Formulas

Chapter 1: Mathematics of Merchandising

Profit  = Sales – Costs

[latex]\text{Gross Profit} = Sales - \text{Cost of Goods Sold} = Sales - COGS[/latex]

[latex]\text{Net Profit} = Sales - \text{Total Costs} = GP - \text{Operating Expenses}[/latex]

[latex]\text{Percent Markup} = \frac{Profit}{Cost}[/latex]

[latex]\text{Percent Margin} = \frac{Profit}{Sales}[/latex]

[latex]Sales = Cost \times (1+ \% Markup)[/latex]

[latex]Net = List(1-d_1)(1-d_2)(1-d_3)[/latex]

Chapter 2: Functions

[latex]Slope = \frac{Rise}{Run} = \frac{y_2-y_1}{x_2-x_1}[/latex]

[latex]\text{Equation of a line: }Y = Intercept + slope \times X[/latex]

[latex]Revenue = price \times Quantity = price\times X[/latex]

[latex]Costs = \text{Fixed Costs}-\text{Variable Costs}\times Quantity = FC+VC X[/latex]

[latex]Profit = Revenue - Costs = price\times X - FC - VC X = (price- VC)X-FC[/latex]

[latex]\text{Contribution Margin} = price - VC = \text{markup in dollars for 1 item}[/latex]

Chapter 3: Simple Interest

[latex]I = Prt[/latex]

[latex]FV = P + I = P(1+rt)[/latex]

[latex]P = \frac{FV}{1+rt}[/latex]

Chapter 4: Compound Interest

[latex]FV = PV(1+i)^n[/latex]

[latex]i = \frac{j_m}{m}[/latex]

[latex]PV = \frac{FV}{(1+i)^n}= FV(1+i)^{-n}[/latex]

Chapter 5: Annuities

Ordinary Perpetuities:

[latex]PMT = PV\times i[/latex]

[latex]PV = \frac{PMT}{i}[/latex]

Perpetuities Due

[latex]PMT_{Due} = \frac{PV\times i}{1+i}[/latex]

[latex]PV_{Due} = \frac{PMT}{i}+PMT[/latex]

To switch to payments at the beginning of the interval:

• Press 2ND BGN (above the PMT key). The display should show END.
• Press 2ND SET (above the ENTER key). The display should show BGN.
• Press CE/C (bottom left corner) or 2ND QUIT (top left corner).

To go back to payments at the END of the interval:

• Press 2ND BGN (above the PMT key) The display should show BGN.
• Press 2ND SET (above the ENTER key). The display should show END.
• Press CE/C (bottom left corner) or 2ND QUIT  (top left corner)

Extra Annuity Formula (for when you don’t have a BAII Plus)

 Future Value of an Ordinary Annuity

Present Value of an Ordinary Annuity

Future Value of an Annuity Due

 Present Value of an Annuity Due

[latex]PV_{\text{due}} = PMT \cdot \frac{1 - (1 + i)^{-n}}{i} \cdot (1 + i)[/latex]

 Solving for PMT (Periodic Payment) Given Future Value (Ordinary Annuity)

Given Present Value (Ordinary Annuity)

Given Future Value (Annuity Due)

Given Present Value (Annuity Due)

Chapter 6: Investment Decisions