 
Brief User Guide for TI83 Plus
and TI84
Financial Application
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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 by hand,
Loan Amortization Table SemiAutomated
method, Loan Amortization Table Calculator Program,
IV. Investments – Price of a bond; Interest to Maturity of a Bond,
Present Value, Internal Rate of
return (Irr),
Modified Internal Rate of Return (mirr),
RELEASE DATE: 5/1/06 DATE LAST
REVISED: 8/18/09
© 2003 Frank Kizer
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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 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, 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 semiannually. 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 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, 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 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 
Semiautomated 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, Y_{7}, 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
Y_{7}, Y_{8,}Y_{9,}Y_{0.
}(You could enter them in Y_{1}, 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 Y_{7} and press 2ND, CATALOG, T.
Now move the cursor down to tmv_Pmt
and press ENTER to paste tmv_Pmt opposite Y_{7}.
g) Place the cursor opposite Y_{8} and press 2ND, CATALOG, P.
Now move the cursor down to ΣPrn(
and press ENTER to paste ΣPrn(
opposite Y_{8}.
h) Enter characters so that you have
ΣPrn(X,X) opposite Y_{8}.
i) Place the cursor opposite Y_{9} and press 2ND, CATALOG, B,
ENTER.
j) Enter characters so that you have
bal(X) opposite Y_{9}.
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 Yvariables
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 L_{1}, L_{2}, L_{3}, L_{4,}L_{5
}
:For(P,B,E
:X→L_{1}(X)
:tmv_Pmt→L_{2}(X)
:∑Int( P,P→L_{3}(X)
:∑Prn( P,P→L_{4}(X)
:bal(P→L_{5}(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, }L_{2}, L_{3}, and
L_{4}.
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, 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) 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, 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;
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?
PERIOD 
CASH FLOWS 
0 
0 
1 
100 
2 
200 
3 
300 
4 
400 
5 
500 
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 L_{1},
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, L_{1}.
To enter L_{1}, press 2nd L_{1}. (L_{1}
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 L_{1}, L_{2}
.
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, L_{1}. 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 L_{1}.
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, L_{1}.Your
answer should be 19.538. This
assumes that the numbers in the table of cash flows above have been entered in
list L_{1}.
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 L_{1},
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, L_{1}).
To enter L_{1}, press 2nd L_{1}. (L_{1} 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, L_{1})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.
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