59 lines
1.2 KiB
Markdown
59 lines
1.2 KiB
Markdown
---
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id: 2026-01-25T18:46:00-0500
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title: 2026-01-25 18:46:??
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tags: []
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daily: "[[2026-01-25]]"
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---
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# 2026-01-25 18:46:??
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### Calculating Monthly Principal & Interest Payment
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Relevant to [[finance]]:
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For a **fixed-rate, fully-amortizing mortgage**,
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the monthly payment is computed using the **standard amortization formula**:
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#### Standard Amortization Formula
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$$
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A = P \cdot \frac{i(1+i)^n}{(1+i)^n-1}
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$$
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Where:
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* $A$ = periodic payment amount
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* $P$ = amount of principal, net of initial payments
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* $i$ = periodic interest rate
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* $n$ = total number of payments
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> [!info]
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> $A$ is constant over the term,
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> the interest portion decreases while the principal portion increases.
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#### Example
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For a 30-year mortgage of $268,000 at 5.75% annual interest:
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$$
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\begin{align*}
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P &= 268000
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i &= \frac{0.0575}{12} = 0.004791\bar{6} \\
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n &= 30 \cdot 12 = 360
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\end{align*}
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$$
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The monthly payment amount $A$ is given by:
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$$
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\begin{align*}
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A &= 268000 \cdot \frac{0.004791\bar{6} \cdot (1+ 0.004791\bar{6})^{360}}{(1+ 0.004791\bar{6})^{360} - 1} \\
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A &\approx 1563.98
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\end{align*}
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$$
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### Calculating Annual Percentage Rate (APR)
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$$
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\text{APR} = \frac{\frac{\text{Interest} + \text{Fees}}{\text{Principle}}}{\text{Term Years}}
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$$
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