough money to buy a car, pay off a loan, or any other purpose.
         Follow the same procedure for these as for annuities.

     4.  Mortgages:
          Suppose a family buys a home for $200000 and makes a down payment of $20000.  They take  
          out a $180000 mortgage at 7.5% for 30 years.  What is the monthly payment required to
          amortize this loan?
          a) Press APPS, ENTER, ENTER to display the TMV Solver.
          b)  Enter values so that the following display is completed:  N=360; I%=7.5; PV =
              180000; FV=0; PMT=0; P/Y =12; C/Y=12; END.
          c)  Set the cursor on PMT and press ALPHA, SOLVE.  Note that SOLVE is the third function of 
               the ENTER key. Your answer should be 1258.59, rounded to 2 decimal places.
          NOTE:  To find the total interest paid on this loan, use this formula:
          Total Interest = Monthly Payment*Number of Months - Original Amount of Loan.
                              =  1258.59*360 -180000
                              = $273092.4

       5.  Mortgage Loan Calculations:
            Calculate Individual values:
                  Suppose you have an 10-year loan of $80,000.00 at 8.5 percent with payments each month. 
                   Make an amortization table for the first three payments.  You might first want to make a table  
                   such as the following to enter your data.  The calculated data has already been entered in
                   this table.
             To Calculate the Monthly Payment::
                   a)  Press APPS,  ENTER, ENTER
                   b)  Put the following information in the display that appears:  N=10*12; I% = 8.5; PV=-80000;
                        FV=0; P/Y=12;C/Y = 12; END.
                  c)  Put the cursor at PMT, press ALPHA, SOLVE  and the payment of 991.885 will be displayed
                       opposite PMT.
             To Calculate a Specific Principal Balance:
                  a)  From the Home screen, press 2ND,  CATALOG, B, ENTER. The term "bal" will be pasted to the
                  Home screen.  We will now calculate the balance after  each of the three payments.
                c)  Enter values so that your display looks like this:  bal(3) . The numbers inside the parentheses  indicate the  
                      balance will be calculated after the third payment.
                 d)  Press ENTER and the value indicated in the table below for the third payment will be displayed.
              To Calculate a Specific  Principal Payment: 
             a)  From the Home screen, press 2ND,  CATALOG, P;  then cursor down a few items and highlight
                       ∑Prn.   Press ENTER and the term ∑Prn will be pasted to the
                  Home screen.  We will now calculate the principal payment  after  the third payment.
                b)  Enter values so that your display looks like this: ∑Prn(3, 3) . The numbers inside the parentheses 
                       indicate the principal payment will be calculated for  the third payment.
                 c)  Press ENTER and the value indicated in the table below for the third payment will be displayed.
              To calculate a Specific  Interest Payments.
                 a)  From the Home screen, press 2ND,  CATALOG, I;  then cursor down a few items and highlight
                       ∑Int.   Press ENTER and the term ∑Int will be pasted to the
                  Home screen.  We will now calculate the interest  payment  for  the third payment.
                b)  Enter values so that your display looks like this: ∑Int(3, 3) . The numbers inside the parentheses 
                       indicate the principal payment will be calculated for  the third payment.
                 c)  Press ENTER and the value indicated in the table below for the third payment will be displayed.
                 Of course you could fill out a few lines of a table such as that below using this method, but there's a better method
                 for that which I've included in the amortization table method below.

 5.  Amortization Table for a Loan:
           General:  The manual procedure, which I will explain first, takes a lot of time if you have to
           calculate  several loans or several lines on a table. Therefore, I have added a little program
           that I wrote to save you some work.  The program follows  this explanation. 

  6. Amortization Table for a Loan:
          General:  The manual procedure, which I will explain first, takes quite a lot of time if you have to
           calculate  several loans. Therefore, I have added a little program that I wrote to save you some work. 
          The program follows  this explanation. 

          Manual Method:
              Suppose you have a 10-year loan of $80,000.00 at 8.5 percent with payments each month. 
              Make an amortization table for the first three payments.  You might first want to make a table  
              such as the following to enter your data.  The calculated data has already been entered in
              this table.                

                      Semi-automated Method Using TVM Solver, Graph, and Table:
                      In previous versions I had not included this version because I thought that the program would be
                      used by those who have considerable work of this type to do.  The programs seems not to have been
                      used much, so I am including this,  somewhat tedious, I'm afraid, method to add more flexibility.
                      a)  First, I recommend that you make a table such as the one in the manual procedure immediately
                            above.  Put in parentheses X, Y₇, Y_8,Y_9,Y_0. 
                      b)  Press APPS, ENTER, ENTER to display the TMV Solver.
                      c)  Put the following information in the display that appears:  N=10*12; I% = 8.5; PV=80000;
                           FV=0; P/Y=12;C/Y = 12; END.
                      d)  Put the cursor at PMT, press ALPHA, ENTER, and the payment of 991.885 will be displayed
                            opposite PMT.
                       e)  Press 2ND, QUIT to quit the Solver and press Y= to go to the graphing screen.  We are going
                            to enter some financial functions in positions Y₇, Y_8,Y_9,Y_0. (You could enter them in Y₁, etc. if you
                            prefer, but I am entering them so that the upper variables can be used for other functions.)
                       f)  Place the cursor opposite Y₇ and press 2ND, CATALOG, T.  Now move the cursor down to tmv_Pmt
                           and press ENTER to paste tmv_Pmt opposite Y₇.
                       g)  Place the cursor opposite Y₈ and press 2ND, CATALOG, P.  Now move the cursor down to ΣPrn(
                           and press ENTER to paste ΣPrn(  opposite Y₈.
                       h) Enter characters so that you have ΣPrn(X,X) opposite Y₈.
                       i)  Place the cursor opposite Y₉ and press 2ND, CATALOG, B, ENTER. 
                       j) Enter characters so that you have bal(X) opposite Y₉.
                       k)  Press 2ND, TBLSET, and set TblStart = 0 and ΔTbl=1 and Indpnt to Ask
                 l)  Press 2ND, TABLE and enter the payment number or numbers that you want information for..
                 Obviously, if you want to calculate a table for a different mortgage, just do the calculation for the
                  payment again and then use the table to get the values for the second mortgage without having
                  to make new entries in the Y= positions. Be sure to deselect the Y-variables before graphing a
                  function or you'll time your calculator up for some time graphing unwanted stuff.

                      Using the Program:  This is a simple program that should take only a few minutes to enter if you  
                      have some rudimentary knowledge of how to enter programs.  You can find information on entering
                      programs in your TI User Manual  or in the programs section on this  Website.  (Click on TI  
                      Programming Keystrokes near the bottom of the navigation panel to the left.)   After one student has the
                      program stored in a calculator,  it takes less than three minutes, including setup to transfer the program to
                      in another student's calculator.  NOTE:  The colons to the left on the lines of code are automatically entered
                     when you enter the program  by hand.

                     :PROGRAM: LAONAMRT
                     :"FKIZER  V:050106"
                     : Disp "ENTR DATA IN APPS"
                     :Input "1ST PMT NO. ", B
                     :Input "LAST PMT NO. ", E
                     :1→X
                     :ClrList L₁, L₂, L₃, L_4,L₅
                     :For(P,B,E
                     :X→L₁(X)
                     :tmv_Pmt→L₂(X)
                     :∑Int( P,P→L₃(X)
                     :∑Prn( P,P→L₄(X)
                     :bal(P→L₅(X)
                     :X+1→X
                     :End
                     :Stop

                     Using the Program:  Here's how to use this program, assuming you already have it entered.
                      1)  Follow the first three steps in the manual method described above; then press 2nd, QUIT.
                      2)  Pres, PRGM; move the cursor down to the name of the program you want to use and press ENTER.
                      3) The statement 1ST PMT NO. will appear.  Enter the number of the first payment you want to 
                          calculate data for and press ENTER. 
                      4)  LAST PMT NO. will then appear.  Enter the number for the last payment you want to calculate
                           and  press ENTER.  Obviously, if you want only one payment, that number will be entered for
                           both the first and last payment number.
                      5)  The calculator will store the amounts for Payment, Interest, Principal Payment, and Principal
                           Balance in that order in lists L_1, L₂, L₃, and L₄.
                      6)  To access the data tables, press STAT, ENTER.  
                      7)  You will notice that the data has only five characters (Numbers plus decimal and negative sign, if
                            any.).  If you want a more accurate answer, scroll to the number of interst and a more accurate value
                             will be displayed below the tables containing the lists.
                       
III.  Loans:
      Loans, car loans for example, have the same structure as ordinary annuities.  Let's do an example
      to demonstrate that.
      Ex 1:  Suppose that a car costs $26,000 and your down payment is $4000.  The balance will be paid off in
      36 monthly payments with a interest of 10% per year on the unpaid balance. Find the monthly
      payment.
      a)  Press APPS, ENTER, ENTER to display the TMV Solver.
      b)  Enter values so that the following display is completed:  N=36; I%=10; PV = 22000;PMT=0;
           FV=0; P/Y =12; C/Y=12; END.
      c)  Set the cursor on PMT and press ALPHA, SOLVE.  Note that SOLVE is the third function of
           the ENTER key. Your answer should be 709.88, rounded to 2 decimal places.

IV.  Investments:

      1. Bonds:
          Ex 1:  Suppose that a $1000, 10-year, 8% bond is issued when the market rate is 7.5%. 
          Interest is paid semiannually.  What can you expect to pay for the bond?
          a) Press APPS, ENTER, ENTER to display the TMV Solver.
          b)  Enter values so that the following display is completed:  N=20; I%=7.5; PV =0;PMT=40;
           FV=1000; P/Y =2; C/Y=2; END.  It's important to realize that the cost is based on the interest
           to maturity.
          c)  Set the cursor on PV and press ALPHA, SOLVE.  Note that SOLVE is the third function of
           the ENTER key. Your answer should be -1034.74, rounded to 2 decimal places.

           Ex 2:  Suppose that you have to pay $1034.74 for a $1000, 10-year, 8% bond with interest paid
           twice a year.  What is the interest to maturity for the bond?
           a)  Enter values so that the following display is completed:  N=20; I%=0; PV =-1034.74;PMT=40;
                FV=1000; P/Y =2; C/Y=2; END.
           b)  Set the cursor on I% and press ALPHA, SOLVE.  Note that SOLVE is the third function of
           the ENTER key. Your answer should be 7.5%.

       2.  Present value:
             The syntax for Net Present Value (NPV) is:  npv(interest rate, CFO, CFList[CFFreq]).  Now,
             let's define what these mean: 
             Interest Rate = the rate by which to discount the cash flows over one period.
             CFO = the initial cash flow at time zero.
             CFOList = A list of cash flow amounts AFTER the initial cash flow, CFO.
             CFFreq = How many there are of each amount.  The default is 1.
             Ex. 1:  Suppose you are offered an investment that will pay the cash flows in the table below at
             the end of each year for the next 5 years.  How much would you be willing to pay for it if you
             wanted 10 percent interest per year?
             

               a) Press STAT, ENTER to go to the lists.  It there are numbers in the list you choose to use,
                   you can erase those numbers by highlighting the list name, for example L₁, pressing CLEAR;
                   then ENTER.  Do not use DEL.
               b) Enter the numbers starting with 100 in list L_1.   To enter a number, just enter it and press ENTER. 
               c)  Press 2nd, QUIT to leave the list.
               d)  Press APPS, ENTER, 7. "npv(" will be pasted to the home screen.
               e)  Make entries so that you have the following: npv(10, 0, L₁.  To enter L₁, press 2nd L₁.  (L₁
                    is the second function of the number 1 key.)
               f)  Press ENTER.  Your answer should be 1065.26 rounded to two decimal places.
               NOTE 1:  Instead of using the lists, you could enter the following:
               npv(10, 0, {100, 200, 300, 400, 500}). Then press ENTER.  I frankly prefer to use lists because
               of the increased flexibility.
               NOTE:  If you have several CONSECUTIVE cash flows, you can create a frequency table in
              another list, L_2, for example.  You will need to enter the frequency for each of the CFO values,
              even if it is 1.  Your entry then would be npv(10, 0 L₁, L₂ .
              Ex. 2: Suppose that we wanted to find the future value.  Rather than using the TMV solver for
              each cash flow and adding them up, just multiply the answer from Ex. 1 by (1+.10)^5.  To do
              that, press 2nd, Ans, x (multiply), (1+.10)^5.  Your answer should be 1715.61.
              Ex. 3: Suppose that you were offered the above investment for $800.  What is the NPV?
              CFO is now -800.  The cash outflow is negative.  So, we would enter, npv(10, -800, L₁.  Your
              answer should be 265.26 rounded to 2 decimal places.  
     
       3.  Internal Rate of Return (Irr):  
            Suppose you wanted to find the Irr for the npv example above.
            a)  First enter all of the cash flows except the first in list L₁.
           b)  Press APPS, ENTER, 8.  The term "irr(" will be displayed on the home screen.
           c)  Make entries so that you have the following:  irr(-800, L₁.Your answer should be 19.538.  This
                assumes that the numbers in the table of cash flows above have been entered in list L₁.
           Comments:  If you get an error message using this procedure and don't understand why, go to
           the home page, click on "More Detalied P2" under TI FAQs, and read FAQ 56.

         4.  Modified Internal Rate of Return (MIrr):  
           Step 1:  First we'll find the Future Value:
           a) Press STAT, ENTER to go to the lists.  It there are numbers in the list you choose to use,
                   you can erase those numbers by highlighting the list name, for example L₁, pressing CLEAR;
                   then ENTER.  Do not use DEL.
           b) Enter the numbers starting with 100 in list L_1.   To enter a number, just enter it and press ENTER. 
           c)  Press 2nd, QUIT to leave the list.
           d) Press APPS, ENTER, ENTER to display the TMV Solver.
                e)  Enter values in the display as follows::  N=5; I%=0; PV =-800; PMT=0;
                 FV=1715.61; P/Y =1; C/Y=; END.
            Now, we want to enter a calculated value into FV. To do that, place the cursor opposite FV, press
            CLEAR to clear the value there; the do the following:
           f)  Press APPS, ENTER, 7. "npv(" will be pasted to the home screen.
           g)  Make entries so that you have the following: npv(10, 0, L₁).  To enter L₁, press 2nd L₁.  (L₁ is the
                second function of the number 1 key.)
           h) Now, we want to multiply this by (1.1)^5.  To do that enter 1.1^5.  You should now have
              the this expression:  npv(10, 0, L₁)1.1^5.  When you move the cursor away from FV you
              should have 1715.61
           i) Set the cursor on I% and press ALPHA, SOLVE.  Note that SOLVE is the third function of
                 the ENTER key. Your answer should be 16.48 rounded to two decimal places.