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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 =$1CPI/100
  • (4.5) Real Income RI =Nominal IncomeCPI/100
  • (5.1) Unit Variable Cost VC =TVCn
  • (5.2) Net Income Using A Total Revenue And Cost Approach NI =n(S)(TFC+n(VC))
  • (5.3) Unit Contribution Margin \text{CM } = \text{ S} – \text{VC} \nonumber
  • (5.4) Net Income Using Total Contribution Margin Approach \text{NI } = \text{n}(\text{CM}) – \text{TFC} \nonumber
  • (5.5) Contribution Rate If Unit Information Known \text{CR } = \frac{\text{CM}}{\text{S}} \times 100 \nonumber
  • (5.6) Contribution Rate If Aggregate Information Known \text{CR } = \frac{\text{ TR − TVC}}{\text{TR}} \times 100 \nonumber
  • (5.7) Unit Break-even n = \frac{\text{TFC}}{\text{CM}} \nonumber
  • (5.8) Dollar Break-even \text{TR} = \frac{\text{TFC}}{\text{CR}} \nonumber
  • (6.1) Single Discount \text{N} = \text{L} \times (1 - \text{d}) \nonumber
  • (6.2a & 6.2b) Discount Amount \text{D} \$ = \text{L} \times \text{d} \text{ or } \text{D} \$ = \text{L} – \text{N} \nonumber
  • (6.3) Multiple Discounts \text{N} = \text{L} \times \left( 1− \text{d}_1 \right) \times \left( 1− \text{d}_2 \right) \times \cdots \times \left( 1− \text{d}_n \right) \nonumber
  • (6.4) Single Equivalent Discount \text{d } = 1 − \left( 1 − \text{d}_1 \right) \times \left( 1 − \text{d}_2 \right) \times \cdots \times \left( 1 − \text{d}_n \right) \nonumber
  • (6.5) The Selling Price Of A Product \text{S} = \text{C} + \text{E} + \text{P} \nonumber
  • (6.6) Markup Amount \text{M} \$ = \text{E} + \text{P} \nonumber
  • (6.7) The Selling Price Of A Product Using Markup Amount \text{S} = \text{C} + \text{M} \$ \nonumber
  • (6.8) Markup On Cost Percentage \text{MoC} \% = \text{M} \$ \text{C} \times 100 \nonumber
  • (6.9) Markup On Selling Price Percentage \text{MoS} \% = \frac{\text{M} \$}{\text{S}} \times 100 \nonumber
  • (6.10) The Sale Price Of A Product \text{S}_{\text{on sale}} = \text{S} \times \left( 1 − \text{d} \right) \nonumber
  • (6.11a & 6.11b) Markdown Amount \text{D}$ = \text{S} \times \text{d} \text{ or } \text{D} \$ = \text{ S} − \text{S}_{\text{on sale}} \nonumber
  • (6.12) Markdown Percentage \text{d} = \frac{\text{D} \$}{\text{S}} \times 100 \nonumber
  • (6.13) Maintained Markup \text{MM } = \frac{ \text{M} \$ \left( \text{n}_1 \right) + \left( \text{M} \$ − \text{D} \$ \right) \left( \text{n}_2 \right)}{\text{n}_1 + \text{n}_2} \nonumber
  • (7.1) Selling Price Including Tax \text{S}_{\text{tax}} = \text{S} + (\text{S} \times \text{Rate}) \nonumber
  • (7.2) GST/HST Remittance \text{Remit } = \text{ Tax Collected} − \text{Tax Paid} \nonumber
  • (7.3) Property Taxes \text{Property Tax } = \Sigma ( \text{AV} \times \text{PTR}) \nonumber
  • (7.4) Currency Exchange \text{Desired Currency } = \text{ Exchange Rate} \times \text{Current Currency} \nonumber

Part 3: Single Payment Financial Applications

  • (8.1) Simple Interest \text{I }= \text{ Prt} \nonumber
  • (8.2) Simple Interest For Single Payments \text{S }= \text{ P(1+rt)} \nonumber
  • (8.3) Interest Amount For Single Payments \text{I } = \text{ S} − \text{P} \nonumber
  • (9.1) Periodic Interest Rate \text{i } = \frac{ \text{IY}}{\text{CY}} \nonumber
  • (9.2) Number of Compound Periods For Single Payments \text{N } = \text{ CY} \times \text{Years} \nonumber
  • (9.3) Compound Interest For Single Payments \text{FV } = \text{ PV} (1 + \text{i})^{\text{N}} \nonumber
  • (9.4) Interest Rate Conversion \text{i}_{\text{New}} = \left( 1 + \text{i}_{\text{Old}} \right)^{\frac{\text{CY}_{\text{Old}}}{\text{CY}_{\text{New}}}} − 1 \nonumber
  • (10.1) Periodic Interest Amount \text{I } = \text{ PV} \times \text{i} \nonumber
  • (10.2) Purchasing Power Of A Dollar (Compound Interest Method) \text{PPD } = \frac{$1}{(1 + \text{i})^{ \text{N}}} \times 100 \nonumber

Part 4: Annuity Payments Financial Applications

  • (11.1) Number Of Annuity Payments \text{N } = \text{ PY} \times \text{Years} \nonumber
  • (11.2) Ordinary Annuity Future Value \text{FV}_{\text{ORD}} = \text{ PMT} \left[ \frac{ \left[ (1 + \text{i})^{\frac{\text{CY}}{\text{PY}}} \right]^\text{N} − 1}{(1 + \text{i} )^{\frac{\text{CY}}{\text{PY}}} − 1} \right] \nonumber
  • (11.3) Annuity Due Future Value \text{FV}_{\text{DUE}} = \text{ PMT} \left[ \frac{ \left[ (1 + \text{i})^{\frac{\text{CY}}{\text{PY}}} \right]^\text{N} − 1}{(1 + \text{i} )^{\frac{\text{CY}}{\text{PY}}} − 1} \right] \times (1 + \text{i} )^{ \frac{\text{CY}}{\text{PY}}} \nonumber
  • (11.4) Ordinary Annuity Present Value \text{FV}_{\text{ORD}} = \text{ PMT} \left[ \frac{ 1 - \left[ \frac{1}{(1 + \text{i})^{\frac{\text{CY}}{\text{PY}}}} \right]^\text{N}}{(1 + \text{i} )^{\frac{\text{CY}}{\text{PY}}} − 1} \right] \nonumber
  • (11.5) Annuity Due Present Value \text{FV}_{\text{DUE}} = \text{ PMT} \left[ \frac{ 1 - \left[ \frac{1}{(1 + \text{i})^{\frac{\text{CY}}{\text{PY}}}} \right]^\text{N}}{(1 + \text{i} )^{\frac{\text{CY}}{\text{PY}}} − 1} \right] \times (1 + \text{i} )^{ \frac{\text{CY}}{\text{PY}}} \nonumber
  • (12.1) Future Value Of A Constant Growth Ordinary Annuity \text{FV}_{\text{ORD}} = \text{ PMT} (1 + \Delta \%)^{\text{N}−1} \left[ \frac{ \left[ \frac{ (1+ \text{i})^{\frac{\text{CY}}{\text{PY}}}}{1 + \Delta \%} \right]^{\text{N}} - 1}{ \frac{ (1+ \text{i})^{\frac{\text{CY}}{\text{PY}}} }{1 + \Delta \%} - 1} \right] \nonumber
  • (12.2) Future Value Of A Constant Growth Annuity Due \text{FV}_{\text{DUE}} = \text{ PMT} (1 + \Delta \%)^{\text{N}−1} \left[ \frac{ \left[ \frac{ (1+ \text{i})^{\frac{\text{CY}}{\text{PY}}}}{1 + \Delta \%} \right]^{\text{N}} - 1}{ \frac{ (1+ \text{i})^{\frac{\text{CY}}{\text{PY}}} }{1 + \Delta \%} - 1} \right] \times (1 + \text{i} )^{ \frac{\text{CY}}{\text{PY}}} \nonumber
  • (12.3) Present Value Of A Constant Growth Ordinary Annuity \text{PV}_{\text{ORD}} = \frac{\text{PMT}}{1 + \Delta \%} \left[ \frac{1 - \left[ \frac{1 + \Delta \%}{ (1+ \text{i})^{\frac{\text{CY}}{\text{PY}}}} \right]^{\text{N}}}{ \frac{(1+ \text{i})^{\frac{\text{CY}}{\text{PY}}}}{1 + \Delta \%} - 1} \right] \nonumber
  • (12.4) Present Value Of A Constant Growth Annuity Due \text{PV}_{\text{DUE}} = \frac{\text{PMT}}{1 + \Delta \%} \left[ \frac{1 - \left[ \frac{1 + \Delta \%}{ (1+ \text{i})^{\frac{\text{CY}}{\text{PY}}}} \right]^{\text{N}}}{ \frac{(1+ \text{i})^{\frac{\text{CY}}{\text{PY}}}}{1 + \Delta \%} - 1} \right] \times (1 + \text{i} )^{ \frac{\text{CY}}{\text{PY}}} \nonumber
  • (12.5) Ordinary Perpetuity Present Value \text{PV}_{\text{ORD}} = \frac{\text{PMT}}{(1 + \text{i})^{\frac{\text{CY}}{\text{PY}}} − 1} \nonumber
  • (12.6) Perpetuity Due Present Value \text{PV}_{\text{DUE}} = \text{PMT} \left( \frac{1}{(1+ \text{i})^{\frac{\text{CY}}{\text{PY}}} − 1} + 1 \right) \nonumber

Part 5: Amortization & Special Financial Concepts

  • (13.1) Interest Portion Of An Ordinary Single Payment \text{INT } = \text{ BAL} \times ((1+ \text{i})^{\frac{\text{CY}}{\text{PY}}} − 1) \nonumber
  • (13.2) Principal Portion Of A Single Payment \text{PRN } = \text{ PMT} − \text{INT} \nonumber
  • (13.3) Principal Portion For A Series Of Payments \text{PRN } = \text{BAL}_{\text{P}1} − \text{BAL}_{\text{P}2} \nonumber
  • (13.4) Interest Portion For A Series Of Payments \text{INT } = \text{ N} \times \text{PMT} − \text{PRN} \nonumber
  • (13.5) Interest Portion Of A Due Single Payment \text{INT}_{\text{DUE}} = ( \text{BAL} − \text{PMT}) \times ((1+ \text{i})^{\frac{\text{CY}}{\text{PY}}} − 1) \nonumber
  • (14.1) The Cash Price For Any Bond \text{Cash Price } = \text{ PRI} + \text{AI} \nonumber
  • (14.2) Bond Coupon Annuity Payment Amount \text{PMT}_{\text{BOND}} = \text{ Face Value} \times \frac{\text{CPN}}{\text{CY}} \nonumber
  • (14.3) Bond Price On An Interest Payment Date \text{Date Price } = \frac{\text{FV}}{(1+\text{i})^{\text{N}}} + \text{PMT}_{\text{BOND}} \left[ \frac{1-\frac{1}{[1+\text{i}]^\text{N}}}{\text{i}} \right] \nonumber
  • (14.4) Bond Premium or Discount \text{Premium or Discount } = \text{ PRI} − \text{Face Value} \nonumber
  • (14.5) Bond Cash Price On A Non-Interest Payment Date \text{Cash Price } = (\text{Date Price})(1 + \text{i})^{\text{t}} \nonumber
  • (14.6) Accrued Interest On A Non-Interest Payment Date \text{AI} = \text{PMT}_{\text{BOND}} \times \text{t} \nonumber
  • (14.7) Interest Portion Of A Sinking Fund Single Payment Due \text{INT } = ( \text{BAL} + \text{PMT}) \times ((1 + \text{i})^{\frac{\text{CY}}{\text{PY}}} − 1) \nonumber
  • (14.8) The Annual Cost Of The Bond Debt \text{ACD} = (\text{Face Value} \times \text{CPN}) + (\text{PMT} \times \text{PY}) \nonumber
  • (14.9) The Book Value Of The Bond Debt \text{BVD} = \text{Bonds Outstanding} − \text{BAL} \nonumber
  • (15.1) Net Present Value \text{NPV } = (\text{Present Value Of All Future Cash Flows}) − (\text{Initial Investment}) \nonumber
  • (15.2) Net Present Value Ratio \text{NPV}_{\text{RATIO}} = \frac{\text{NPV}}{\text{CFo}} \nonumber

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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