vault backup: 2026-02-20 14:53:32

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

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+# 2026-01-25 18:46:??
+
+#topic/finance
+
+### Calculating Monthly Principal & Interest Payment
+
+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)
+
+$$
+\text{APR} = \frac{\frac{\text{Interest} + \text{Fees}}{\text{Principle}}}{\text{Term Years}}
+$$