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Mathematics LibreTexts

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=(nNewOld1)×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 =$1CPI/100
  • (4.5) Real Income RI =Nominal IncomeCPI/100
  • (5.1) Unit Variable Cost VC =TVCn
  • (5.2) Net Income Using A Total Revenue And Cost Approach NI =n(S)(TFC+n(VC))
  • (5.3) Unit Contribution Margin CM = SVC
  • (5.4) Net Income Using Total Contribution Margin Approach NI =n(CM)TFC
  • (5.5) Contribution Rate If Unit Information Known CR =CMS×100
  • (5.6) Contribution Rate If Aggregate Information Known CR = TR − TVCTR×100
  • (5.7) Unit Break-even n=TFCCM
  • (5.8) Dollar Break-even TR=TFCCR
  • (6.1) Single Discount N=L×(1d)
  • (6.2a & 6.2b) Discount Amount D$=L×d or D$=LN
  • (6.3) Multiple Discounts N=L×(1d1)×(1d2)××(1dn)
  • (6.4) Single Equivalent Discount =1(1d1)×(1d2)××(1dn)
  • (6.5) The Selling Price Of A Product S=C+E+P
  • (6.6) Markup Amount M$=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×(1d)
  • (6.11a & 6.11b) Markdown Amount D$=S×d or D$= SSon 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 CollectedTax 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 = Prt
  • (8.2) Simple Interest For Single Payments = P(1+rt)
  • (8.3) Interest Amount For Single Payments = SP
  • (9.1) Periodic Interest Rate =IYCY
  • (9.2) Number of Compound Periods For Single Payments = CY×Years
  • (9.3) Compound Interest For Single Payments FV = PV(1+i)N
  • (9.4) Interest Rate Conversion iNew=(1+iOld)CYOldCYNew1
  • (10.1) Periodic Interest Amount = 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 = PY×Years
  • (11.2) Ordinary Annuity Future Value FVORD= PMT[[(1+i)CYPY]N1(1+i)CYPY1]
  • (11.3) Annuity Due Future Value FVDUE= PMT[[(1+i)CYPY]N1(1+i)CYPY1]×(1+i)CYPY
  • (11.4) Ordinary Annuity Present Value FVORD= PMT[1[1(1+i)CYPY]N(1+i)CYPY1]
  • (11.5) Annuity Due Present Value FVDUE= PMT[1[1(1+i)CYPY]N(1+i)CYPY1]×(1+i)CYPY
  • (12.1) Future Value Of A Constant Growth Ordinary Annuity FVORD= PMT(1+Δ%)N1[[(1+i)CYPY1+Δ%]N1(1+i)CYPY1+Δ%1]
  • (12.2) Future Value Of A Constant Growth Annuity Due FVDUE= PMT(1+Δ%)N1[[(1+i)CYPY1+Δ%]N1(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)CYPY1
  • (12.6) Perpetuity Due Present Value PVDUE=PMT(1(1+i)CYPY1+1)

Part 5: Amortization & Special Financial Concepts

  • (13.1) Interest Portion Of An Ordinary Single Payment INT = BAL×((1+i)CYPY1)
  • (13.2) Principal Portion Of A Single Payment PRN = PMTINT
  • (13.3) Principal Portion For A Series Of Payments PRN =BALP1BALP2
  • (13.4) Interest Portion For A Series Of Payments INT = N×PMTPRN
  • (13.5) Interest Portion Of A Due Single Payment INTDUE=(BALPMT)×((1+i)CYPY1)
  • (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[11[1+i]Ni]
  • (14.4) Bond Premium or Discount Premium or Discount = PRIFace 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)CYPY1)
  • (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 OutstandingBAL
  • (15.1) Net Present Value NPV =(Present Value Of All Future Cash Flows)(Initial Investment)
  • (15.2) Net Present Value Ratio NPVRATIO=NPVCFo

This page titled 16.4: Formula Sheet is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jean-Paul Olivier via source content that was edited to the style and standards of the LibreTexts platform.

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