# Appendix A Summary of Formulas

### Accumulated value of a series of deposits:

$D\times \left({\left(1+R\right)}^{n}-1\right)\xf7R=A$

where: D | = | periodic deposit amount |

R | = | periodic interest rate |

n | = | number of periods |

A | = | accumulated value |

### Adding fractions:

$\begin{array}{l}\left({n}_{1}\times {d}_{2}\right)+\left({d}_{1}\times {n}_{2}\right)={n}_{a}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{d}_{1}\times {n}_{2}={d}_{a}\end{array}$

where: n1 | = | numerator, first fraction |

d1 | = | denominator, first fraction |

n2 | = | numerator, first fraction |

d2 | = | numerator, second fraction |

na | = | numerator, answer |

da | = | denominator, answer |

### After-tax return:

$O\times \left(1-T\right)=A$

where: O | = | operating (pre-tax) profit |

T | = | combined federal and state tax rate (in decimal form) |

A | = | after-tax profit |

### Amortization:

$C\xf7M=A$

where: C | = | total cost |

M | = | months to amortize |

A | = | amortization per month |

### Annual compounding:

${}^{}$

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