 
Brief User Guide for TI89
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, r^{2}
, 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
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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 cashflow 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 semiannually. Which one is the best
investment?
a) From the Home screen, press 2ND, VARLINK, 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 10year 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, VARLINK, 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, VARLINK, 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, VARLINK, 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 10year 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 TI83+/TI84 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 TI89 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, VARLINK, 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 email 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, 10year, 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, 10year, 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, VARLINK, 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, VARLINK, 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, VARLINK, 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, VARLINK,
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 "TI89 FAQs" under TI FAQs, and read FAQ 10.
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 yintercept of the line y=mx +b
that you learned about in seventh grade and
β is the slope of that line.
Comments about alpha and
beta:
Although the terms r, and r^{2}
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
r^{2} , in statistics called the
coefficient of determination, is as
follows: r^{2} = (explained variation)/(total
variation), where explained variation is that
predicted by the bestfit line.
For example, if r^{2 } is 90%, then 90% of the variation in the
bestfit line is explained by the
variation of the S&P 500.
Comments about r and r^{2}:
So, let's calculate these
values for two different international funds.
FUND OR BENCHMARK 
YEARLY RETUNS 
α 
β 
r^{2} 
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 VarLink (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 VarLink (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.
Comments:
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 r^{2 }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 "Email
Webmaster," site the item number, and tell me
your suggested change.
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