Chapter Financial Calculation (TVM) 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 2-10 2-11 Before Performing Financial Calculations Simple Interest Compound Interest Cash Flow (Investment Appraisal) Amortization Interest Rate Conversion Cost, Selling Price, Margin Day/Date Calculations Depreciation Bonds TVM Graph 20010101 2
-1-1 Before Performing Financial Calculations 2-1 Before Performing Financial Calculations k TVM Mode On the Main Menu, select the TVM icon. * The above shows the ALGEBRA FX 2.0 PLUS screen. Entering the TVM Mode displays the Financial screen like the one shown below. Financial 1 screen Financial 2 screen • 1(SMPL) .... Simple interest • 2(CMPD) ... Compound interest • 3(CASH) .... Cash flow (investment appraisal) • 4(AMT) ...... Amortization • 5(CNVT) .... Interest rate conversion • 6(g)1(COST) ...
2-1-2 Before Performing Financial Calculations k SET UP Items u Payment • {BGN}/{END} ........ Specifies {beginning of the period} / {end of the period} payment u Date Mode • {365}/{360} ......... Specifies calculation according to a {365-day} / {360-day} year u Periods/YR. (Bond) • {Annual}/{SEMI} ... Indicates an {annual} / {semi-annual} period Note the following points regarding SET UP screen settings whenever using the Financial Mode.
2-2-1 Simple Interest 2-2 Simple Interest This calculator uses the following formulas to calculate simple interest. u Formula 365-day Mode 360-day Mode SI' = n × PV × i 365 SI' = n × PV × i 360 I% 100 I% i= 100 i= SI n : interest : number of interest periods PV : principal I% : annual interest SFV : principal plus interest SI = –SI' SFV = –(PV + SI') Press 1(SMPL) from the Financial 1 screen to display the following input screen for simple interest. 1(SMPL) n ..................................
2-2-2 Simple Interest • An error (Ma ERROR) occurs if parameters are not configured correctly. Use the following function keys to maneuver between calculation result screens. • 1(REPT) ... Parameter input screen • 6(GRPH) ... Draws graph After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph. Each press of e while trace is turned on cycles the displayed value in the sequence: present value (PV) → simple interest (SI) → simple future value (SFV).
2-3-1 Compound Interest 2-3 Compound Interest This calculator uses the following standard formulas to calculate compound interest. u Formula I PV+PMT × (1+ i × S)[(1+ i)n–1] n i(1+ i) + FV 1 n (1+ i) =0 i= I% 100 Here: PV= –(PMT × α + FV × β ) PMT × α + PV FV= – β PV + FV × β PMT= – log n= α= β= PV : present value FV : future value PMT : payment n : number of compound periods I% : annual interest rate i is calculated using Newton’s Method.
2-3-2 Compound Interest FV = – (PMT × n + PV ) PMT = – PV + FV n PV + FV n=– PMT • A deposit is indicated by a plus sign (+), while a withdrawal is indicated by a minus sign (–). u Converting between the nominal interest rate and effective interest rate The nominal interest rate (I% value input by user) is converted to an effective interest rate ( I%') when the number of installments per year (P/Y ) is different from the number of compound interest calculation periods ( C/Y ).
2-3-3 Compound Interest Press 2(CMPD) from the Financial 1 screen to display the following input screen for compound interest. 2(CMPD) n .................................. number of compound periods I% ............................... annual interest rate PV ............................... present value (loan amount in case of loan; principal in case of savings) PMT ............................ payment for each installment (payment in case of loan; deposit in case of savings) FV .........................
2-3-4 Compound Interest After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation. • 1(n) ............ Number of compound periods • 2(I%) .......... Annual interest rate • 3(PV) ......... Present value (Loan: loan amount; Savings: balance) • 4(PMT) ....... Payment (Loan: installment; Savings: deposit) • 5(FV) .......... Future value (Loan: unpaid balance; Savings: principal plus interest) • 6(AMT) .......
2-4-1 Cash Flow (Investment Appraisal) 2-4 Cash Flow (Investment Appraisal) This calculator uses the discounted cash flow (DCF) method to perform investment appraisal by totalling cash flow for a fixed period. This calculator can perform the following four types of investment appraisal. • Net present value (NPV ) • Net future value (NFV ) • Internal rate of return (IRR ) • Pay back period (PBP ) A cash flow diagram like the one shown below helps to visualize the movement of funds.
2-4-2 Cash Flow (Investment Appraisal) u PBP PBP is the value of n when NPV > 0 (when investment can be recovered). • Press 3(CASH) from the Financial 1 screen to display the following input screen for Cash Flow. 3(CASH) I% ............................... interest rate (%) Csh .............................. list for cash flow If you have not yet input data into a list, press 5('LIST) and input data into a list.
2-4-3 Cash Flow (Investment Appraisal) After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph. Press i to turn off trace. Press i again to return to the parameter input screen.
2-5-1 Amortization 2-5 Amortization This calculator can be used to calculate the principal and interest portion of a monthly installment, the remaining principal, and amount of principal and interest repaid up to any point.
2-5-2 Amortization u Converting between the nominal interest rate and effective interest rate The nominal interest rate (I% value input by user) is converted to an effective interest rate ( I%') for installment loans where the number of installments per year is different from the number of compound interest calculation periods.
2-5-3 Amortization After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation. • 1(BAL) ......... Balance of principal after installment PM2 • 2(INT) .......... Interest portion of installment PM1 • 3(PRN) ......... Principal portion of installment PM1 • 4(Σ INT) ....... Total interest paid from installment PM1 to installment PM2 • 5(Σ PRN) ...... Total principal paid from installment PM1 to installment PM2 • 6(CMPD) ......
2-6-1 Interest Rate Conversion 2-6 Interest Rate Conversion The procedures in this section describe how to convert between the annual percentage rate and effective interest rate. u Formula n EFF = 1 + APR/100 –1 × 100 n APR = 1 + EFF 100 1 n APR : annual percentage rate (%) EFF : effective interest rate (%) n : number of compoundings –1 × n ×100 Press 5(CNVT) in the Financial 1 screen to display the following input screen for interest rate conversion. 5(CNVT) n ...................................
2-7-1 Cost, Selling Price, Margin 2-7 Cost, Selling Price, Margin Cost, selling price, or margin can be calculated by inputting the other two values. u Formula CST = SEL 1– MRG 100 CST MRG 1– 100 CST × 100 MRG(%) = 1– SEL SEL = CST : cost SEL : selling price MRG : margin Press 1(COST) from the Financial 2 screen to display the following input screen. 6(g)1(COST) Cst ............................... cost Sel ............................... selling price Mrg ..............................
2-8-1 Day/Date Calculations 2-8 Day/Date Calculations You can calculate the number of days between two dates, or you can determine what date comes a specific number of days before or after another date. Press 2(DAYS) from the Financial 2 screen to display the following input screen for day/ date calculation. 6(g)2(DAYS) d1 ................................ date 1 d2 ................................ date 2 D ................................. number of days To input a date, first highlight d1 or d2.
2-8-2 Day/Date Calculations Input the month, day, and year, pressing w after each. After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation. • 1(PRD) ........ Number of days from d1 to d2 (d2 – d1) • 2(d1+D) ....... d1 plus a number of days (d1 + D) • 3(d1 – D) ..... d1 minus a number of days (d1 – D) • An error (Ma ERROR) occurs if parameters are not configured correctly.
2-9-1 Depreciation 2-9 Depreciation Any of the following four methods can be used to calculated depreciation. u Straight-Line Method The straight-line method calculates depreciation for a given period.
2-9-2 Depreciation u Sum-of-the-Year's Digits Method The sum-of-the-year's-digits method calculates depreciation for a given period.
2-9-3 Depreciation Press 3(DEPR) from the Financial 2 screen to display the following input screen for depreciation. 6(g)3(DEPR) n .................................. I% ............................... PV ............................... FV ............................... j ................................... Y–1 ..............................
2-9-4 Depreciation • An error (Ma ERROR) occurs if parameters are not configured correctly. Use the following function keys to maneuver between calculation result screens. • 1(REPT) ...... Parameter input screen • 6(TABL) ....... Calculation result table The following function keys are on the calculation result table screen. • 1(REPT) ...... Parameter input screen • 6(GRPH) ..... Draws graph After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph.
2-10-1 Bonds 2-10 Bonds The bond calculation function calculates the price and yield of a bond.
2-10-2 Bonds Press 4(BOND) from the Financial 2 screen to display the following input screen for band calculation. 6(g)4(BOND) d1 ................................ purchase date d2 ................................ redemption date RDV ............................ redemption price or call price per $100 of face value CPN ............................ annual coupon rate (%) PRC ............................ price per $100 of face value YLD .............................
2-10-3 Bonds • An error (Ma ERROR) occurs if parameters are not configured correctly. Use the following function keys to maneuver between calculation result screens. • 1(REPT) ....... Parameter input screen • 5(MEMO) ..... Screen of various bond calculation values* • 6(GRPH) ...... Draws Graph Pressing 5(MEMO) displays various bond calculation values, like those shown here. *The interest payment date is calculated from d2 when 365 is specified for the Date Mode item in the SET UP screen.
2-11-1 TVM Graph 2-11 TVM Graph The TVM Graph lets you assign two of the five parameters ( n, I%, PV, PMT, FV) to the x-axis and y-axis of a graph, and plot changes in y as the value of x changes. Press 5(TVMG) from the Financial 2 screen to display the following input screen for TVM Graph. 6(g)5(TVMG) After configuring the parameters, press the function keys noted below to assign parameters to the x-axis and y-axis. • 1(X) ... Assigns highlighted parameter to the x-axis • 2(Y) ...
2-11-2 TVM Graph Pressing 6(Y-CAL) after drawing a graph displays the screen shown below. Inputting an x-axis value on this screen and pressing w displays the corresponding y-axis value. Press i again to return to the parameter input screen. • Calculation may take some time to perform when you specify I% as the y-axis parameter.
