## Equations and Procedures

The equation for determining an amortized payment is:

Where:

P = Periodic Payment

Pr = Principal

n = Number of Payments

i = Periodic Interest (Interest rate / number of payments per year)

Example

$10,000 amortized over one year at 12% with monthly payments.Pr = 10,000

n = 12

i = .01

The summation sign tells us to take the sum of the following 12 quotients:

1 divided by 1.01 raised to the power of 1 |

1 divided by 1.01 raised to the power of 2 |

1 divided by 1.01 raised to the power of 3 |

1 divided by 1.01 raised to the power of 4 |

1 divided by 1.01 raised to the power of 5 |

1 divided by 1.01 raised to the power of 6 |

1 divided by 1.01 raised to the power of 7 |

1 divided by 1.01 raised to the power of 8 |

1 divided by 1.01 raised to the power of 9 |

1 divided by 1.01 raised to the power of 10 |

1 divided by 1.01 raised to the power of 11 |

1 divided by 1.01 raised to the power of 12 |

This sum is 11.25509

$10,000 / 11.25509 = $888.49

The Nortridge Loan System uses this equation indirectly. A complex algebraic equation has been derived from this summation series, and it is this equation that is directly used by the loan system to derive the payment amount.