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Formulas: finance and economics, grade 10 (3 units)

Buying and selling

  • The unit price – P\displaystyle P the price of the pack, n\displaystyle n the number of units in it (grams, litres, items)
    u=Pn\displaystyle u=\frac{P}{n}
  • A p%\displaystyle p\% discount – a\displaystyle a the price before the discount, b\displaystyle b the price after it
    b\displaystyle b =\displaystyle = (100%−p%)⋅a\displaystyle (100\%-p\%)\cdot a
  • A price with 18% VAT – a\displaystyle a the price without VAT, b\displaystyle b the price with VAT
    b\displaystyle b =\displaystyle = 1.18⋅a\displaystyle 1.18\cdot a

A linear model

  • The total cost – x\displaystyle x the number of units, m\displaystyle m the cost per unit (the slope), b\displaystyle b the fixed cost
    y=mx+b\displaystyle y=mx+b
  • The cost per unit from two points (x1,y1)\displaystyle (x_1,y_1), (x2,y2)\displaystyle (x_2,y_2) on the line
    m=y2−y1x2−x1\displaystyle m=\frac{y_2-y_1}{x_2-x_1}
  • Two plans cost the same – where their two lines meet
    m1x+b1\displaystyle m_1x+b_1 =\displaystyle = m2x+b2\displaystyle m_2x+b_2

Profit and loss

  • The total cost – F\displaystyle F the fixed costs, c\displaystyle c the cost of one unit, x\displaystyle x the number of units
    C=F+c⋅x\displaystyle C=F+c\cdot x
  • The revenue – s\displaystyle s the selling price of one unit
    R=s⋅x\displaystyle R=s\cdot x
  • The profit – the revenue minus the cost (a negative profit is a loss)
    P=R−C\displaystyle P=R-C
  • The profit percent – out of the cost
    r%=PC\displaystyle r\%=\frac{P}{C}
  • The break-even point – the revenue equals the cost
    s⋅x\displaystyle s\cdot x =\displaystyle = F+c⋅x\displaystyle F+c\cdot x

Wages

  • Pay – w\displaystyle w the hourly wage, h\displaystyle h the number of hours
    S=w⋅h\displaystyle S=w\cdot h
  • The pay for an overtime hour, in the first two overtime hours of a day
    1.25⋅w\displaystyle 1.25\cdot w
  • The pay for an overtime hour, from the third overtime hour of a day
    1.5⋅w\displaystyle 1.5\cdot w
  • Net pay – G\displaystyle G the gross pay, D\displaystyle D the deductions
    N=G−D\displaystyle N=G-D

Measures of centre

  • The mean of n\displaystyle n values
    xˉ=x1+x2+⋯+xnn\displaystyle \bar{x}=\frac{x_1+x_2+\dots+x_n}{n}
  • The mean from a frequency table – fi\displaystyle f_i the frequency of the value xi\displaystyle x_i
    xˉ=x1f1+x2f2+⋯+xkfkf1+f2+⋯+fk\displaystyle \bar{x}=\frac{x_1f_1+x_2f_2+\dots+x_kf_k}{f_1+f_2+\dots+f_k}
  • The place of the median in an ordered list of n\displaystyle n values
    n+12\displaystyle \frac{n+1}{2}