INDEX:

General: 
*  TMV Solver - Unless otherwise indicated,  all calculations will be with the TMV Solver.  To access
   this, press APPS, select the Financial icon, and press 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 sheet 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, PpY, and CpY - 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 PpY is set at 1.  CpY will be set to
   the number of compounding periods a year.  Notice that for daily compounding, CpY will be set at 360
   for some problems.  For loans, annuities, and other such things with periodic payments, PpY will be
   set for the number of payments a year, "N"  will be the number of payments, and CpY 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)  Select the Finance APP and press ENTER; then enter values so that the display appears as follows: 
             N=1; I%=8*11/12; PV = 5000; PMT=0; PpY =1; CpY=1; END.
        b)  Set the cursor on FV and press F2.
        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)  Select the Finance APP and press ENTER; then enter values so that the following display is completed: 
              N=6.5; I%=5.25; PV = -5000; PMT=0; PpY =1; CpY=4; END.
        b)  Set the cursor on FV and press F2 for Calculate.   Your answer should be 7017.93.
        c)  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;; PV = -1200;  
             PMT=0; FV=1800,  P/Y =1; CpY=4; END.
        b)  Set the cursor on I%, and press F2 for Calculate. Your answer should be 5.834 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.  Now, continue with item b) as in Ex 2.

 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)  From the Home screen, press 2ND, VAR-LINK, 2ND, F2, either cursor down to Eff or press the "e" key until
         you get there. 
     b)  Press ENTER and "TIFinance.Eff" will be pasted to the Home screen.
     c)  Enter  (, 3.9, 12, ). (The commas are separators and are not used in the statement.)  The entry will now be  
          "TIFinance.Eff(3.9, 12).
     d)  Press ENTER.  The effective interest rate will be 3.97%.
     e)  Press the right cursor arrow to clear the highlight from the commands and edit the entry so that it reads
          "TIFinance.Eff(4, 2).
      f)  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 be 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)  Enter values so that the following display is completed:  N=7; I%=6; PV = 0;PMT=-20000;
              P/Y =1; CpY=1; END.
         b)  Set the cursor on FV and press F2 for calculate. 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, select the finance icon, and press ENTER.
         b)  Enter values so that the following display is completed:  N=7; I%=6; PV = 0;PMT=-500;
              P/Y =1; CpY=1; BEGIN
         c)  Set the cursor on FV and press F2 for calculate.  Your answer should be 4448.73, 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)  Enter values so that the following display is completed:  N=360; I%=7.5; PV =
              180000; FV=0; PMT=0; P/Y =12; CpY=12; END.
          b)  Set the cursor on PMT and press F2 for calculate.  Your answer should be -1258.59.
          Addendum:  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, select the Finance icon, and press  ENTER.
                   b)  Put the following information in the display that appears:  N=10*12; I% = 8.5; PV=-80000;
                        FV=0; PpY=12;CpY = 12; END.
                  c)  Put the cursor at PMT, press F2, and the payment of 991.885 will be displayed
                       opposite PMT.
             To Calculate a Specific Principal Balance:
                  a)  From the Home screen, press 2ND, VAR-LINK, 2ND, F2, either cursor down to bal or press the "b" key
                 until you get there.  Note that you can also obtain tifinance.bal( by pressing CATALOG, F3, B, highlighting
                 bal, and pressing ENTER.  That method can also be used to obtain any of the tifinance variables mentioned
                 in this document. 
             b)  Press ENTER and "TIFinance.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 Payments: 
             a) Press 2ND, VAR-LINK, 2ND, F2, either cursor down to ∑Prn, and press ENTER.  TiFinance.∑Prn will be
                 pasted to the Home screen. 
                 b)  To calculate the principal for the first payment, enter numbers so that the entry looks as follows: ∑Prn(
                       1,1). 
                  c) Press ENTER and the value indicated in the table below will be displayed.
               To calculate a Specific  Interest Payments.
                 a)  Now, we will calculate the Interest Payments.  Press 2ND, VAR-LINK, 2ND, F2, cursor down to
                 ∑Int and press ENTER.
                b)  The term  TIFnance.∑Int will be displayed.  Calculate the the interest amount using the same procedure as with the
                     principal balance and interest payments. 
                 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.

 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 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.
                 

                
                 a)  Press APPS, select the Finance icon, and press  ENTER.
                 b)  Put the following information in the display that appears:  N=10*12; I% = 8.5; PV=-80000;
                      FV=0; PpY=12;CpY = 12; END.
                 c)  Put the cursor at PMT, press F2, and the payment of 991.885 will be displayed
                       opposite PMT.  Since all payments are the same you need calculate it only once.
                 d)  Press ♦, Y= and set the cursor  to y1=.
                 e)  From the y2 position, press CATALOG, F3, Z.  Then select ΣPrn and press ENTER. 
                 f)  Enter values so that your display looks like this:  TiFinance.∑Prn bal(x, x) .  Press ENTER and the
                       expression will be transferred to the y1 position.
                  Now, we will set up  for the Interest Payments. 
                  e)  From the graph screen, press CATALOG, F3, Z.  Then select ΣInt and press ENTER. 
                 f)  Enter values so that your display looks like this:  TiFinance.ΣIntl(x,x) .  Press ENTER and the
                       expression will be transferred to the y2 position.
                 Now, we will set up  the Balances:
                 e)  From the graph screen set the cursor to y3, press CATALOG, F3, B.  Then select bal and press ENTER. 
                 f)  Enter values so that your display looks like this:  TiFinance.bal(x,x) .  Press ENTER and the
                       expression will be transferred to the y3 position.
                  g)  Press ♦, TABLE and the values will be stored in the table except for the payment which only needs
                        one entry.
                  h)  Press ♦, TBLSET and enter 1 in the box for tblStart and Δtbl.
                  i)   Press ♦, TABLE, and the values will be stored in the table except for the payment which only needs
                        one entry.
                       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 if you have not deleted those entries.  You may want to
                  put them in positions lower down in the y= list.

                      Using a Program:  This is a simple program that should you be able to enter if you have some  knowledge of how to
                      find and enter variables.  Frankly, for students who are taking only one math course with financial calculations,
                      entering this program may be more trouble than it is worth.  I am including it mostly to make this guide a complement
                      to the TI-83+/TI-84 Guide.  The program for those calculators is easier and more straightforward to enter.  Anyway,
                      if you want to us it, it is here.   Most of the steps are included in the hand calculations above.  You can also find some      
                      help in the large TI user manual for the TI-89 Titanium. 

                      :Amortize() 
                      :Prgm                
                     :FKizer  7907
                     :Local i :1→i
                     :{0}→list1 :{0}→list2 :[0}→list3 :{0}→list4
                     : Disp "Entr Data in APP"
                     :Input "1st pmt no.. ", b
                     :Input "Last pmt no.. ", e
                     :For p,b,e
                     :tifinance.∑int( p,p)→list2[i]
                     :tifinance.∑Prn( p,p)→list3[i]
                     :tifinance.bal(p,p)→list4[i]
                     :i+1→i
                     :EndFor
                     :EndPrgm

                     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)  Press Home, 2ND, VAR-LINK, a, select "Amortize" and press ENTER. The statement Amortiz( will appear
                           on the Home screen.  CLOSE THE PARENTHESES 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 list1_, list2, list3, and list4. You can see these numbers by pressing APPS,
                           going to the Stats/List icon, and pressing ENTER.                            
                     6)  You will notice that the data has only five characters (Numbers plus decimal and negative sign, if
                            any, or it may be in exponential form..).  If you want a more accurate answer, scroll to the number of
                            interest and a more accurate value  will be displayed below the tables containing the lists.
                          NOTE:  If anyone has a better idea on this program, send me an e-mail about it.

                    
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)  Enter values so that the following display is completed:  N=36; I%=10; PV = 22000;PMT=0;
           FV=0; P/Y =12; CpY=12; END.
      b)  Set the cursor on PMT and press F2 for Calculate. 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)  Enter values so that the following display is completed:  N=20; I%=7.5; PV =0;PMT=40;
           FV=1000; P/Y =2; CpY=2; END.  It's important to realize that the cost is based on the interest
           to maturity.
          b)  Set the cursor on PV and press F2 for calculate. Your answer should be -1034.74, rounded to 2 decimal
              places.  (Notice that the PMT is $1000*.08/2.

           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; CpY=2; END.
           b)  Set the cursor on I% and press F2 for calculate.  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 APPS, s, highlight the Stats/List icon and press ENTER. If you want to clear a list first, highlight
                   the list name; then press CLEAR, ENTER.  Enter the numbers starting with 100 in list list1_.   To enter
                   a number, just enter it and press ENTER after pressing the number.  Make sure there are no entries following 
                   your  list, not even zeros. 
               b)  Press Home to leave the list.
               c)  Press 2ND, VAR-LINK, 2ND, F2, either cursor down to npv or continually press "n" until npv appears.
               d)  Press ENTER and "TIFinance.npv" will be pasted to the Home screen.  We will now calculate the balance
                        after  each of the three payments. 
               e)  Make entries so that you have the following: npv(10, 0, list1).  To enter list1, press 2ND, VAR-LINK, l,
                    (L, not 1), select the list where your data is stored and press ENTER 
               f)  Press ENTER.  Your answer should be 1065.26 rounded to two decimal places.
               NOTE:  If you have several CONSECUTIVE cash flows, you can create a frequency table in
              another list, list2_, 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 list1, list2) .
              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 1715.6.
              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, list1).  Your
              answer should be 265.26 rounded to 2 decimal places. 

         3.  Investment Index:
              Some people prefer to use the profitability index (also known as the benifit/cost ratio).  That is easily obtained
              from the NPV using the following equation:
              Investment Index = (NPV +I_o)/I_o , where I_o is the initial investment.

        4.  Internal Rate of Return (Irr):  
            Suppose you wanted to find the Irr for the npv example above.
            a)  From the Home screen, press 2ND, VAR-LINK, 2ND, F2, I (the letter I,  not 1). The cursor should now be
                  located at "irr."
             b)  Press ENTER and the term "TIFnance.irr" will be displayed on the Home screen.
             c)  Make entries so that you have the following:  TIFnance.irr(-800, list1). (To enter list1, press 2ND, VAR-LINK,
                  l (L, not 1), and press ENTER.  If your data is in another list, select that list and press ENTER.)
             d)  Your answer should be 19.538.  This  assumes that the numbers in the table of cash flows above have
                 been entered in list list1.
             Comments:  If you get an error message using this procedure and don't understand why, go to
             the home page, click on "TI-89 FAQs" under TI FAQs, and read FAQ 10.