---
id: 2026-01-25T18:46:00-0500
title: 2026-01-25 18:46:??
tags: []
daily: "[[2026-01-25]]"
---
# 2026-01-25 18:46:??

### Calculating Monthly Principal & Interest Payment

Relevant to [[finance]]:

For a **fixed-rate, fully-amortizing mortgage**,
the monthly payment is computed using the **standard amortization formula**:

#### Standard Amortization Formula

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

Where:

* $A$ = periodic payment amount
* $P$ = amount of principal, net of initial payments
* $i$ = periodic interest rate
* $n$ = total number of payments

> [!info]
> $A$ is constant over the term,
> the interest portion decreases while the principal portion increases.

#### Example

For a 30-year mortgage of $268,000 at 5.75% annual interest:

$$
\begin{align*}
P &= 268000
i &= \frac{0.0575}{12} = 0.004791\bar{6} \\
n &= 30 \cdot 12 = 360
\end{align*}
$$

The monthly payment amount $A$ is given by:

$$
\begin{align*}
A &= 268000 \cdot \frac{0.004791\bar{6} \cdot (1+ 0.004791\bar{6})^{360}}{(1+ 0.004791\bar{6})^{360} - 1} \\
A &\approx 1563.98
\end{align*}
$$

### Calculating Annual Percentage Rate (APR)

$$
\text{APR} = \frac{\frac{\text{Interest} + \text{Fees}}{\text{Principle}}}{\text{Term Years}}
$$
