Chapter. Financial Calculations

Transcription

1 Chapter Finanial Calulations Before Performing Finanial Calulations 19-2 Simple Interest Calulations 19-3 Compound Interest Calulations 19-4 Investment Appraisal 19-5 Amortization of a Loan 19-6 Conversion between Perentage Interest Rate and Effetive Interest Rate 19-7 Cost, Selling Prie, Margin Calulations 19-8 Day/Date Calulations

2 19-1 Before Performing Finanial Calulations The Finanial Mode provides you with the tools to perform the following types of finanial alulations. Simple interest Compound interest Investment appraisal (Cash Flow) Amortization Interest rate onversion (annual perentage rate and effetive interest rate) Cost, selling prie, margin Day/date alulations ugraphing in the Finanial Mode After performing a finanial alulation, you an use 6 (GRPH) to graph the results as shown below. Pressing!1 (TRCE) while a graph is on the display ativates Trae, whih an be used to look up other finanial values. In the ase of simple interest, for example, pressing e displays PV, SI, and SFV. Pressing d displays the same values in reverse sequene. Zoom, Sroll, Sketh, and G-Solve annot be used in the Finanial Mode. In the Finanial Mode, horizontal lines are blue and vertial lines are red. These olors are fixed and annot be hanged. The present value is positive when it represents reeipt of money, and a negative value when it represents a payment. Note that alulation results produed in this mode should be regarded as referene values only. Whenever performing an atual finanial transation, be sure to hek any alulation results obtained using this alulator with against the figures alulated by your finanial institution. uset up sreen settings P.6 Note the following points regarding set up sreen settings whenever using the Finanial Mode. The following graph set up sreen settings are all turned off for graphing in the Finanial Mode: Axes, Grid, Dual Sreen. 320

3 Before Performing Finanial Calulations 19-1 P.6 Drawing a finanial graph while the Label item is turned on, displays the label CASH for the vertial axis (deposits, withdrawals), and TIME for the horizontal axis (frequeny). The number of display digits applied in the Finanial Mode is different from the number of digits used in other modes. The alulators automatially reverts to Norm 1 whenever you enter the Finanial Mode, whih anels a Si (number of signifiant digits) or Eng (engineering notation) setting made in another mode. k Entering the Finanial Mode On the Main Menu, selet the TVM ion to enter the Finanial Mode. When you do, the Finanial 1 sreen appears on the display. Finanial 1 sreen Finanial 2 sreen {SMPL}/{CMPD}/{CASH}/{AMT}/{CNVT}/{COST}/{DAYS}... {simple interest}/ {ompound interest}/{ash flow}/{amortization}/{onversion}/{ost, selling prie, margin}/{day/date} alulation 321

4 19-2 Simple Interest Calulations This alulator uses the following formulas to alulate simple interest. 365-day Mode 360-day Mode SI' = 365 n PV i SI' = 360 n PV i SI = SI' SFV = (PV + SI') I% i = 100 I% i = 100 SI : simple interest n : number of simple interest periods PV : present value I% : periodi interest rate SFV : simple future value Press 1 (SMPL) from the Finanial 1 sreen to display the following input sreen for simple interest alulation. n... number of simple interest periods (days) I%... annual interest rate PV... present value {SI}/{SFV}... alulates {simple interest}/{simple future value} What would the interest amount and prinipal plus interest be for a loan of $1,500 borrowed for 90 days at an annual rate of 7.25%? Use the 360-day mode and two deimal plaes. P.6 In the set up sreen, speify 360 for Date Mode and Fix2 for Display and then press J. jaw h.fw -bfaaw 1(SI) 322

5 Simple Interest Calulations 19-2 Now you an perform the following key operation to return to the input sreen and then display the prinipal plus interest. 1(REPT) (Returns to the input sreen) 2(SFV) You an also press 6(GRPH) to draw a ash flow graph. 6(GRPH) The left side is PV, while the right side is SI and SFV. The upper part of the graph is positive (+), while the bottom part is negative ( ). V-Window values vary in aordane with simple interest onditions. Press J (or!6 (G T)) to return to the input sreen. Press J again to return to the Finanial 1 sreen. 323

6 19-3 Compound Interest Calulations This alulator uses the following standard formulas to alulate ompound interest. uformula I PV+PMT u Here: (1+ i u S)[(1+ i) n 1] + FV 1 i(1+ i) n (1+ i) n I = 0 i = 100 PV= (PMT u α + FV u β ) FV= PMTu α + PV β PV + FV u β PMT= α (1+ i S ) PMT FVi log{ (1+ i S ) PMT+PVi } n = log(1+ i) PV : present value FV : future value PMT : payment n : number of ompound periods I% : annual interest rate i is alulated using Newton s Method. S = 0 assumed for beginning of term S = 1 assumed for end of term α = β = (1+ i u S)[(1+ i) n 1] 1 (1+ i) n i(1+ i) n F(i) = Formula I PMT (1+ i S)[1 (1+ i) n ] F(i)'= + (1+ i S)[n(1+ i) n 1 ]+S [1 (1+ i) n i [ i ] + FV n(1+ i) n 1 uformula II (I% = 0) PV + PMT n + FV = 0 Here: PV = (PMT u n + FV ) FV = (PMT u n + PV ) 324

7 Compound Interest Calulations 19-3 PMT = PV + FV n n = PV + FV PMT A deposit is indiated by a plus sign (+), while a withdrawal is indiated by a minus sign ( ). uconverting between the nominal interest rate and effetive interest rate The nominal interest rate (I% value input by user) is onverted to an effetive interest rate (I%') when the number of installments per year (P/Y) is different from the number of ompound interest alulation periods (C/Y). This onversion is required for installment savings aounts, loan repayments, et. [C / Y ] P/Y : installment I% [P / Y ] I%' = {(1+ ) [C / Y ] } 100 periods per year C/Y : ompounding periods per year When alulating n, PV, PMT, FV The following alulation is performed after onversion from the nominal interest rate to the effetive interest rate, and the result is used for all subsequent alulations. i = I%' 100 When alulating I% After I% is obtained, the following alulation is performed to onvert to I%'. [P / Y ] P/Y : installment I% [C / Y ] I%' = { (1+ ) } [C / Y ] 100 periods per year C/Y : ompounding periods per year The value of I%' is returned as the result of the I% alulation. Press 2 (CMPD) in the Finanial 1 sreen to display the input sreen for ompound interest alulation. n... number of ompound periods I%... annual interest rate PV... present value (loan amount in ase of loan; balane in ase of savings) 325

8 19-3 Compound Interest Calulations PMT... payment for eah installment (payment in ase of loan; deposit in ase of savings) FV... future value (unpaid balane in ase of loan; prinipal plus interest in ase of savings) P/Y... installment periods per year C/Y... ompounding periods per year Inputting Values A period (n) is expressed as a positive value. Either the present value (PV) or future value (FV) is positive, while the other (PV or FV) is negative. Preision This alulator performs interest alulations using Newton s Method, whih produes approximate values whose preision an be affeted by various alulation onditions. Beause of this, interest alulation results produed by this alulator should be used keeping the above limitation in mind or the results should be verified. k Compound Interest s This setion shows how ompound interest alulations an be used in a variety of appliations. usavings (standard ompound interest) Input Condition: Future value is greater than present value. Formula Representation of Input Condition: PMT = 0 PV < FV Calulate the interest rate required to inrease a prinipal of $10,000 to $12,000 in three years, when ompounding is performed semiannually. d*bw(input n = 3 12.) -baaaaw(pv = 10,000) aw baaaw(fv = 12,000) bw w(semiannual ompounding) 2(I%) 326

9 Compound Interest Calulations 19-3 Now you an press 6 to draw a ash flow graph. 6(GRPH) The left side is PV, while the right side is FV. The upper part of the graph is positive (+), while the bottom part is negative ( ). uinstallment savings Input Condition: Future value is greater than the total of payments. Formula Representation of Input Condition: PMT and FV have different signs (positive, negative) when PV = 0. FV < n PMT when FV > 0 FV > n PMT when FV < 0 Calulate the interest rate required to have a $2,500 balane in an installment savings aount in two years when $100 is deposited eah month and interest is ompounded semiannually. *bw(input n = 2 12.) aw(pv = 0) -baaw(pmt = 100) faaw(fv = 2,500) bw(monthly installment) w(compounding every six months) 2(I%) uloans Input Condition: Total of payments is greater than loan amount. Formula Representation of Input Condition: PMT and PV have different signs (positive, negative) when FV = 0. PV > n PMT when PV > 0 PV < n PMT when PV < 0 327

10 19-3 Compound Interest Calulations Calulate the interest rate required to repay a $2,300 balane on a loan in two years paying bak $100 per month, when interest is ompounded monthly. *bw(input n = 2 12.) daaw(pv = 2,300) -baaw(pmt = 100) aw(fv = 0) bw(monthly installment) (Monthly ompounding) 2(I%) The value you input for P/Y (the number of installment periods per year) is also automatially input for C/Y (the number of ompounding periods per year). You an input another value for C/Y if you want. uloan when final installment is greater than other installments Input Condition: Total of equal amount payments is greater than the differene between the loan amount and final payment amount. Formula Representation of Input Condition: PV, PMT, FV do not equal zero. PV + FV > n PMT when FV > PV PV + FV < n PMT when FV < PV Calulate the interest rate required to repay a $2,500 balane on a loan in two years (24 installments) paying bak $100 per month and a final $200 installment, when interest is ompounded monthly. *bw(input n = 2 12.) faaw(pv = 2,500) -baaw(pmt = 100) -aaw(fv = 200) bw(monthly installment) (Monthly ompounding) 2(I%) 328

11 Compound Interest Calulations 19-3 k Savings ufuture value Calulate the future value after 7.6 years for a prinipal of $500 and an interest rate of 6%, ompounded annually. h.gw(n = 7.6 years) gw(i = 6%) -faaw(pv = 500) aw(pmt = 0) aw(fv = 0) bw bw(annual ompounding) 5(FV) uprinipal Calulate the prinipal required at 5.5%, ompounded monthly, to produe a total of $20,000 in a year. b*bw(input n = 1 12.) f.fw(i = 5.5%) aw(pmt = 0) aaaaw(fv = 20,000) bw bw(monthly ompounding) 3(PV ) ucompound interest rate Calulate the interest required, ompounded monthly, to produe a total of $10,000 in 10 years on an initial investment of $6,000. In the set up sreen, speify Begin for Payment and then press J. 329

12 19-3 Compound Interest Calulations ba*bw(input n = ) -gaaaw(pv = 6,000) aw(pmt = 0) baaaaw(fv = 10,000) bw bw(monthly ompounding) 2(I%) ucompound interest period Calulate the amount of time required to inrease an initial investment of $5,000 to a total of $10,000 at an annual rate of 4%, ompounded monthly. In the set up sreen, speify End for Payment and then press J. ew(i% = 4) -faaaw(pv = 5,000) aw(pmt = 0) baaaaw(fv = 10,000) bw bw(monthly ompounding) 1(n) uinstallment savings Calulate (to two deimal plaes) the prinipal plus interest for $250 monthly installments for five years at 6% annual interest, ompounded monthly. Calulate amounts for when installments are made at the beginning of eah month and at the end of eah month. P.6 In the set up sreen, speify End for Payment and Fix2 for Display, and then press J. 330

13 Compound Interest Calulations 19-3 f*bw(input n = 5 12.) gw(i = 6.0%) aw(pv = 0) -faw bw(monthly installments) (Monthly ompounding) 5(FV ) Speifying Begin for Payment in the set up sreen hanges to alulation of installments at the beginning of eah month. 5(FV ) uinstallment amount Calulate the amount required for eah installment to aumulate a total of $10,000 in 5 years at an annual interest rate of 6%, ompounded semiannually. P.6 In the set up sreen, speify End for Payment, Norm1 for Display, and then press J. f*bw(input n = 5 12.) gw(i = 6.0%) aw(pv = 0) baaaaw(fv = 10,000) bw(monthly installments) w(semiannual ompounding) 4(PMT) 331

14 19-3 Compound Interest Calulations unumber of installments Calulate the number of monthly $84 installments required to aumulate a total of $6,000 at an annual interest rate of 6%, ompounded annually. In the set up sreen, speify End for Payment and then press J. gw aw(pv = 0) -iew(pmt = 84) gaaaw(fv = 6,000) bw(monthly installments) bw(annual ompounding) 1(n) uinterest rate Calulate the annual interest rate required to aumulate a total of $10,000 in 10 years with $60 monthly installments. In the set up sreen, speify End for Payment and then press J. ba*bw(input n = ) aw(pv = 0) -gaw(pmt = 60) baaaaw(fv = 10,000) bw(monthly installments) bw(annual ompounding) 2(I%) uprinipal plus interest with initial deposit Calulate the prinipal plus interest after one year for an installment savings aount with an interest rate of 4.5%, ompounded monthly, opened with an initial deposit of $1,000, with $500 installments added eah month. In the set up sreen, speify End for Payment and then press J. 332

15 Compound Interest Calulations 19-3 b*bw(input n = 1 12.) e.fw -baaaw(pv = 1,000) -faaw(pmt = 500) bw(monthly installments) (Monthly ompounding) 5(FV) uborrowing power Calulate how muh an be borrowed on a 15-year loan at a 7.5% annual interest rate, ompounded monthly, if a payment of $450 per month an be made. In the set up sreen, speify End for Payment and then press J. bf*bw(input n = ) h.fw -efaw(pmt = 450) aw(fv = 0) bw(monthly installments) (Monthly ompounding) 3(PV) uloan installments Calulate the size of the monthly installment for a 25-year $300,000 home loan made at 6.2%, ompounded semiannually. In the set up sreen, speify End for Payment and then press J. f*bw(input n = ) g.w daaaaaw(pv = 300,000) aw(fv = 0) bw(monthly installments) w(semiannual ompounding) 4(PMT) 333

16 19-3 Compound Interest Calulations unumber of installments Calulate the number of years it will take to repay a $60,000 loan borrowed at 5.5%, ompounded monthly, with monthly installments of $840. In the set up sreen, speify End for Payment and then press J. f.fw gaaaaw(pv = 60,000) -ieaw(pmt = 840) aw(fv = 0) bw(monthly installments) (Monthly ompounding) 1(n) ueffetive interest rate Calulate (to two deimal plaes) the effetive interest rate ompounded monthly, on a 25-year $65,000 loan repaid with $460 monthly installments. P.6 In the set up sreen, speify End for Payment, Fix2 for Display, and then press J. f*bw(input n = ) gfaaaw(pv = 65,000) -egaw(pmt = 460) aw(fv = 0) bw(monthly installments) (Monthly ompounding) 2(I%) 334

17 19-4 Investment Appraisal This alulator uses the disounted ash flow (DCF) method to perform investment appraisal by totalling ash flow for a fixed period. This alulator an perform the following four types of investment appraisal. Net present value (NPV) Net future value (NFV) Internal rate of return (IRR) Pay bak period (PBP) A ash flow diagram like the one shown below helps to visualize the movement of funds. CF7 CF5 CF3 CF6 CF2 CF4 CF0 CF1 With this graph, the initial investment amount is represented by CF0. The ash flow one year later is shown by CF1, two years later by CF2, and so on. Investment appraisal an be used to learly determine whether an investment is realizing profits that were originally targeted. unpv CF1 CF2 CF3 CFn NPV = CF (1+ i) (1+ i) 2 (1+ i) 3 (1+ i) n I i = 100 n: natural number up to 254 unfv uirr NFV = NPV (1 + i ) N CF1 CF2 CF3 0 = CF (1+ i) (1+ i) 2 (1+ i) 3 CFn (1+ i) n In this formula, NPV = 0, and the value of IRR is equivalent to i 100. It should be noted, however, that minute frational values tend to aumulate during the subsequent alulations performed automatially by the alulator, so NPV never atually reahes exatly zero. IRR beomes more aurate the loser that NPV approahes to zero. 335

18 19-4 Investment Appraisal upbp Initial value of N when NPV > 0. Press 3 (CASH) from the initial sreen 1 to display the following input sreen for investment appraisal. I%... interest rate Csh... list for ash flow {NPV}/{IRR}/{PBP}/{NFV}... {net present value}/{internal rate of return}/ {pay bak period}/{net future value} {LIST}... {speifies a list for ash flow} An investment of $86,000 in mahinery projets the annual revenues shown in the table below (all revenues realized at the end of the fisal year). What is the net profit or loss of this investment if the useful servie life of the mahine is six years, the resale value after six years is $14,000, and the apital ost is 11%? Year Revenues 1 5, , , , , , ,000 On the Main Menu, selet the LIST ion to enter the LIST Mode and perform the following key operation. e(list 2) -igaaaw -faaaw eaaaw dbaaaw eaaaw daaaw baaa+beaaaw Return to the Main Menu by pressing m. Selet the TVM ion to enter the Finanial Mode, and then press 3 (CASH). 336

19 bbw(i% = 11) 6(List)2(List2) 1(NPV) Investment Appraisal 19-4 Now you an press 6(GRPH) to draw a ash flow graph. 6(GRPH) Pressing!1 (TRCE) ativates trae, whih an be used to look up the following values.!6(g T) 4(NFV) 1(REPT) 3(PBP) An investment of $10,000 in mahinery projets the annual revenues shown in the table below (all revenues realized at the end of the fisal year). What is the internal rate of return of this investment if the useful servie life of the mahinery is five years and the resale value after five years is $7,000? Year Revenues 1 2, , , , , ,

20 19-4 Investment Appraisal On the Main Menu, selet the LIST ion to enter the LIST Mode and perform the following key operation. ee(list 3) -baaaaw aaaw eaaw aaw aaaw biaa+daaaw Return to the Main Menu by pressing m. Selet the TVM ion to enter the Finanial Mode, and then press 3 (CASH). 6(List)3(List 3) 2(IRR) Now you an press 6 to draw a ash flow graph. 6(GRPH) 338

21 Investment Appraisal Amortization of a Loan This alulator an be used to alulate the prinipal and interest portion of a monthly installment, the remaining prinipal, and amount of prinipal and interest repaid up to any point. Amount of single payment e,,,,,,,,,,,,,,, a,,,,,,,,,,,,,,,,,,,, b,,,,,,,,,, 1 2 m n,,,,,,, d,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, (Number of payments) a: Interest portion of installment PM1 (INT) b: Prinipal portion of installment PM1 (PRN) : Balane of prinipal after installment PM2 (BAL) d: Total prinipal from installment PM1 to payment of installment PM2 (ΣPRN) e: Total interest from installment PM1 to payment of installment PM2 (ΣINT) * a + b = one repayment (PMT) a : INTPM1 = I BALPM1 1 i I (PMT sign) b : PRNPM1 = PMT + BALPM1 1 i : BALPM2 = BALPM2 1 + PRNPM2 PM2 d : Σ PRN = PRNPM1 + PRNPM PRNPM2 PM1 PM2 e : Σ INT = INTPM1 + INTPM INTPM2 PM1 BAL0 = PV (INT1 = 0 and PRN1 = PMT at beginning of installment term) uconverting between the nominal interest rate and effetive interest rate The nominal interest rate (I% value input by user) is onverted to an effetive interest rate (I%') for installment loans where the number of installments per year is different from the number of ompound interest alulation periods. [C / Y ] I% [P / Y ] I%' = {(1+ ) [C / Y ] }

22 19-5 Amortization of a Loan The following alulation is performed after onversion from the nominal interest rate to the effetive interest rate, and the result is used for all subsequent alulations. i = I%' 100 Press 4 (AMT) from the initial sreen 1 to display the following input sreen for amortization. PM1... first installment of installments 1 through n PM2... seond installment of installments 1 through n n... installments I%... interest rate PV... prinipal PMT... payment for eah installment FV... future value P/Y... installments per year C/Y... ompoundings per year {BAL}... {balane of prinipal after installment PM2} {INT}/{PRN}... {interest}/{prinipal} portion of installment PM1 {ΣINT}/{ΣPRN}... {total prinipal}/{total interest} from installment PM1 to payment of installment PM2 Calulate the monthly installment due on a $140, year home mortgage at an annual rate of 6.5%, ompounded semiannually. Also alulate PRN and INT for the seond year (24th installment), BAL for installment 49, and ΣINT, ΣPRN for installments 24 through 49. Display the TVM Menu and then press 2. In the set up sreen, speify End for Payment and then press J. 340

23 Amortization of a Loan 19-5 bf*bw (Input n = ) g.fw beaaaaw (PV = 140,000) aw (FV = 0) bw(monthly installments) w(semiannual ompounding) 4(PMT) Pressing 4(AMT) displays the amortization input sreen. Input 24 for PM1 and 49 for PM2. ewejw Calulate PRN. 3(PRN) 1(REPT) 2(INT) 1(REPT) 1(BAL) 341

24 19-5 Amortization of a Loan Calulate ΣINT from installment 24 to (REPT) 4 (ΣINT) Calulate ΣPRN. 1 (REPT) 5 (ΣPRN) Now you an press 6 to draw a ash flow graph. 6(GRPH) Trae an be ativated following the alulation. Pressing e displays INT and PRN when n = 1. Eah subsequent press of e displays INT and PRN for n = 2, n = 3, and so on. 342

25 19-6 Conversion between Perentage Interest Rate and Effetive Interest Rate Press 5 (CNVT) in the Finanial 1 sreen to display the following input sreen for interest rate onversion. n... number of ompoundings I%... interest rate {'EFF}/{'APR}... {annual perentage rate to effetive interest rate}/{effetive interest rate to annual perentage rate} onversion k Converting the Annual Perentage Rate (APR) to the Effetive Interest Rate (EFF) EFF = n APR/ n Calulate (to two deimal plaes) the effetive interest rate for an aount paying an interest rate of 12%, ompounded quarterly. P.6 In the set up sreen, speify Fix2 for Display and then press J. ew(n = 4) bw(i% = 12%) 1('EFF) The obtained value is assigned to I%. k Converting the Effetive Interest Rate (EFF) to the Annual Perentage Rate (APR) APR = 1 n EFF 1+ 1 n

26 19-6 Conversion between Perentage Interest Rate and Effetive Interest Rate Calulate the annual perentage rate for an aount paying an effetive interest rate of 12.55%, ompounded quarterly. P.6 In the set up sreen, speify Norm1 for Display and then press J. ew (n = 4) b.ffw(i% = 12.55%) 2 ('APR) The obtained value is assigned to I%. 344

27 19-7 Cost, Selling Prie, Margin Calulations Cost, selling prie, or margin an be alulated by inputting the other two values. MAR CST = SEL SEL = CST MAR CST MAR(%) = SEL Press 1 (COST) from the initial sreen 2 to display the following input sreen. Cst... ost Sel... selling prie Mrg... margin {COST}/{SEL}/{MRG}... alulates {ost}/{selling prie}/{margin} k Cost Calulate the ost for a selling prie of $2,000 and a margin of 15%. aaaw(sel = 2,000) bfw(mrg = 15) 1(COST) 345

28 19-7 Cost, Selling Prie, Margin Calulations k Selling Prie Calulate the selling prie for a ost of $1,200 and a margin of 45%. baaw(cst = 1,200) efw(mrg = 45) 2(SEL) k Margin Calulate the margin for a selling prie of $2,500 and a ost of $1,250. bfaw(cst = 1,250) faaw(sel = 2,500) 3(MRG) 346

29 19-8 Day/Date Calulations You an alulate the number of days between two dates, or you an determine what date omes a speifi number of days before or after another date. Press 2 (DAYS) from the initial sreen 2 to display the following input sreen for day/date alulation. d1... date 1 d2... date 2 D... number of days {PRD}... {alulates number of dates between two dates (d2 d1)} {d1+d}/{d1 D}... Calulates {future date/previous date} The set up sreen an be used to speify either a 365-day or 360-day year for finanial alulations. Day/date alulations are also performed in aordane with the urrent setting for number of days in the year, but the following alulations annot be performed when the 360-day year is set. Attempting to do so auses an error. (Date) + (Number of Days) (Date) (Number of Days) The allowable alulation range is January 1, 1901 to Deember 31, The format for inputting a date is: <month>. <day> <year> Two digits must always be input for the day, so a leading zero must be input for days 1 through 9. January 2, 1990 b.abjja Deember 31, 2099 b.dbajj Calulate the number of days from August 8, 1967 to July 15, 1970, using a 365-day year. In the set up sreen, speify 365 for Date Mode and then press J. 347

30 19-8 Day/Date Calulations i.aibjghw (d1 = August 8, 1967) h.bfbjhaw (d2 = July 15,1970) 1(PRD) Prd... number of days Determine the date that is 1,000 days after June 1, Note that the attempting to perform the following alulation while the 360-day year is in effet auses an error. g.abbjjhw (d1 = June 1, 1997) (d2 = Any date) baaaw 2(d1+D) d+d... future date alulation February 26, 2000 To determine the date that is 1,000 days before January 1, 2001, usig a 365-day year. Note that the attempting to perform the following alulation while the 360-day year is in effet auses an error. b.abaabw (d1 = January 1, 2001) (d2 = Any date) baaaw 3(d1 D) d D... previous date alulation April 7,