ti83 finance

8/6/2019 TI83 Finance

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Financial Functions 14-1

14Financial

Functions

Getting Started: Financing a Car ......................... 14-2

Getting Started: Computing Compound Interest.......... 14-3

Using the TVM Solver .................................... 14-4

Using the Financial Functions ........................... 14-5

Calculating Time Value of Money (TVM) ................. 14-6

Calculating Cash Flows .................................. 14-8

Calculating Amortization ................................ 14-9Calculating Interest Conversion.......................... 14-12

Finding Days between Dates/Defining Payment Method ..... 14-13

Using the TVM Variables ................................. 14-14

Contents


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14-2 Financial Functions

Getting Started is a fast-paced introduction. Read the chapter for details.

You have found a car you would like to buy. The car costs 9,000. You canafford payments of 250 per month for four years. What annual percentage rate

(APR) will make it possible for you to afford the car?

1. Pressz~~~ to set thefixed-decimal mode setting to 2. The TI-83will display all numbers with two decimal

places.

2. Pressy [FINANCE] to display theFINANCE CALC menu.

3. Press to select 1:TVM Solver. TheTVM Solver is displayed.

Press 48 to store 48 months to .Press9000 to store 9,000 to PV.Press250 to store L250 to PMT.(Negation indicates cash outflow.) Press 0 to store 0 to FV. Press 12 tostore 12 payments per year to P/Y and 12compounding periods per year to C/Y.Setting P/Y to 12 will compute an annual

percentage rate (compounded monthly)

for. Press to select PMT:END,which indicates that payments are due atthe end of each period.

4. Press}}}}}} to move the cursorto the prompt. Press [SOLVE] tosolve for . What APR should you lookfor?

Getting Started: Financing a Car


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At what annual interest rate, compounded monthly, will 1,250 accumulate to2,000 in 7 years?

Note: Because there are no payments when you solve compound interest problems, PMTmust be set to 0 and P/Y must beset to 1.

1. Pressy [FINANCE] to display theFINANCE CALC menu.

2. Press to select 1:TVM Solver. Press 7to enter the number of periods in years.Press1250 to enter the present

value as a cash outflow (investment).Press0 to specify no payments. Press2000 to enter the future value as a cashinflow (return). Press1 to enter

payment periods per year. Press12 toset compounding periods per year to 12.

3. Press}}}}} to place the cursor onthe prompt.

4. Press [SOLVE] to solve for, theannual interest rate.

Getting Started: Computing Compound Interest


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The TVM Solver displays the time-value-of-money (TVM)variables. Given four variable values, the TVM Solver solvesfor the fifth variable.

The FINANCE VARS menu section (page 14.

14) describesthe five TVM variables (, , PV, PMT, and FV) and P/Y andC/Y.

PMT: END BEGIN in the TVM Solver corresponds to theFINANCE CALC menu items Pmt_End (payment at the endof each period) and Pmt_Bgn (payment at the beginning ofeach period).

To solve for an unknown TVM variable, follow these steps.

1. Pressy [FINANCE] to display the TVM Solver. Thescreen below shows the default values with the fixed-decimal mode set to two decimal places.

2. Enter the known values for four TVM variables.

Note: Enter cash inflows as positive numbers and cash

outflows as negative numbers.

3. Enter a value for P/Y, which automatically enters thesame value for C/Y; ifP/YC/Y, enter a unique value forC/Y.

4. SelectEND

orBEGIN

to specify the payment method.5. Place the cursor on the TVM variable for which you

want to solve.

6. Press [SOLVE]. The answer is computed,displayed in the TVM Solver, and stored to theappropriate TVM variable. An indicator square in the leftcolumn designates the solution variable.

Using the TVM Solver

Using the TVMSolver


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When using the TI-83 financial functions, you must entercash inflows (cash received) as positive numbers and cashoutflows (cash paid) as negative numbers. The TI-83follows this convention when computing and displaying

answers.

To display the FINANCE CALC menu, pressy [FINANCE].

CALC VARS

1: TVM Solver... Displays the TVM Solver.2:tvm_Pmt Computes the amount of each payment.3:tvm_ Computes the interest rate per year.4:tvm_PV Computes the present value.

5:tvm_ Computes the number of payment periods.6:tvm_FV Computes the future value.7:npv( Computes the net present value.8:irr( Computes the internal rate of return.9:bal( Computes the amortization sched. balance.0:GPrn( Computes the amort. sched. principal sum.A:GInt( Computes the amort. sched. interest sum.B: 4Nom( Computes the nominal interest rate.C: 4Eff( Computes the effective interest rate.D:dbd( Calculates the days between two dates.E:Pmt_End Selects ordinary annuity (end of period).F:Pmt_Bgn Selects annuity due (beginning of period).

Use these functions to set up and perform financialcalculations on the home screen.

TVM Solver displays the TVM Solver (page 14.4).

Using the Financial Functions

Entering CashInflows and CashOutflows

FINANCE CALCMenu

TVM Solver


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Use time-value-of-money (TVM) functions (menu items 2through 6) to analyze financial instruments such asannuities, loans, mortgages, leases, and savings.

Each TVM function takes zero to six arguments, whichmust be real numbers. The values that you specify asarguments for these functions are not stored to the TVM

variables (page 14.14).

Note: To store a value to a TVM variable, use the TVM Solver (page14.4) or use and any TVM variable on the FINANCE VARSmenu (page 14.14).

If you enter less than six arguments, the TI-83 substitutes apreviously stored TVM variable value for each unspecified

argument.

If you enter any arguments with a TVM function, you mustplace the argument or arguments in parentheses.

tvm_Pmt computes the amount of each payment.

tvm_Pmt[(,,PV,FV,P/Y,C/Y)]

Note: In the example above, the values are stored to the TVMvariables in the TVM Solver. Then the payment (tvm_Pmt) iscomputed on the home screen using the values in the TVM Solver.Next, the interest rate is changed to 9.5 to illustrate the effect on the

payment amount.

Calculating Time Value of Money (TVM)

Calculating TimeValue of Money

tvm_Pmt


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tvm_ computes the annual interest rate.

tvm_[(,PV,PMT,FV,P/Y,C/Y)]

tvm_PV computes the present value.

tvm_PV[(,,PMT,FV,P/Y,C/Y)]

tvm_ computes the number of payment periods.

tvm_[(,PV,PMT,FV,P/Y,C/Y)]

tvm_FV computes the future value.

tvm_FV[(,,PV,PMT,P/Y,C/Y)]

tvm_

tvm_PV

tvm_

tvm_FV


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Use the cash flow functions (menu items 7 and 8) toanalyze the value of money over equal time periods. Youcan enter unequal cash flows, which can be cash inflows oroutflows. The syntax descriptions for npv(and irr(use

these arguments.

interest rate is the rate by which to discount the cashflows (the cost of money) over one period.

CF0 is the initial cash flow at time 0; it must be a realnumber.

CFList is a list of cash flow amounts after the initialcash flow CF0.

CFFreq is a list in which each element specifies thefrequency of occurrence for a grouped (consecutive)

cash flow amount, which is the corresponding elementofCFList. The default is 1; if you enter values, theymust be positive integers < 10,000.

For example, express this uneven cash flow in lists.

2000 40002000 2000

- 3000

4000

CF0 = 2000CFList = {2000,L3000,4000}CFFreq = {2,1,2}

npv( (net present value) is the sum of the present valuesfor the cash inflows and outflows. A positive result for npvindicates a profitable investment.

npv(interest rate,CF0,CFList[,CFFreq])

irr( (internal rate of return) is the interest rate at which thenet present value of the cash flows is equal to zero.

irr(CF0,CFList[,CFFreq])

300050001000

- 2000 - 2500

0

Calculating Cash Flows

Calculating aCash Flow

npv(, irr(


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Use the amortization functions (menu items 9, 0, and A) tocalculate balance, sum of principal, and sum of interest foran amortization schedule.

bal( computes the balance for an amortization scheduleusing stored values for , PV, and PMT.npmt is thenumber of the payment at which you want to calculate abalance. It must be a positive integer < 10,000.roundvaluespecifies the internal precision the calculator uses tocalculate the balance; if you do not specifyroundvalue,then the TI-83 uses the current Float/Fix decimal-modesetting.

bal(npmt[,roundvalue])

GPrn( computes the sum of the principal during a specifiedperiod for an amortization schedule using stored values for, PV, and PMT.pmt1 is the starting payment.pmt2 is the

ending payment in the range.pmt1 andpmt2 must bepositive integers < 10,000.roundvalue specifies the internalprecision the calculator uses to calculate the principal; if youdo not specifyroundvalue, the TI-83 uses the currentFloat/Fix decimal-mode setting.

Note: You must enter values for , PV, PMT, and before computingthe principal.

GPrn(pmt1,pmt2[,roundvalue])

GInt( computes the sum of the interest during a specifiedperiod for an amortization schedule using stored values for, PV, and PMT.pmt1 is the starting payment.pmt2 is theending payment in the range. pmt1 andpmt2 must be

positive integers < 10,000.roundvalue specifies theinternal precision the calculator uses to calculate theinterest; if you do not specifyroundvalue, the TI-83 usesthe current Float/Fix decimal-mode setting.

GInt(pmt1,pmt2[,roundvalue])

Calculating Amortization

Calculating anAmortizationSchedule

bal(

GPrn(, GInt(


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You want to buy a home with a 30-year mortgage at 8percent APR. Monthly payments are 800. Calculate theoutstanding loan balance after each payment and displaythe results in a graph and in the table.

1. Pressz. Press~~~ to set thefixed-decimal mode setting to 2. Press~ toselect Par graphing mode.

2. Pressy [FINANCE] to display the TVM Solver.

3. Press 360 to enter number of payments. Press8 toenter the interest rate. Press800 to enter the

payment amount. Press0 to enter the future value ofthe mortgage. Press12 to enter the payments per

year, which also sets the compounding periods per yearto 12. Press to select PMT:END.

4. Press}}}}} to place the cursor on the PV prompt.Press [SOLVE] to solve for the present value.

5. Presso to display the parametric Y= editor. Turn off allstat plots. Press to define X1T as T. Pressy

[FINANCE] 9 to define Y1T as bal(T).

AmortizationExample:Calculating anOutstanding

Loan Balance


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6. Pressp to display the window variables. Enterthe values below.Tmin=0 Xmin=0 Ymin=0

Tmax=360 Xmax=360 Ymax=125000

Tstep=12 Xscl=50 Yscl=10000

7. Pressr to draw the graph and activate the tracecursor. Press~ and| to explore the graph of theoutstanding balance over time. Press a number and then

press to view the balance at a specific time T.

8. Pressy [TBLSET] and enter the values below.TblStart=0

@Tbl=12

9. Pressy [TABLE] to display the table of outstandingbalances (Y1T).

10.Pressz~~ to select G.Tsplit-screen mode, in which the graph and table are

displayed simultaneously.

Pressr to display X1T (time) and Y1T (balance) inthe table.


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Use the interest conversion functions (menu items B andC) to convert interest rates from an annual effective rate toa nominal rate (4Nom( ) or from a nominal rate to an annualeffective rate (4Eff( ).

4Nom( computes the nominal interest rate. effective rateand compounding periods must be real numbers.compounding periods must be >0.

4Nom(effective rate,compounding periods)

4Eff( computes the effective interest rate.nominal rate andcompounding periods must be real numbers.compounding periods must be >0.

4Eff(nominal rate,compounding periods)

Calculating Interest Conversion

Calculating anInterestConversion

4Nom(

4Eff(


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Use the date function dbd( (menu item D) to calculate thenumber of days between two dates using the actual-day-count method. date1 and date2 can be numbers or lists ofnumbers within the range of the dates on the standard

calendar.

Note: Dates must be between the years 1950 through 2049.

dbd(date1,date2)

You can enter date1 and date2 in either of two formats.

MM.DDYY (United States)

DDMM.YY (Europe)

The decimal placement differentiates the date formats.

Pmt_End and Pmt_Bgn (menu items E and F) specify atransaction as an ordinary annuity or an annuity due. When

you execute either command, the TVM Solver is updated.

Pmt_End (payment end) specifies an ordinary annuity,where payments occur at the end of each payment period.Most loans are in this category. Pmt_End is the default.

Pmt_End

On the TVM Solvers PMT:END BEGIN line, select END to setPMT to ordinary annuity.

Pmt_Bgn (payment beginning) specifies an annuity due,where payments occur at the beginning of each paymentperiod. Most leases are in this category.

Pmt_Bgn

On the TVM Solvers PMT:END BEGIN line, select BEGIN toset PMT to annuity due.

Finding Days between Dates/Defining Payment Method

dbd(

Defining thePayment Method

Pmt_End

Pmt_Bgn


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14 14 Financial Functions

To display the FINANCE VARS menu, pressy [FINANCE]~. You can use TVM variables in TVM functions and store

values to them on the home screen.

CALC VARS1: Total number of payment periods2: Annual interest rate3: PV Present value4: PMT Payment amount5: FV Future value6: P/Y Number of payment periods per year7: C/Y Number of compounding periods/year

, , PV, PMT, and FV are the five TVM variables. Theyrepresent the elements of common financial transactions,as described in the table above. is an annual interest ratethat is converted to a per-period rate based on the valuesofP/Y and C/Y.

P/Y is the number of payment periods per year in afinancial transaction.

C/Y is the number of compounding periods per year in thesame transaction.

When you store a value to P/Y, the value for C/Yautomatically changes to the same value. To store a unique

value to C/Y, you must store the value to C/Y after you havestored a value to P/Y.

Using the TVM Variables

FINANCE VARSMenu

, , PV, PMT,FV

P/Y and C/Y

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