16.4: Formula Sheet
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Part 1: Mathematics Fundamentals
- (2.1) Percentage Conversion %= dec×100
- (2.2) Rate, Portion, Base Rate =PortionBase
- (3.1) Percent Change: Δ%=New − OldOld×100
- (3.2) Rate Of Change Over Time RoC=(n√NewOld−1)×100
- (3.3) Simple Average SAvg=Σxn
- (3.4) Weighted Average WAvg=ΣwxΣw
- • (3.5) Geometric Average GAvg=[n√(1+Δ%1)×(1+Δ%2)×⋯×(1+Δ%n)−1]×100
Part 2: Business Applications
- (4.1) Salary and Hourly Gross Earnings GE = Regular Earnings+Overtime Earnings+Holiday Earnings+Statutory Holiday Worked Earnings
- (4.2) Annual Income Tax Income Tax =Σ(Eligible Income In Tax Bracket × Tax Bracket Rate)
- (4.3) Index Numbers Index Number =Chosen quantity Base quantity× Base value
- (4.4) Purchasing Power Of A Dollar PPD =$1CPI/100
- (4.5) Real Income RI =Nominal IncomeCPI/100
- (5.1) Unit Variable Cost VC =TVCn
- (5.2) Net Income Using A Total Revenue And Cost Approach NI =n(S)−(TFC+n(VC))
- (5.3) Unit Contribution Margin CM = S–VC
- (5.4) Net Income Using Total Contribution Margin Approach NI =n(CM)–TFC
- (5.5) Contribution Rate If Unit Information Known CR =CMS×100
- (5.6) Contribution Rate If Aggregate Information Known CR = TR − TVCTR×100
- (5.7) Unit Break-even n=TFCCM
- (5.8) Dollar Break-even TR=TFCCR
- (6.1) Single Discount N=L×(1−d)
- (6.2a & 6.2b) Discount Amount D$=L×d or D$=L–N
- (6.3) Multiple Discounts N=L×(1−d1)×(1−d2)×⋯×(1−dn)
- (6.4) Single Equivalent Discount d =1−(1−d1)×(1−d2)×⋯×(1−dn)
- (6.5) The Selling Price Of A Product S=C+E+P
- (6.6) Markup Amount M$=E+P
- (6.7) The Selling Price Of A Product Using Markup Amount S=C+M$
- (6.8) Markup On Cost Percentage MoC%=M$C×100
- (6.9) Markup On Selling Price Percentage MoS%=M$S×100
- (6.10) The Sale Price Of A Product Son sale=S×(1−d)
- (6.11a & 6.11b) Markdown Amount D$=S×d or D$= S−Son sale
- (6.12) Markdown Percentage d=D$S×100
- (6.13) Maintained Markup MM =M$(n1)+(M$−D$)(n2)n1+n2
- (7.1) Selling Price Including Tax Stax=S+(S×Rate)
- (7.2) GST/HST Remittance Remit = Tax Collected−Tax Paid
- (7.3) Property Taxes Property Tax =Σ(AV×PTR)
- (7.4) Currency Exchange Desired Currency = Exchange Rate×Current Currency
Part 3: Single Payment Financial Applications
- (8.1) Simple Interest I = Prt
- (8.2) Simple Interest For Single Payments S = P(1+rt)
- (8.3) Interest Amount For Single Payments I = S−P
- (9.1) Periodic Interest Rate i =IYCY
- (9.2) Number of Compound Periods For Single Payments N = CY×Years
- (9.3) Compound Interest For Single Payments FV = PV(1+i)N
- (9.4) Interest Rate Conversion iNew=(1+iOld)CYOldCYNew−1
- (10.1) Periodic Interest Amount I = PV×i
- (10.2) Purchasing Power Of A Dollar (Compound Interest Method) PPD =$1(1+i)N×100
Part 4: Annuity Payments Financial Applications
- (11.1) Number Of Annuity Payments N = PY×Years
- (11.2) Ordinary Annuity Future Value FVORD= PMT[[(1+i)CYPY]N−1(1+i)CYPY−1]
- (11.3) Annuity Due Future Value FVDUE= PMT[[(1+i)CYPY]N−1(1+i)CYPY−1]×(1+i)CYPY
- (11.4) Ordinary Annuity Present Value FVORD= PMT[1−[1(1+i)CYPY]N(1+i)CYPY−1]
- (11.5) Annuity Due Present Value FVDUE= PMT[1−[1(1+i)CYPY]N(1+i)CYPY−1]×(1+i)CYPY
- (12.1) Future Value Of A Constant Growth Ordinary Annuity FVORD= PMT(1+Δ%)N−1[[(1+i)CYPY1+Δ%]N−1(1+i)CYPY1+Δ%−1]
- (12.2) Future Value Of A Constant Growth Annuity Due FVDUE= PMT(1+Δ%)N−1[[(1+i)CYPY1+Δ%]N−1(1+i)CYPY1+Δ%−1]×(1+i)CYPY
- (12.3) Present Value Of A Constant Growth Ordinary Annuity PVORD=PMT1+Δ%[1−[1+Δ%(1+i)CYPY]N(1+i)CYPY1+Δ%−1]
- (12.4) Present Value Of A Constant Growth Annuity Due PVDUE=PMT1+Δ%[1−[1+Δ%(1+i)CYPY]N(1+i)CYPY1+Δ%−1]×(1+i)CYPY
- (12.5) Ordinary Perpetuity Present Value PVORD=PMT(1+i)CYPY−1
- (12.6) Perpetuity Due Present Value PVDUE=PMT(1(1+i)CYPY−1+1)
Part 5: Amortization & Special Financial Concepts
- (13.1) Interest Portion Of An Ordinary Single Payment INT = BAL×((1+i)CYPY−1)
- (13.2) Principal Portion Of A Single Payment PRN = PMT−INT
- (13.3) Principal Portion For A Series Of Payments PRN =BALP1−BALP2
- (13.4) Interest Portion For A Series Of Payments INT = N×PMT−PRN
- (13.5) Interest Portion Of A Due Single Payment INTDUE=(BAL−PMT)×((1+i)CYPY−1)
- (14.1) The Cash Price For Any Bond Cash Price = PRI+AI
- (14.2) Bond Coupon Annuity Payment Amount PMTBOND= Face Value×CPNCY
- (14.3) Bond Price On An Interest Payment Date Date Price =FV(1+i)N+PMTBOND[1−1[1+i]Ni]
- (14.4) Bond Premium or Discount Premium or Discount = PRI−Face Value
- (14.5) Bond Cash Price On A Non-Interest Payment Date Cash Price =(Date Price)(1+i)t
- (14.6) Accrued Interest On A Non-Interest Payment Date AI=PMTBOND×t
- (14.7) Interest Portion Of A Sinking Fund Single Payment Due INT =(BAL+PMT)×((1+i)CYPY−1)
- (14.8) The Annual Cost Of The Bond Debt ACD=(Face Value×CPN)+(PMT×PY)
- (14.9) The Book Value Of The Bond Debt BVD=Bonds Outstanding−BAL
- (15.1) Net Present Value NPV =(Present Value Of All Future Cash Flows)−(Initial Investment)
- (15.2) Net Present Value Ratio NPVRATIO=NPVCFo