A loan amortization schedule is a complete table of periodic loan payments, showing the amount of principal and interest that comprise each payment until the loan is paid off at the end of its term. It's a crucial tool for understanding how your loan balance decreases over time and how much of each payment goes towards interest versus principal.

The formula used to calculate the monthly payment for an amortizing loan is:

\[P = L\frac{r(1+r)^n}{(1+r)^n-1}\]Where:

- \(P\) = Monthly payment
- \(L\) = Loan amount
- \(r\) = Monthly interest rate (annual rate divided by 12)
- \(n\) = Total number of months in the loan term

- Calculate the monthly payment using the formula above.
- For each payment period:
- Calculate the interest portion: \(\text{Interest} = \text{Current Balance} \times r\)
- Calculate the principal portion: \(\text{Principal} = \text{Monthly Payment} - \text{Interest}\)
- Update the loan balance: \(\text{New Balance} = \text{Current Balance} - \text{Principal}\)

- Repeat step 2 for each period until the loan is fully paid off.

Let's calculate the amortization schedule for a $200,000 loan at 4% annual interest for 30 years:

- \(r = \frac{4\%}{12} = 0.3333\%\) per month
- \(n = 30 \times 12 = 360\) months
- \(P = 200000 \times \frac{0.003333(1+0.003333)^{360}}{(1+0.003333)^{360}-1} = $954.83\)
- First month's breakdown:
- Interest: $200,000 × 0.003333 = $666.67
- Principal: $954.83 - $666.67 = $288.16
- New Balance: $200,000 - $288.16 = $199,711.84

This chart shows the proportion of principal ($200,000) to total interest ($143,739.80) for the example loan over its entire term.

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