Interactive Manual › Chapter 14

Chapter 14: Applications

The APPS menu and the built-in Finance application: the TVM Solver, time-value-of-money functions, cash flows (npv, irr), amortization (bal, ΣPrn, ΣInt), interest conversion, dbd( and the payment method, plus notes on the other preloaded apps.

The Applications Menup. 251

Press APPS to open the APPLICATIONS menu. Apps are extra programs stored in the calculator's flash memory. They add whole tools (finance, spreadsheets, algebra helpers and so on) beyond the built-in keys and menus.

A TI-84 Plus Silver Edition normally ships with the following apps on the APPLICATIONS menu:

Preloaded apps listed in the guidebook
App	In this emulator
Finance	Available. This is the only app on the emulator's APPLICATIONS menu.
Topics in Algebra 1	Not available
Science Tools	Not available
Catalog Help 1.1	Not available (use the real CATALOG, `2ndCATALOG`, to browse functions)
CellSheet™	Not available
Conic Graphing	Not available
Inequality Graphing	Not available
Transformation Graphing	Not available
Vernier EasyData™	Not available (needs data-collection hardware; see The EasyData App)
DataMate	Not available
Polynomial Root Finder and Simultaneous Equation Solver	Not available (the equation solver and polynomial tools of the base OS are covered in other chapters)
StudyCards™	Not available
LearningCheck™	Not available

Note The emulator is a TI-OS reimplementation without a flash-app library, so only Finance exists. Opening APPS here shows a one-item menu. Language-localization apps, app downloading from education.ti.com, adding and deleting apps, and the 1.54 MB flash app area do not apply to the emulator.

On a real calculator every app except Finance can be deleted and re-installed as space permits. Finance is part of the operating system itself and can never be removed.

Steps for Running the Finance Applicationp. 251

Start Finance from anywhere on the home screen: press APPS and then ENTER to pick 1:Finance. You then get the FINANCE menu, where you choose a function (or the TVM Solver) from the CALC tab. The VARS tab holds the finance variables.

The sections below describe each item. Two quick examples come first, and they show the typical workflow: open the TVM Solver, enter what you know, put the cursor on the unknown and press ALPHASOLVE (SOLVE).

Getting Started: Financing a Carp. 252

You want to buy a car that costs 9,000. Your bank offers 5% annual interest, and you can pay 250 a month for four years. What would the monthly payment be, and is it affordable?

Tutorial

Find the monthly payment on a car loan

You will set two decimal places, open the TVM Solver, enter the loan data, and solve for the payment.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the MODE screen, move down to the Float row, move right to 2 and press ENTER so that results show two decimals (Fix 2). Money is easier to read this way.
MODE▼︎▶︎▶︎▶︎ENTER
Press 2ndQUIT (QUIT) to go back to the home screen.
2ndQUIT
Press APPS, then ENTER to choose 1:Finance.
APPSENTER
Press ENTER again to choose 1:TVM Solver. The solver lists N, I%, PV, PMT, FV, P/Y, C/Y and the PMT:END BEGIN line.
ENTER
Enter N, the number of payments: 4 years × 12 = 48.
48
Move down and enter the annual interest rate, 5 (percent).
▼︎5
Move down and enter the present value, the amount you borrow: 9000.
▼︎9000
Skip PMT (that is what we are solving for) and enter the future value FV = 0, since the loan is fully repaid.
▼︎▼︎0
Enter P/Y = 12 payments per year. C/Y (compounding periods per year) is set to the same value automatically.
▼︎12
Move down to the PMT:END BEGIN line. END is already selected (payments at the end of each month); press ENTER to confirm END.
▼︎▼︎ENTER
Move the cursor up to the PMT line and press ALPHASOLVE (SOLVE). PMT is calculated as about -207.26. The negative sign marks money you pay out, so 207.26 is below your 250 budget: you can afford it.
▲︎▲︎▲︎▲︎ALPHASOLVE

Getting Started: Computing Compound Interestp. 253

At what annual interest rate, compounded monthly, does 1,250 grow to 2,000 in 7 years?

Note With no regular payments, set PMT = 0 and P/Y = 1 (one "payment period" per year). Then set C/Y to 12 for monthly compounding. Enter the starting amount as a negative number: it is money you put away.

Tutorial

Find the interest rate for a compound-interest goal

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the TVM Solver: APPS ENTER ENTER.
APPSENTERENTER
Enter N = 7 (years, since P/Y will be 1).
7
Skip I% (the unknown) and enter PV = -1250. Use the (−) key for the minus sign.
▼︎▼︎(−)1250
Enter PMT = 0.
▼︎0
Enter FV = 2000.
▼︎2000
Enter P/Y = 1. This also sets C/Y to 1.
▼︎1
Enter C/Y = 12 for monthly compounding. Set it after P/Y, otherwise P/Y would overwrite it.
▼︎12
Move the cursor back up to I% and press ALPHASOLVE (SOLVE). You need an annual rate of about 6.73%.
▲︎▲︎▲︎▲︎▲︎ALPHASOLVE

Using the TVM Solverp. 253

The TVM Solver shows the time-value-of-money variables on one screen. You fill in any four of the five main variables (N, I%, PV, PMT, FV) and the solver works out the fifth. P/Y and C/Y describe how often payments are made and how often interest compounds.

The PMT:END BEGIN line in the solver matches the commands Pmt_End (payments at the end of each period) and Pmt_Bgn (payments at the beginning). See Defining the Payment Method.

Open the solver with APPS ENTER ENTER.
Enter the four known TVM values. Money you receive is positive, money you pay out is negative.
Enter P/Y. It also fills in C/Y with the same value; if the two differ, enter C/Y afterwards.
Choose END or BEGIN on the PMT line.
Move the cursor onto the variable you want and press ALPHASOLVE (SOLVE).

The answer appears in the solver and is also stored in that TVM variable. A small square in the left column marks the line that was solved. Editing any value afterwards clears the marker.

Tutorial

Solve for a future value with the TVM Solver

If you put 1,000 into an account that earns 6% a year, compounded yearly, what is it worth after 10 years?

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the TVM Solver.
APPSENTERENTER
Enter N = 10.
10
Enter I% = 6.
▼︎6
Enter PV = -1000 (the deposit is money paid out).
▼︎(−)1000
Enter PMT = 0 (no further deposits).
▼︎0
Move to P/Y and enter 1. C/Y becomes 1 too. Leave the PMT:END setting as it is.
▼︎▼︎1
Move the cursor up to FV and press ALPHASOLVE (SOLVE). FV is about 1790.85: the 1,000 grows to roughly 1,790.85.
▲︎ALPHASOLVE

Using the Financial Functionsp. 254

Besides the TVM Solver, the Finance application provides functions you can use directly on the home screen or in programs. They are all on the FINANCE menu.

Entering Cash Inflows and Cash Outflowsp. 254

Finance always works from your point of view. Cash you receive is positive; cash you pay out is negative. You must enter values this way, and the calculator displays answers the same way.

For a loan, the amount you borrow is a positive PV and your repayments are negative PMT values. For savings, your deposits (negative) go in and the final balance (positive) comes out.

FINANCE CALC Menup. 254

Open it with APPS ENTER. Items 1 to 9 are selected with their number keys; the remaining items use the letter shown on the menu: 0 for item 0, then ALPHAA (A), ALPHAB (B) and so on.

1:TVM Solver…	Display the TVM Solver
2:tvm_Pmt	Compute the amount of each payment
3:tvm_I%	Compute the annual interest rate
4:tvm_PV	Compute the present value
5:tvm_N	Compute the number of payment periods
6:tvm_FV	Compute the future value
7:npv(	Compute the net present value
8:irr(	Compute the internal rate of return
9:bal(	Compute the amortization-schedule balance
0:ΣPrn(	Compute the sum of principal paid over a range of payments
A:ΣInt(	Compute the sum of interest paid over a range of payments
B:►Nom(	Compute the nominal interest rate
C:►Eff(	Compute the effective interest rate
D:dbd(	Calculate the number of days between two dates
E:Pmt_End	Select an ordinary annuity (payments at the end of each period)
F:Pmt_Bgn	Select an annuity due (payments at the beginning of each period)

TVM Solver (menu item)p. 255

TVM Solver…

TVM Solver…

Opens the TVM Solver screen, where you enter the time-value-of-money variables and solve for the unknown one. See Using the TVM Solver.

Keys: APPSENTERENTER

Calculating Time Value of Money (TVM)p. 255

Menu items 2 to 6 of FINANCE CALC (tvm_Pmt, tvm_I%, tvm_PV, tvm_N, tvm_FV) are the home-screen versions of the TVM Solver. Use them to analyze annuities, loans, mortgages, leases and savings.

Each function takes from zero to six arguments, and every argument must be a real number.
Arguments you type are used only for that calculation. They are not stored into the TVM variables.
Any argument you leave out is taken from the stored TVM variable (set via the TVM Solver, or with STO► into a variable on the FINANCE VARS menu).
If you give any arguments, they must be inside parentheses. With no arguments, type the bare name.
The arguments you supply are matched to the TVM variables in the order of the syntax line, left to right.

Note To store a value in a TVM variable, use the TVM Solver, or store to a variable from the FINANCE VARS menu, for example 48→N with N pasted from APPS ENTER ▶︎ 1.

Tip The ordinary letter N is a different variable from the TVM variable N. Always paste the TVM N from the FINANCE VARS menu.

tvm_Pmtp. 256

tvm_Pmt

tvm_Pmttvm_Pmt(N,I%,PV,FV,P/Y,C/Y)

Computes the amount of each payment. With no arguments it uses the stored TVM variables N, I%, PV, FV, P/Y, C/Y (and the PMT:END or BEGIN setting). The stored PMT value is not used, because PMT is the result.

Keys: APPSENTER2

tvm_Pmt(48,5,9000,0,12,12) → ⁻207.2636421

Tutorial

Compute a payment on the home screen, then change the rate

The car loan values are stored with the TVM Solver; then tvm_Pmt reads them. Afterwards the rate is raised to 9.5% to show the effect on the payment.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Press APPS ENTER 2 to paste tvm_Pmt and press ENTER. It uses the stored values and shows the payment: about -207.26.
APPSENTER2ENTER
Store 9.5 into I%: type 9.5, press STO►, then choose I% from the FINANCE VARS menu (APPS ENTER ▶︎ 2), and press ENTER.
9.5STO►APPSENTER▶︎2ENTER
Compute the payment again. A higher rate gives a bigger payment: about -226.11.
APPSENTER2ENTER

tvm_I%p. 256

tvm_I%

tvm_I%tvm_I%(N,PV,PMT,FV,P/Y,C/Y)

Computes the annual interest rate (in percent) that fits the other values.

Keys: APPSENTER3

tvm_I%(7,⁻1250,0,2000,1,12) → 6.733156948

Tutorial

Compute an interest rate with tvm_I%

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste tvm_I% from FINANCE CALC item 3, then type the six arguments: N = 7, PV = -1250, PMT = 0, FV = 2000, P/Y = 1, C/Y = 12, and close the parenthesis.
APPSENTER3(7,(−)1250,0,2000,1,12)
Press ENTER. The result is about 6.733 percent, the same as the Getting Started example.
ENTER

tvm_PVp. 256

tvm_PV

tvm_PVtvm_PV(N,I%,PMT,FV,P/Y,C/Y)

Computes the present value, for example how large a loan a given payment can support.

Keys: APPSENTER4

tvm_PV(48,5,⁻250,0,12,12) → 10855.73898

Tutorial

How much car can a 250 payment buy?

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste tvm_PV and enter N = 48, I% = 5, PMT = -250, FV = 0, P/Y = 12, C/Y = 12.
APPSENTER4(48,5,(−)250,0,12,12)
Press ENTER. A 250 monthly payment over 48 months at 5% supports a loan of about 10,855.74.
ENTER

tvm_Np. 256

tvm_N

tvm_Ntvm_N(I%,PV,PMT,FV,P/Y,C/Y)

Computes the number of payment periods. The result is not rounded, so it may include a fraction.

Keys: APPSENTER5

tvm_N(5,9000,⁻250,0,12,12) → 39.08574623

Tutorial

How many 250 payments to repay 9,000?

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste tvm_N and enter I% = 5, PV = 9000, PMT = -250, FV = 0, P/Y = 12, C/Y = 12.
APPSENTER5(5,9000,(−)250,0,12,12)
Press ENTER. It takes about 39.09 monthly payments, so 40 payments with the last one smaller.
ENTER

tvm_FVp. 257

tvm_FV

tvm_FVtvm_FV(N,I%,PV,PMT,P/Y,C/Y)

Computes the future value: the balance left (or owed) after the last payment period.

Keys: APPSENTER6

tvm_FV(10,6,⁻1000,0,1,1) → 1790.847697

Tutorial

Future value of a deposit

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste tvm_FV and enter N = 10, I% = 6, PV = -1000, PMT = 0, P/Y = 1, C/Y = 1.
APPSENTER6(10,6,(−)1000,0,1,1)
Press ENTER. The deposit grows to about 1790.85.
ENTER

Calculating Cash Flowsp. 257

The cash flow functions (menu items 7 and 8, npv( and irr() analyze money that moves at equal time intervals. The amounts can be uneven, and each can be an inflow (positive) or an outflow (negative). They share these arguments:

Argument	Meaning
interest rate	The rate per period used to discount the cash flows (the cost of money), in percent
CF0	The initial cash flow at time 0. It must be a real number
CFList	A list of the cash flows that follow CF0
CFFreq	A list giving how many times in a row each CFList amount repeats. Optional; the default is 1 for every amount. If given, entries must be positive integers below 10,000

Example of the list form: an initial flow of 2000 at time 0, then 2000 for two periods, then -3000 for one period, then 4000 for two periods, is written as CF0 = 2000, CFList = {2000,⁻3000,4000}, CFFreq = {2,1,2}.

npv(p. 258

npv(

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

Net present value: the sum of the present values of all the inflows and outflows. A positive result means the investment is profitable at that discount rate.

Keys: APPSENTER7

npv(10,2000,{2000,⁻3000,4000},{2,1,2}) → 8432.869091

Tutorial

Net present value of an uneven cash flow

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste npv( from FINANCE CALC item 7 and type the discount rate 10 and the initial flow 2000, separated by commas.
APPSENTER710,2000,
Type the CFList. Braces are 2nd{ and 2nd}; use (−) for the minus sign.
2nd{2000,(−)3000,40002nd},
Type the CFFreq list, close the parenthesis, and press ENTER. The NPV is about 8432.87.
2nd{2,1,22nd})ENTER

irr(p. 258

irr(

irr(CF0,CFList[,CFFreq])

Internal rate of return: the discount rate (in percent) at which the net present value of the cash flows is zero. The flows must include both outflows and inflows, otherwise there is no solution.

Keys: APPSENTER8

irr(⁻1000,{300,400,500}) → 8.896339469

Tutorial

Internal rate of return of an investment

You invest 1,000 and receive 300, 400 and 500 in the next three periods.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste irr( from FINANCE CALC item 8, then enter CF0 = -1000 and a comma.
APPSENTER8(−)1000,
Type the CFList {300,400,500}, close the parenthesis and press ENTER. The return is about 8.90% per period.
2nd{300,400,5002nd})ENTER

Calculating Amortizationp. 258

The amortization functions (items 9, 0 and A) split a loan's payments into balance, principal and interest. All three use the stored values of I%, PV and PMT (and also N, P/Y and C/Y), so fill in the TVM variables first. Compute PMT with the TVM Solver or enter it yourself; it must be set before you use these functions.

The optional roundvalue sets how many decimals the calculator rounds each payment's interest to internally. If you leave it out, the current Float/Fix decimal setting is used.

Note The calculator displays these results with the sign convention of the TVM values: with a positive PV (a loan you received) and a negative PMT, the principal and interest sums come out negative (they are money you paid).

bal(p. 258

bal(

bal(npmt[,roundvalue])

Computes the balance of an amortization schedule right after payment number npmt, using the stored I%, PV and PMT. npmt must be a positive integer below 10,000. roundvalue is the internal rounding precision; by default the Float/Fix setting is used.

Keys: APPSENTER9

With the car loan stored: bal(12) → 6915.496770

Tutorial

Loan balance after one year

The car loan from Getting Started is stored (48 payments, 5%, 9,000).

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste bal( from FINANCE CALC item 9 and ask for the balance after payment 12.
APPSENTER912)
Press ENTER. You still owe about 6915.50 after the 12th payment.
ENTER

ΣPrn(p. 259

ΣPrn(

ΣPrn(pmt1,pmt2[,roundvalue])

Sum of the principal paid from payment pmt1 through payment pmt2 of an amortization schedule, using stored I%, PV and PMT. pmt1 and pmt2 must be positive integers below 10,000. Enter I%, PV and PMT before using it.

Keys: APPSENTER0

With the car loan stored: ΣPrn(1,12) → ⁻2084.503230

Tutorial

Principal repaid in the first year

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste ΣPrn( (FINANCE CALC item 0) and enter the range 1 to 12.
APPSENTER01,12)
Press ENTER. About 2084.50 of principal was paid off (shown as a negative amount).
ENTER

ΣInt(p. 259

ΣInt(

ΣInt(pmt1,pmt2[,roundvalue])

Sum of the interest paid from payment pmt1 through payment pmt2, using stored I%, PV and PMT. The argument rules are the same as for ΣPrn(.

Keys: APPSENTERALPHAA

With the car loan stored: ΣInt(1,12) → ⁻402.6604761

Tutorial

Interest paid in the first year

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste ΣInt( (FINANCE CALC item A, key ALPHAA in the menu) and enter the range 1 to 12.
APPSENTERALPHAA1,12)
Press ENTER. You paid about 402.66 in interest during year one.
ENTER

Amortization Example: Calculating an Outstanding Loan Balancep. 259

You want a 30-year mortgage at 8% APR with monthly payments of 800. This example finds the loan amount, then graphs and tabulates the outstanding balance after each payment.

Because bal( takes a payment number, the graph uses parametric mode: X₁T = T (the payment number) and Y₁T = bal(T).

Tutorial

Mortgage: set modes and solve for the loan amount

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open MODE, go to the Float row and choose 2 decimals (Fix 2).
MODE▼︎▶︎▶︎▶︎ENTER
Move down two rows to the Func / Par / Pol / Seq row, move right to Par and press ENTER.
▼︎▼︎▶︎ENTER
Press 2ndQUIT to return home, then open the TVM Solver.
2ndQUITAPPSENTERENTER
Enter N = 360 (30 years × 12).
360
Enter I% = 8.
▼︎8
Skip PV (the unknown), and enter PMT = -800. The mortgage payment is an outflow.
▼︎▼︎(−)800
Enter FV = 0 (the mortgage is paid off completely).
▼︎0
Enter P/Y = 12. C/Y also becomes 12.
▼︎12
Move to the PMT:END BEGIN line and press ENTER to select END.
▼︎▼︎ENTER
Move the cursor back up to PV and press ALPHASOLVE (SOLVE). An 800 payment supports a mortgage of about 109,026.80.
▲︎▲︎▲︎▲︎▲︎ALPHASOLVE

Tutorial

Mortgage: graph and tabulate the outstanding balance

This continues the previous tutorial; the TVM values and Par mode are recreated for you.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Press Y= to open the parametric Y= editor. (Stat plots are off after a reset; if any of yours are on, turn them off first with 2ndSTAT PLOT and PlotsOff.)
Y=
Define X₁T as T by pressing X,T,θ,n, which types T in parametric mode.
X,T,θ,n
Move down to Y₁T and paste bal( from the Finance menu (APPS ENTER 9). Type X,T,θ,n for T and close the parenthesis.
▼︎APPSENTER9X,T,θ,n)
Open the WINDOW editor and set Tmin = 0, Tmax = 360 and Tstep = 12.
WINDOW0▼︎360▼︎12▼︎
Set Xmin = 0, Xmax = 360 and Xscl = 50.
0▼︎360▼︎50▼︎
Set Ymin = 0, Ymax = 125000 and Yscl = 10000.
0▼︎125000▼︎10000▼︎
Press TRACE to draw the graph and start tracing. Use ◀︎ and ▶︎ to move along the balance curve over time, or type a payment number and press ENTER to jump to it.
TRACE
Open the table setup with 2ndTBLSET (TBLSET) and set TblStart = 0 and ΔTbl = 12.
2ndTBLSET0▼︎12
Press 2ndTABLE (TABLE) to see the balances (Y₁T) every 12 payments.
2ndTABLE

Tutorial

Mortgage: graph and table side by side (G-T mode)

The graph and table from the previous example are recreated, then the screen is split.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open MODE, move down to the Full / Horiz / G-T row, and choose G-T.
MODE▼︎▼︎▼︎▼︎▼︎▼︎▶︎▶︎ENTER
Press TRACE. The graph appears on one side and the table (time X₁T and balance Y₁T) on the other.
TRACE

Calculating Interest Conversionp. 261

The conversion functions (items B and C) translate between a nominal annual rate (the quoted rate before compounding) and an effective annual rate (what you actually earn over a year after compounding). Both arguments must be real, and the number of compounding periods must be greater than 0.

►Nom(p. 261

►Nom(

►Nom(effective rate,compounding periods)

Converts an annual effective rate to the equivalent nominal rate compounded the given number of times per year.

Keys: APPSENTERALPHAB

►Nom(8.3,12) → 8.000045843 (an 8.3% effective rate is 8% compounded monthly)

Tutorial

Convert an effective rate to a nominal rate

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste ►Nom( (item B in the FINANCE CALC menu) and type the effective rate 8.3 and 12 compounding periods.
APPSENTERALPHAB8.3,12)
Press ENTER. The nominal rate is about 8.0000 percent.
ENTER

►Eff(p. 261

►Eff(

►Eff(nominal rate,compounding periods)

Converts a nominal annual rate compounded the given number of times per year to the equivalent annual effective rate.

Keys: APPSENTERALPHAC

►Eff(8,12) → 8.299950681

Tutorial

Convert a nominal rate to an effective rate

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste ►Eff( (item C) and type the nominal rate 8 and 12 compounding periods.
APPSENTERALPHAC8,12)
Press ENTER. A rate of 8% compounded monthly is really about 8.30% a year.
ENTER

Finding Days between Datesp. 261

dbd(

dbd(date1,date2)

Counts the days between two dates using the actual calendar (actual-day-count method). date1 and date2 may each be a number or a list of numbers. Dates must fall in the years 1950 through 2049.

Keys: APPSENTERALPHAD

dbd(1.0100,3.0100) → 60 (US format)
dbd(101.00,103.00) → 60 (European format)

Write dates in one of two formats. The position of the decimal point tells the calculator which one you mean:

Format	Pattern	Example for 1 March 2000
United States	MM.DDYY	`3.0100`
Europe	DDMM.YY	`103.00`

Tutorial

Days between 1 January 2000 and 1 March 2000

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Paste dbd( (item D) and enter the dates in US format: January 1, 2000 is 1.0100 and March 1, 2000 is 3.0100.
APPSENTERALPHAD1.0100,3.0100)
Press ENTER. There are 60 days (2000 is a leap year).
ENTER
The same dates in European format are 101.00 (1 January 2000) and 103.00 (1 March 2000). Enter them to get the same answer.
APPSENTERALPHAD101.00,103.00)ENTER

Defining the Payment Methodp. 262

Pmt_End and Pmt_Bgn (items E and F) tell Finance when in each period the payment happens. Running either one updates the PMT:END BEGIN line of the TVM Solver, and the TVM Solver line, in turn, switches the same setting.

Pmt_End

Pmt_End

Selects an ordinary annuity: payments occur at the end of each payment period. Most loans work this way. It is the default. In the TVM Solver, choose END on the PMT:END BEGIN line to get the same effect.

Keys: APPSENTERALPHAE

Pmt_Bgn

Pmt_Bgn

Selects an annuity due: payments occur at the beginning of each payment period. Most leases work this way. In the TVM Solver, choose BEGIN on the PMT:END BEGIN line to get the same effect.

Keys: APPSENTERALPHAF

Tutorial

Switch to payments at the beginning of the period

Compare the car-loan payment for end-of-month and beginning-of-month payments.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

First the default (END): type tvm_Pmt(48,5,9000,0,12,12) and press ENTER. The payment is about -207.26.
APPSENTER2(48,5,9000,0,12,12)ENTER
Choose Pmt_Bgn from FINANCE CALC item F (ALPHAF) and press ENTER.
APPSENTERALPHAFENTER
Run the same calculation again. Paying a month earlier makes each payment smaller: about -206.40.
APPSENTER2(48,5,9000,0,12,12)ENTER
Switch back with Pmt_End (item E, ALPHAE in the menu).
APPSENTERALPHAEENTER

Using the TVM Variablesp. 262

The TVM variables can be used inside TVM functions and calculations, and you can store values in them from the home screen.

FINANCE VARS Menup. 262

Open the menu with APPS ENTER, then press ▶︎ to move from the CALC tab to the VARS tab.

Tutorial

Store values in TVM variables

Set P/Y, then give C/Y a different value of its own.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Type 12, press STO►, then choose P/Y from the VARS tab: APPS ENTER ▶︎ 6. Press ENTER.
12STO►APPSENTER▶︎6ENTER
C/Y followed P/Y automatically. Now store 4 into C/Y (item 7) to compound quarterly while still paying monthly.
4STO►APPSENTER▶︎7ENTER
Store 360 into the TVM variable N (VARS item 1).
360STO►APPSENTER▶︎1ENTER

N, I%, PV, PMT, FVp. 263

These five variables are the building blocks of a financial transaction. I% is always an annual rate; the calculator converts it to a per-period rate using P/Y and C/Y.

Variable	Meaning	Sign
N	Total number of payment periods	Positive
I%	Annual interest rate, in percent	Positive
PV	Present value: the starting amount (loan amount, initial deposit)	Inflow positive, outflow negative
PMT	Payment made each period	Inflow positive, outflow negative
FV	Future value: the amount left at the end (remaining balance, final savings)	Inflow positive, outflow negative

P/Y and C/Yp. 263

P/Y is how many payments are made per year. C/Y is how many times per year interest compounds.

Note Storing a value to P/Y automatically sets C/Y to the same number. If you want a different C/Y, store it after storing P/Y.

The EasyData™ Appp. 263

Note The Vernier EasyData™ app needs real data-collection hardware (CBR 2™, CBL 2™, Vernier LabPro™, Vernier USB sensors, Go!Motion or a Motion Detector). The emulator has no ports and no EasyData app, so none of this section can be run here. It is described for completeness.

EasyData lets you view and analyze real-world measurements on the TI-84 Plus. It comes preinstalled on the calculator. It launches automatically when you plug in a USB sensor such as a CBR 2 or a Vernier USB temperature sensor. Auto-ID sensors are supported only through the CBL 2 and LabPro.

Starting and Quitting the EasyData Appp. 264

Connect the data-collection device firmly to the calculator.
If EasyData did not start by itself, press APPS, use ▲︎ or ▼︎ to highlight EasyData, and press ENTER. An information screen shows for about three seconds, then the main screen.
To quit, choose Quit with the first soft key (GRAPH). A "Ready to quit?" screen confirms that the data have been moved to lists L1 through L4. Choose OK (again GRAPH) to leave.

EasyData™ Settingsp. 264

The main screen shows the most common settings before collection begins. To change them:

From the EasyData main screen, choose Setup and then 2:Time Graph. The current settings appear.
Press Next (the ZOOM soft key) to move to the setting you want. CLEAR clears a setting.
To change a value, type 1 or 2 digits, then choose Next. Keep choosing Next to cycle through the options.
When everything is right, choose OK (GRAPH) to return to the main menu, then Start (ZOOM) to begin collecting.

Note With a motion detector, the settings for 3:Distance Match and 4:Ball Bounce in the Setup menu are preset and cannot be changed.

The default settings suit most sampling jobs. If you are unsure, start with them and adjust. To restore the defaults while a device is connected, choose File and then 1:New.

Starting and Stopping Data Collectionp. 265

Start: choose Start (ZOOM). Sampling stops by itself when the number of samples set in the Time Graph settings is reached, and a graph of the data appears.
Stop early: press and hold the Stop soft key (ZOOM) during sampling. A graph of what was collected is displayed.
Saving: the data are transferred automatically to lists L1 to L4 when collection finishes. On exit, a prompt reminds you which lists hold time, distance, velocity and acceleration.

The guidebook only covers basic operation of EasyData 2. For more detail see the Vernier website (www.vernier.com).

1:N	Total number of payment periods
2:I%	Annual interest rate
3:PV	Present value
4:PMT	Payment amount
5:FV	Future value
6:P/Y	Number of payment periods per year
7:C/Y	Number of compounding periods per year

Chapter 14: Applications

The Applications Menup. 251

Open the APPLICATIONS menu

Steps for Running the Finance Applicationp. 251

Getting Started: Financing a Carp. 252

Find the monthly payment on a car loan

Getting Started: Computing Compound Interestp. 253

Find the interest rate for a compound-interest goal

Using the TVM Solverp. 253

Solve for a future value with the TVM Solver

Using the Financial Functionsp. 254

Entering Cash Inflows and Cash Outflowsp. 254

FINANCE CALC Menup. 254

TVM Solver (menu item)p. 255

Calculating Time Value of Money (TVM)p. 255

tvm_Pmtp. 256

Compute a payment on the home screen, then change the rate

tvm_I%p. 256

Compute an interest rate with tvm_I%

tvm_PVp. 256

How much car can a 250 payment buy?

tvm_Np. 256

How many 250 payments to repay 9,000?

tvm_FVp. 257

Future value of a deposit

Calculating Cash Flowsp. 257

npv(p. 258

Net present value of an uneven cash flow

irr(p. 258

Internal rate of return of an investment

Calculating Amortizationp. 258

bal(p. 258

Loan balance after one year

ΣPrn(p. 259

Principal repaid in the first year

ΣInt(p. 259

Interest paid in the first year

Amortization Example: Calculating an Outstanding Loan Balancep. 259

Mortgage: set modes and solve for the loan amount

Mortgage: graph and tabulate the outstanding balance

Mortgage: graph and table side by side (G-T mode)

Calculating Interest Conversionp. 261

►Nom(p. 261

Convert an effective rate to a nominal rate

►Eff(p. 261

Convert a nominal rate to an effective rate

Finding Days between Datesp. 261

Days between 1 January 2000 and 1 March 2000

Defining the Payment Methodp. 262

Switch to payments at the beginning of the period

Using the TVM Variablesp. 262

FINANCE VARS Menup. 262

Store values in TVM variables

N, I%, PV, PMT, FVp. 263

P/Y and C/Yp. 263

The EasyData™ Appp. 263

Starting and Quitting the EasyData Appp. 264

EasyData™ Settingsp. 264

Starting and Stopping Data Collectionp. 265