Partnerships

At a glance 7 formulas

1. 1Capital times time$A : B = C_A T_A : C_B T_B$$\text{same time: } A : B = C_A : C_B$
2. 2Late join, early exitCount only the months the money is in: joining after $m$ months of a year gives $12 - m$ months, and leaving after $m$ months gives $m$.
3. 3Capital changed midway$\text{capital-months} = C_1 t_1 + C_2 t_2 + \cdots$
4. 4Working partner firstPay the working partner's salary or commission out of the profit first; only what is left is split in the capital-time ratio.
5. 5Time or capital back$T_A : T_B = \dfrac{P_A}{C_A} : \dfrac{P_B}{C_B}$$C_A : C_B = \dfrac{P_A}{T_A} : \dfrac{P_B}{T_B}$
6. 6Total from one share$\text{total} = \text{share} \times \dfrac{a + b + c}{a}$$\text{gap of } (c - a) \text{ parts} \Rightarrow 1 \text{ part} = \dfrac{\text{gap}}{c - a}$
7. 7Share as a percentA partner's percent is their capital-months over everyone's. Extra capital also raises the total, so redo the fraction instead of scaling the percent.