Fin Calculations

8/12/2019 Fin Calculations

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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


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will be

set for the number of compoundings per year.

* Note to Students: The presence of this document does not imply that students should rely

solely on the calculator

to find the answers to their problems. Doing the problems by hand definitely helps to understand

the problem and

gives good practice in manipulating the formulas. I encourage students to use the calculator to

check their answers

and to obtain answers only when allowed by the professor.

I. Simple and Compound Interest.

1. Simple Interest:

Comment: Simple interest can be easily obtained from the formula I=PRT, but for non-students

and others who may rely solely on the

calculator, I will include simple interest. Suppose a student had $1000 which she did not need for

3 years. If she invested it for 3 years at 5%

annual interest, how much did she have at the end of the 3 years?

a) Enter values so that the display appears as follows: N=1; I%=5*3; PV = 1000; 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. The answer will be -1150.

Ignore the negative sign.

c) Note that if you want the interest accumulated, then just subtract $1000 from the answer


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obtained in the above operation.

Note that this works fine in all cases except when you want to find the interest. Suppose that

instead of the above

problem, the problem was the same except that the student wanted to know what interest she

would need to have $1150 in three years.

a) Enter values so that the display appears as follows: N=1; PV = 1000; PMT=0; FV=-1150; P/Y

=1; C/Y=1; END.

b) Set the cursor opposite I% and press ALPHA; SOLVE. The answer will be 15.

c) Move the cursor over past 15 and enter , 3; then press ENTER. The correct answer, 5, will bedisplayed.

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.


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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 to work with as using the Finance APP, some

users have difficulty

working with 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.

EX 4: Time to Double Investment at Continuous Compounding:

Suppose you want to know how long would be required to double your investment at an interest


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rate of 5 percent with continuous

compounding.

a) Take any convenient value such as $100 and double it to get $200.

b) Enter values so that the following display is completed: N=; I%=5; PV = -100; PMT=0;

FV=200, P/Y =1; C/Y=1E9; END

c) Set the cursor opposite N a nd press ALPHA; SOLVE. . The answer would be 13.86 or

about 13 7/8 years.

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%


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compounded annually, how much will you have at the end of the period?


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?


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 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.


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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?


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.


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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


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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 methodfor 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.


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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

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, Y 7, Y8,Y9,Y0.

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.


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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, Y8,Y9,Y0. (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

Prn(and press ENTER to paste Prn( opposite Y 8.

h) Enter characters so that you have Prn(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 Tbl=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


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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

:1X

:ClrList L1, L

2, L

3, L

4,L

5

:For(P,B,E

:XL 1(X)

:tmv_PmtL 2(X)

:Int( P,PL 3(X)

:Prn( P,PL 4(X)

:bal(PL 5(X)

:X+1X

:End

:Stop


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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 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


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36 monthly payments with a interest of 10% per year on the unpaid balance. Find the monthly

payment.


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?


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.


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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.


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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. (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 becauseof 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, 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, 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.


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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. (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


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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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