You purchase a cottage for $175,000. You obtain a 30-year, fixed rate mortgage loan at 12.5% after paying a down payment of 25%. Of the second month's mortgage payment, how much is interest and how much is applied to the principal?

Let's work through the details step by step:

### Step 1: Calculate the loan amount
The price of the cottage is \$175,000, and the down payment is 25%. 

\[
\text{Down payment} = 25\% \times 175,000 = 0.25 \times 175,000 = 43,750
\]

So, the loan amount is:

\[
\text{Loan amount} = 175,000 - 43,750 = 131,250
\]

### Step 2: Set up the loan parameters
The loan is for 30 years with an annual interest rate of 12.5%, which means the monthly interest rate is:

\[
\text{Monthly interest rate} = \frac{12.5\%}{12} = \frac{0.125}{12} = 0.01041667
\]

The loan term is 30 years, which is:

\[
\text{Loan term in months} = 30 \times 12 = 360 \text{ months}
\]

### Step 3: Calculate the monthly payment using the mortgage formula
The formula for the monthly mortgage payment is:

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

Where:
- $P$ is the loan amount (\$131,250),
- $r$ is the monthly interest rate (0.01041667),
- $n$ is the number of months (360).

Substitute the values into the formula:

\[
M = 131,250 \times \frac{0.01041667(1+0.01041667)^{360}}{(1+0.01041667)^{360} - 1}
\]

Let me calculate the monthly payment.The monthly mortgage payment is approximately \$1,400.78.

### Step 4: Calculate the interest and principal for the second month's payment

For the second month, we first need to determine the interest applied to the remaining balance and the portion of the payment that will reduce the principal.

#### Interest for the second month:
The balance after the first month is still close to the original loan amount since little principal is paid early on in a fixed-rate mortgage. In the first month, the interest is:

\[
\text{First month's interest} = \text{Loan amount} \times \text{Monthly interest rate}
= 131,250 \times 0.01041667 = 1,367.71
\]

The remaining part of the first payment goes towards the principal:

\[
\text{Principal payment (first month)} = 1,400.78 - 1,367.71 = 33.07
\]

After the first month, the new principal balance is:

\[
\text{New balance} = 131,250 - 33.07 = 131,216.93
\]

Now, for the second month, the interest will be:

\[
\text{Second month's interest} = 131,216.93 \times 0.01041667
\]

Let's calculate the interest for the second month and determine the principal payment.For the second month's mortgage payment:
- Interest: \$1,366.84
- Principal: \$33.94

This shows how the majority of the payment in the early months goes toward interest, with only a small portion applied to the principal.

Would you like more details or have any further questions?

Here are some related questions:
1. How does the amortization schedule change over time?
2. What impact does making extra payments toward the principal have?
3. How is the total interest over the loan term calculated?
4. How do different interest rates affect monthly payments?
5. What is the effect of a shorter loan term on interest paid?

**Tip:** Making extra payments toward the principal early on can significantly reduce the total interest paid over the life of the loan.

You purchase a cottage for $175,000. You obtain a 30-year, fixed-rate mortgage loan at 12.5% after paying a down payment of 25%. Of the second month's mortgage payment, how much is interest and how much is applied to the principal?

Learn how to calculate the interest and principal for the second month of a 30-year, fixed-rate mortgage loan on a $175,000 cottage with a 12.5% annual interest rate. This example walks through loan amortization, monthly payment formulas, and the breakdown of interest and principal payments.

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