You borrow $212,000 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 is5.0%, how much principal is amortized in payment #31

To calculate the principal amortized in payment #31, we need to break the problem into steps. The loan is repaid through monthly installments, so we will first calculate the monthly payment and then use that information to find how much of the 31st payment goes toward reducing the principal.

### Step 1: Calculate the monthly payment (M)

The formula for the monthly payment $M$ for a fixed-rate loan is:

\[
M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $P = 212,000$ is the loan amount.
- $r = \frac{0.05}{12} = 0.00416667$ is the monthly interest rate (5% annual interest rate divided by 12 months).
- $n = 25 \times 12 = 300$ is the total number of monthly payments over 25 years.

### Step 2: Calculate the outstanding loan balance after 30 payments

The outstanding balance after $t$ payments is calculated using the following formula:

\[
B_t = P \times \frac{(1 + r)^n - (1 + r)^t}{(1 + r)^n - 1}
\]

Where $B_t$ is the balance remaining after $t$ payments.

We will first calculate the monthly payment, then the outstanding balance after 30 payments, and finally the portion of the 31st payment that goes toward reducing the principal. Let's compute these.The monthly payment for the loan is approximately **$1,239.33**.

After 30 payments, the outstanding loan balance is approximately **$200,649.01**.

In the 31st payment, the amount of principal that is amortized (i.e., reducing the principal) is approximately **$403.29**.

Would you like further details or explanations? Here are five related questions to explore:

1. How is the monthly interest portion calculated for each payment?
2. What happens to the principal amortized over time in an amortization schedule?
3. How would an extra payment affect the loan balance?
4. How would the monthly payment change if the interest rate were different?
5. What is the total interest paid over the life of the loan?

**Tip:** In an amortizing loan, the interest portion of each payment decreases over time, while the principal portion increases.

You borrow $212,000 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 5.0%, how much principal is amortized in payment #31?

Discover how to calculate the principal amortized in payment #31 for a $212,000 loan with a 5% annual interest rate over 25 years. This guide walks through the steps of calculating monthly payments, outstanding loan balance, and the portion of the payment going towards the principal.

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