# TI-86 Financial Functions

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4 Assemly Language Programming: Financial Functions 4 The TVM (Time-Value-of-Money) Variales FIN VARS (Finance Variales) Menu ( ç I PV PMT FV 4 PY CY Prompts that correspond to some TVM variales are shown in parentheses. N Numer of payment periods FV Future value of loan or lease I Interest rate (I%=) PY Payments per year (P/Y=) PV Present value of loan or lease CY Compounding periods per year(c/y=) PMT Payment amount When you enter a value at prompts in the payment format editor (page 4) or the TVM Solver (page 5), the corresponding variale values are updated. When you solve for a TVM variale using the TVM Solver, the corresponding variale value is updated. When you enter numers as arguments for a TVM function, the corresponding variale values are not updated. When you solve for a TVM variale using a TVM function, the corresponding variale value is not updated. Setting the Payment Format Payment Format Editor ) The payment format settings define the numer of payments per year (P/Y), the numer of compounding periods per year (C/Y), and whether the payments are received at the end or eginning of each period (PMT:END BEGIN). You also can change a setting y storing a value to PY or CY or y executing pend or pbegin (page 11). The payment format editor to the right shows the defaults. To change payments per year or compounding periods per year, enter a new value. To change the payment due setting, move the cursor onto END or BEGIN, and then press. Entering Cash Inflows and Cash Outflows When using the financial functions, you must enter cash inflows (cash received) as positive numers and cash outflows (cash paid) as negative numers. The financial functions follow this convention when computing and displaying answers.

5 Assemly Language Programming: Financial Functions 5 Using the TVM (Time-Value-of-Money) Solver FIN TVM Solver Menu & TVM FUNC VARS FORMT SOLVE When the TVM Solver is displayed, SOLVE replaces Uninst on the FIN menu. The TVM Solver displays prompts for the five time-value-of-money (TVM) variales. To solve for an unknown variale, enter the four known variale values, move the cursor to the unknown variale prompt, and then select SOLVE (*) from the FIN TVM Solver menu. Values displayed on the TVM Solver are stored to corresponding TVM variales. Solving for an Unknown TVM Variale (Payment Amount) You want to uy a \$100,000 house with a 30-year mortgage. If the annual percentage rate (APR) is 18%, what are the monthly payments? Enter cash inflows as positive numers and cash outflows as negative numers. Set the fixed-decimal mode to 2 decimal places to display all numers as dollars and cents. Select FIN from the MATH menu to display the FIN menu. Select FORMT from the FIN menu to display the payment format editor. Set 12 payments per year, 12 compounding periods per year, and payments received at the end of each payment period. Display the TVM Solver and enter the known values for four TVM variales. The N value of 360 was derived from 30 (years) M 12 (months). Move the cursor to the PMT TVM variale. - m # " " " ) 12 # 12 # & 360 # 18 # # # 0 \$ You cannot leave a variale lank. If you do not have a value, set it to zero. Select SOLVE to compute the answer. A small square is displayed next to the solution variale. The answer is stored to the corresponding TVM variale. *

6 Assemly Language Programming: Financial Functions 6 Financing a Car You have found a car you would like to uy. The car costs \$9,000. You can afford payments of \$250 per month for four years. What annual percentage rate (APR) will make it possile for you to afford the car? When you change P/Y, C/Y changes automatically. As you enter a value at any TVM Solver prompt, the corresponding TVM variale value is updated. Set the fixed-decimal mode to 2 decimal places to display all numers as dollars and cents. Display the payment format editor. Set payments per year and compounding periods per year to 12. Set payment due at the end of each period. Display the TVM Solver. Enter 48 monthly payments, present value of \$9,000, payment amount of L\$250 (negation indicates cash outflow), and future value of \$0. The N value (48) was derived from 4 (years) M 12 (months). Move the cursor to æ= (interest rate) and then select SOLVE from the TVM Solver menu. A small square is displayed next to the solution. The solution value is stored to the TVM variale I. - m # " " " ) 12 # # & 48 # # 9000 # a 250 # 0 \$ \$ \$ * Because there are no payments when you solve compound interest prolems, you must set PMT to 0 and set P/Y to 1. The decimal mode is fixed at 2 from the previous example. Computing Compound Interest At what annual interest rate, compounded monthly, will \$1,250 accumulate to \$2,000 in 7 years? Display the payment format editor. Set payments per year to 1 and compounding periods per year to 12. Set payment due at the end of each period. Display the TVM Solver. Enter 7 annual payments, present value of L\$1,250 (negation indicates cash outflow), payment amount of \$0, and future value of \$2,000. ) 1 # 12 # & 7 # # a 1250 # 0 # 2000 Move the cursor to æ= (interest rate) and then select SOLVE from the TVM Solver menu. A small square is displayed next to the solution. The solution value is stored to the TVM variale I. \$ \$ \$ *

7 Assemly Language Programming: Financial Functions 7 Using the Financial Functions Entering Cash Inflows and Cash Outflows When using the financial functions, you must enter cash inflows (cash received) as positive numers and cash outflows (cash paid) as negative numers. The financial functions follow this convention when computing and displaying answers. FIN FUNC (Financial Functions) Menu tvmn tvmi tvmpv tvmp tvmfv 4 npv irr al Gprn Gint 4 nom eff dd pbegin pend Calculating Time-Value-of-Money The first five items on the FIN FUNC menu are the time-value-of-money (TVM) functions. You can use them to analyze financial instruments, such as annuities, loans, mortgages, leases, and savings, on the home screen or in a program. All arguments and punctuation inside the [ ] rackets are optional. tvmn [(æ,pv,pmt,fv,p/y,c/y)] tvmi [(N,PV,PMT,FV,P/Y,C/Y)] Computes the numer of payment periods Computes the annual interest rate To store a value to a TVM variale, use the TVM Solver or use X and any TVM variale on the FIN VARS menu. tvmpv [(N,æ,PMT,FV,P/Y,C/Y)] tvmp [(N,æ,PV,FV,P/Y,C/Y)] tvmfv [(N,æ,PV,PMT,P/Y,C/Y)] Computes the present value Computes the amount of each payment Computes the future value Each TVM function takes zero to six arguments. Each argument must e a real numer or a TVM variale. The values that you specify as arguments for these functions are not stored to the TVM variales. If you enter less than six arguments, you must enter arguments in the order of the syntax, up to the last argument you want to enter. The program sustitutes a previously stored TVM variale value for each susequent unspecified argument. If you enter any arguments with a TVM function, you must place the argument or arguments in parentheses. The following examples show some ways to use the TVM functions.

8 Assemly Language Programming: Financial Functions 8 Assume these values are stored to the TVM variales in the payment format editor and TVM Solver. When you execute a TVM function on the home screen with no specified arguments, the TVM function (tvmpmt in the example) uses stored TVM variale values. You can enter arguments directly on the home screen. Rememer, neither the answer nor the arguments are stored to the TVM variales. To change an argument without changing the value stored to a TVM variale, enter arguments up to the argument you want to change. In the example, the interest rate is changed to 9.5. To store an answer to the appropriate TVM variale, use X and the FIN VARS menu. If you prefer, you can store values to the TVM variales on the home screen. When you execute a TVM function (tvmpv in the example), it uses the newly stored TVM variale values. Calculating Cash Flows The next FIN FUNC menu items are cash flow functions. Use them to analyze the value of money over equal time periods. You can enter unequal cash flows. You can enter cash inflows or outflows. npv(interestrate,cashflow0, cashflowlist[,cashflowfrequency]) irr(cashflow0,cashflowlist [,cashflowfrequency]) Returns the sum of the present values for the cash inflows and outflows Returns the interest rate at which the net present value of the cash flows is equal to 0 interestrate is the rate y which to discount the cash flows (the cost of money) over one period. cashflow0 is the initial cash flow at time 0; it must e a real numer. cashflowlist is a list of cash flow amounts after the initial cash flow cashflow0. cashflowfrequency is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of cashflowlist. The default is 1; if you enter values, they must e positive integers <10,000.

9 Assemly Language Programming: Financial Functions 9 The uneven cash flow elow is expressed in lists. cashflowfrequency indicates that the first element in cashflowlist (2000) occurs twice (2), the second element (L3000) occurs once (1), and the third element (4000) occurs twice (2) CF 0 CF 1 CF 2 CF 3 CF 4 CF 5 L3000 cashflow0 = 2000 cashflowlist = {2000,L3000,4000} cashflowfrequency = {2,1,2} I% = CF 0 CF 1 CF 2 CF 3 CF 4 CF 5 CF 6 L2000 L2000 L2500 cashflow0 = L2000 cashflowlist = {L2000,1000, L2500,0,5000,3000} cashflowfrequency = N/A roundvalue specifies the internal precision used to calculate the alance. effectiverate, nominalrate, and compoundingperiods must e real numers; compoundingperiods must e > 0. al(, GPrn(, and GInt( use stored values for æ, PV, and PMT. You must store values to these variales efore computing the principal. Calculating Amortization Items eight, nine, and ten are the amortization functions. Use them to calculate alance, sum of principal, and sum of interest for an amortization schedule. al(npayment[,roundvalue]) GPrn(paymentA,paymentB [,roundvalue]) GInt(paymentA,paymentB [,roundvalue]) Computes the alance for an amortization schedule; npayment (the numer of the payment at which to calculate a alance) must e a positive integer <10,000 Computes the sum of the principal during a specified period for an amortization schedule; paymenta (the starting payment) and paymentb (the ending payment in the range) must e positive integers <10,000 Computes the sum of the interest during a specified period for an amortization schedule; paymenta (the starting payment) and paymentb (the ending payment in the range) must e positive integers <10,000

10 Assemly Language Programming: Financial Functions 10 Amortization Example: Calculating an Outstanding Loan Balance You want to uy a home with a 30-year mortgage at 8 percent annual percentage rate (APR). Monthly payments are \$800. Calculate the outstanding loan alance after each payment and display the results in a graph and in the tale. Display the mode screen and set the fixed-decimal setting to 2, as in dollars and cents. Also, set Param graphing mode. - m # " " " # # # " " Display the payment format editor, and then set payments and compounding periods per year to 12, to e received at the end of each period. Display the TVM Solver, and then enter the known TVM variale values: N=360 PMT=L800 I=8 FV=0 Move the cursor to the PV= prompt and solve for the present value of the loan. A small square specifies the solution. ) 12 # # & 360 # 8 # # a 800 # 0 \$ \$ * A stat plot is turned on if it is highlighted with a ox. Display the parametric equation editor. Turn off all stat plots. Define xt1 as t and yt1 as al(t). Display the window variale editor, and then enter these window variale values as shown. 6 & (if a plot is on, press \$, " to highlight it, and ; then #) & # - Œ / ' ' / ( - & E 6 ' 0 # 360 # 12 # 0 # 360 # 50 # 0 # # Draw the graph and activate the trace cursor. Explore the graph of the outstanding alance over time. * )! " Enter a value for t to view the alance at a specific time. 24

11 Assemly Language Programming: Financial Functions 11 Display the tale setup editor, and then enter these values: Indpnt: Auto Display the tale of outstanding alances, where xt1 represents time and yt1 represents alance at that point in time. 7 ' 0 # 12 # & Calculating Interest Conversion Use the interest conversion functions nom and eff to convert interest rates from an annual effective rate to a nominal rate (nom), or from a nominal rate to an annual effective rate (eff). nom(effectiverate,compoundingperiods) eff(nominalrate,compoundingperiods) Computes the nominal interest rate Computes the effective interest rate Finding Days Between Dates Use the date function dd to calculate the numer of days etween two dates using the actual-day-count method. datea and dateb can e numers or lists of numers within the range of the dates on the standard calendar. Dates must fall etween the years 1950 and dd(datea,dateb) Calculates the numer of days etween dates; enter datea and dateb in either of two formats: MM.DDYY (for U.S.) or DDMM.YY (for Europe) Defining the Payment Method pend and pbegin specify a transaction as an ordinary annuity or an annuity due. Executing either instruction sets the payment method for susequent financial calculations. The current setting is displayed in the payment format editor (page 4). On the payment format editor s PMT:END BEGIN line, select END to set ordinary annuity or select BEGIN to set annuity due. pbegin pend Specifies an annuity due, where payments occur at the eginning of each payment period (Most leases are in this category.) 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.)

12 Assemly Language Programming: Financial Functions 12 Menu Map for Financial Functions MATH Menu (where FIN is automatically placed) - Œ NUM PROB ANGLE HYP MISC 4 INTER FIN (MATH) FIN (Financial) Menu FIN TVM (Time-Value-of-Money) Solver Menu & TVM FUNC VARS FORMT SOLVE FIN FUNC (Financial Functions) Menu ' tvmn tvmi tvmpv tvmp tvmfv 4 npv irr al Gprn Gint 4 nom eff dd pbegin pend FIN VARS (Financial Variales) Menu ( ç I PV PMT FV 4 PY CY FIN FORMT (Financial Format) Menu ) TVM FUNC VARS FORMT

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