Formulas

Chris Kellman; Leslie Major; Don Mallory; Frank Gruen; Amy Goldlist

Formulas

Chapter 1: Mathematics of Merchandising

Profit = Sales – Costs

$Gross Profit = S a l e s - Cost of Goods Sold = S a l e s - C O G S$

$Net Profit = S a l e s - Total Costs = G P - Operating Expenses$

$Percent Markup = \frac{P r o f i t}{C o s t}$

$Percent Margin = \frac{P r o f i t}{S a l e s}$

$S a l e s = C o s t \times (1 + % M a r k u p)$

$N e t = L i s t (1 - d_{1}) (1 - d_{2}) (1 - d_{3})$

Chapter 2: Functions

$S l o p e = \frac{R i s e}{R u n} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$Equation of a line: Y = I n t e r c e p t + s l o p e \times X$

$R e v e n u e = p r i c e \times Q u a n t i t y = p r i c e \times X$

$C o s t s = Fixed Costs - Variable Costs \times Q u a n t i t y = F C + V C X$

$P r o f i t = R e v e n u e - C o s t s = p r i c e \times X - F C - V C X = (p r i c e - V C) X - F C$

$Contribution Margin = p r i c e - V C = markup in dollars for 1 item$

Chapter 3: Simple Interest

$I = P r t$

$F V = P + I = P (1 + r t)$

$P = \frac{F V}{1 + r t}$

Chapter 4: Compound Interest

$F V = P V (1 + i)^{n}$

$i = \frac{j_{m}}{m}$

$P V = \frac{F V}{(1 + i)^{n}} = F V (1 + i)^{- n}$

Chapter 5: Annuities

Ordinary Perpetuities:

$P M T = P V \times i$

$P V = \frac{P M T}{i}$

Perpetuities Due

$P M T_{D u e} = \frac{P V \times i}{1 + i}$

$P V_{D u e} = \frac{P M T}{i} + P M T$

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

F V = P M T \cdot \frac{(1 + i)^{n} - 1}{i}

Present Value of an Ordinary Annuity

$P V = P M T \cdot \frac{1 - (1 + i)^{- n}}{i}$

Future Value of an Annuity Due

F V_{due} = P M T \cdot \frac{(1 + i)^{n} - 1}{i} \cdot (1 + i)

Present Value of an Annuity Due

$P V_{due} = P M T \cdot \frac{1 - (1 + i)^{- n}}{i} \cdot (1 + i)$

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

P M T = \frac{F V \cdot i}{(1 + i)^{n} - 1}

Given Present Value (Ordinary Annuity)

P M T = \frac{P V \cdot i}{1 - (1 + i)^{- n}}

Given Future Value (Annuity Due)

P M T = \frac{F V \cdot i}{[(1 + i)^{n} - 1] \cdot (1 + i)}

Given Present Value (Annuity Due)

P M T = \frac{P V \cdot i}{[1 - (1 + i)^{- n}] \cdot (1 + i)}

Chapter 6: Investment Decisions

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