Commercial mathematics

Here a whole of mathematical formulas used in different trade S related to the money - banking, Commercial, etc

Percentages

  • Increase of 25% : one multiplies per 1,25

  • Diminution in 25% : one multiplies by 0,75
  • Prendre 10% of 20% : one multiplies by 0,2 then by 0,1 (thus by 0,02, which amounts taking 2%)
  • Rate of variation = \ frac {\ mbox {variation of the value}} {\ mbox {value before the variation}}
  • Taux of percentage (or relative percentage ) of has compared to B = \ frac {has} {B}

Pricing of the rates

  • Purchase price Net = rough Purchase price - Reduction
  • Selling price Net = rough Selling price - Reduction
  • Cost of purchase = Purchase price Net + Fresh of purchase
  • Production costs = Cost of purchase + Fresh of production
  • Cost price = Production costs + Fresh of distribution
  • Gross margin = Selling price Net net of tax - Cost of purchase
  • Result = Selling price - Cost price (benefit or loss)
  • Rate of mark = \ frac {\ mbox {Gross margin}} {\ mbox {statement HT}}
  • Rate of margin = \ frac {\ mbox {Gross margin}} {\ mbox {Pa HT}}

VAT

  • PVTTC = PVHT + VAT
  • VAT poured with the state = collected VAT - deductible VAT

Simple interests

  • acquired Value : A=C+i
  • Interest : i=Ctn (T rate over one period, N many periods)
  • Periods
    • year = 360 days
    • months = 1/12 year = 30 days
    • about fifteen = 1/24 year
    • days = exact Nb days (one counts the last but not the first)
  • Average rate : when several capital is placed atdifferent rates, average rate is the single rate for which it would be necessary to place the same capital during same time to obtain the same total interest ( attention , it is not the average of the rates).

Made up interests

A=C (1+t) ^n

Arithmetic continuations of reason R

  • Relation of recurrence: u_ {n+1} =u_n+r
  • general Term: u_n=u_1+ (n-1) r

Geometrical continuations of reason Q

  • Relation of recurrence: u_ {n+1} =qu_n
  • general Term: u_n=u_1q^{n-1}

Discount commercial

  • Face value of a effect: summon to pay at the limit
  • Agio = Escompte + Commissions + VAT
  • net Amount = Face value - Agio
  • Escompte : e=Vtn (V = face value)
  • Current value : a=V-e=V-Vtn=V (1-tn)
  • real Rate of discount : it is the rate T which it would be necessary to apply to the face value to find the amount of the agio: \ mbox {Agio} =VTn with N in years. T is also called rate global manpower (TEG).

Equivalence of capital

  • Two capital placed atthe same rate is known as equivalent to a given date if they have the same current value on this date.
  • an effect can be replaced by another if the two effects are equivalent the day of the replacement.
  • a whole of effects can be replaced by a single effect if, the day of the replacement, the current value of the effect of replacement is equal to the sum of the current values of the replaced effects.

Index of V1 at the date t1 compared to V0 at the date t0

I_ {\ frac {V_1} {V_0}} = \ frac {V_1} {V_0}

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