You borrow $223,000 to be repaid in monthly installments over the next 25 years. The first payment occurs one month from today. If the annualized interest rate for the loan is4.8%, how much principal is amortized in payment #46? Enter your answer as a positive number, and round to the nearest dollar.

To solve this problem, we will follow these steps:

1. **Calculate the monthly interest rate.**
   Since the annual interest rate is 4.8%, the monthly interest rate is calculated as:
   \[
   r = \frac{4.8\%}{12} = \frac{0.048}{12} = 0.004
   \]

2. **Determine the monthly payment amount (PMT) using the amortization formula.**
   The formula for monthly payments on an amortized loan is:
   \[
   PMT = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
   \]
   where:
   - $P = 223,000$ (the principal amount),
   - $r = 0.004$ (the monthly interest rate),
   - $n = 25 \times 12 = 300$ (the total number of payments).

3. **Find the outstanding balance after payment #45.**
   The outstanding loan balance after $k$ payments is calculated using:
   \[
   B_k = P \cdot \frac{(1 + r)^n - (1 + r)^k}{(1 + r)^n - 1}
   \]
   where $B_k$ is the outstanding balance after $k$ payments.

4. **Calculate the interest portion of payment #46.**
   The interest portion of any payment is calculated as:
   \[
   I_{46} = r \cdot B_{45}
   \]

5. **Find the principal portion of payment #46.**
   The principal portion of any payment is:
   \[
   \text{Principal portion} = PMT - I_{46}
   \]

Let's calculate these step-by-step.The amount of principal amortized in payment #46 is **$462**, rounded to the nearest dollar.

Do you want more details or have any questions?

Here are five related questions to further explore the topic:
1. How much total interest will you pay over the 25-year loan period?
2. What is the remaining loan balance after 10 years of payments?
3. How does the total interest paid change if the loan term is reduced to 20 years?
4. What happens to the monthly payment if the interest rate is reduced to 4%?
5. How much of the loan is paid off after the first 5 years?

**Tip:** Early in an amortized loan, most of your payments go towards interest, but over time, more of each payment goes towards the principal.

You borrow $223,000 to be repaid in monthly installments over the next 25 years. The first payment occurs one month from today. If the annualized interest rate for the loan is 4.8%, how much principal is amortized in payment #46? Enter your answer as a positive number, and round to the nearest dollar.

Calculate how much principal is amortized in payment #46 of a $223,000 loan repaid over 25 years with a 4.8% annualized interest rate. Learn key formulas such as the amortization formula, interest calculation, and outstanding balance, with a step-by-step solution.

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