E-mail Webmaster

_____________

Home
________________

________________
English Section

Math Tutorials

TI Graphing Calculators

TI Program Descriptions

Casio Graphing    Calculator

Casio Program Descriptions

Casio Programs
CFX-9850 & CFX-9750

Brief  Guides

CFX-9850 & CFX-9750
User Manual

Statistics Guide

Casio Programming Keystrokes
________________
Brief Guides Other Calculators
HP 43S Calculator

Scientific Calculators
FAQs for Scientific Calculators

===============

Sección Española

FAQs en Español
FAQs Basicos
Mas Dificil Pagina 1
Mas Dificil Pagina 2

Guías en Espaňol
TI-82 Espanol
TI-82 Estidisticas
TI-83 Plus Espanol
TI-83 Plus Estidisticas
TI-83 Plus Guía Financiera
TI-89 Titanium Guía
TI-89 Estidisticas
TI-89 Guía Financiera

Breve Guía Español
Cfx-9850 & Cfx-9750

Casio FAQs en Espanol

FAQs en Espanol
________________
Programs at Other Sites

Brief User Guide for TI-89 Titanium Financial APP & Financial Calculations

Contents: This page covers simple and compound interest, effective interest, annuities, mortgages, sinking funds, loan amortization,
bond maturities, internal rate of return (Irr), Alpha, Beta,r, r2 , and much more.
Last Revised:
5/18/2014

INDEX:
To facilitate lookup, the instructions are divided into the following categories:

I.   Interest - Simple Interest, Compound Interest, Interest Compounded Continuously, Effective Interest
Rate
II.   Annuities and Mortgages - Ordinary Annuities,  Annuities Due, Sinking Funds,
III.   Loans -  Car Loans, Loan Amortization Table
IV.  Investments – Price of a bond; Interest to Maturity of a Bond, Present Value, Internal Rate of
return (Irr) , Investment Index

V. A Smidgen of Portfolio Calculations - Alpha, Beta, CorrCoef, and R Squared

RELEASE DATE: 8/17/09        DATE LAST REVISED:  5/17/14
NOTE:  See copy restrictions and printing hints at the end of this document.

Printer friendly page here.

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=Pert 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
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.

 Payment Number Amount of Payment Principal Payment Interest Payment Principal Balance 0 \$80,000.00 1 \$991.89 \$425.22 \$566.67 \$79574.80 2 \$991.89 \$428.23 \$563.65 79146.54 3 \$991.89 \$431.26 \$560.62 78715.285

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?

 PERIOD CASH FLOWS 0 0 1 100 2 200 3 300 4 400 5 500

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 +Io)/Io , where Io 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

V. A Smidgen of Portrolio Calculations:

1.  Alpha, Beta, CorrCoef, and RSquared:

Although they may seem quite complex so far as their uses in a portfolio, in concept,
α and β are quite simple mathematically.
The
α term is just the y-intercept of the line y=mx +b that you learned about in seventh grade and β is the slope of that line.
Although the terms r, and r2 are somewhat more complex because of the arithmetic calculations involved, the calculator
takes care of all of the arithmetic.  The correlation coefficient, r, is an indication of how strongly the two data
groups are correlated. In our case, how strongly is a fund correlated to th S&P 500. The term r2 , in statistics called the
coefficient of determination, is as follows: r2 = (explained variation)/(total variation), where explained variation is that
predicted by the best-fit line.
For example, if r2  is 90%, then 90% of the variation in the best-fit line is explained by the
variation of the S&P 500.

So, let's calculate these values for two different international funds.

 FUND OR BENCHMARK YEARLY RETUNS α β r2 r S& P 500 10.88, 4.91, 15.79, 5.49, -37.00, 26.46, 15.06, 2.11, 16.00, 32.39, Fund A 13.89,16.27,19.26,13.43, -48.02, 52.20, 14.48,-12.33, 18.72, 14.27 -0.73078 1.1888 0.7600 0.8718 Fund B 20.84, 15.57, 26.64, 15.52, -44.10, 36.73, 11.04, -14.52,18.21. 15.14 0.8707 1.0691 0.7582 0.8707

Find the Various Relationships:

Relationship between MSCI and Fund A:
a) Press APPS, S, highlight the Stats/Lists icon and press ENTER and enter the data S&P 500 data in list list 1 and the Fund A data
in list list 2.
b) Press F4, go to Regression and press the right arrow; then select 1: LinReg(a +bx).
c) Place the cursor opposite list 1, press 2nd Var-Link (the subtract sign), press L, select list 1 and press ENTER. Do the same
thing for list 2.

d) Press ENTER. The values listed in the table will appear.

Relationship between MSCI and Fund B:

a) Press APPS, S, highlight the Stats/Lists icon and press ENTER. The data for the S&P 500 should already be in list 1. Enter the data
for Fund B in list 3.
b) Press F4, go to Regression and press the right arrow; then select 1: LinReg(a +bx).
c) Place the cursor opposite list 1, press 2nd Var-Link (the subtract sign), press L, select list 1 and press ENTER. Do the same
thing for list 3.

d) Press ENTER. The values listed in the table  on the same line as Fund B will appear.

Funds A and B are two different international funds. You'll notice the two funds have about the same correlation as
indicated by the values of r. The values for β indicate how much a fund return moves when the benchmark moves a unit value. You'll
notice that Fund A moves somewhat more than Fund B. The r2 values indicate that slightly more of the volatility of Fund A is explained
by the volatility of the S&P 500 than is Fund B. Finally, alpha indicates the difference between the value as prdicted
by the slope, β, and the market return, in this case the S&P 500. For the market return,
α is zero. You'll notice that Fund B is
somewhat higher.

Making it Better:  I would be grateful if you would report any errors or suggestions for improvements to me.  Just click "E-mail
Webmaster," site the item number, and tell me your suggested change.

Printing Hint:  Most browsers will send both the navigation bar and the text to the printer, and, as a result, some printers will cut
off the right edge of this document if  the file is printed directly.  To prevent this, you can use landscape, of course.   But if you'd like
to get rid of the navigation panel,  highlight the instructions portion only (not the navigation panel) and check "Selection" on the
Print dialog box; then click "Apply."  This will eliminate the navigation panel and get all of the instructions on the printed pages.
Some newer printers have a special Web Page function for printing that will print the page without cutting part of it off.

Copy Restrictions:  You may make single copies of this document for your own personal use and for the use of other students, but
inclusion in another document, publication,  or any use for profit requires my permission.  Teachers may make multiple copies of
this document for their students if they first get my permission.  Merely send me an email (Just click on Webmaster in the navigation
bar.) with a one-sentence explanation of what you’re using the document for.  I’ll give you permission in a timely manner.