zmVault/timestamped/2026-01-25_18-46-00.md

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id	title	tags	daily
2026-01-25T18:46:00-0500	2026-01-25 18:46:??	topic/finance	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}}