You purchase a cottage for $185,000. You obtain a 20-year, fixed rate mortgage loan at 13.0% 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? (Round your answers to the nearest cent.)

Let's break down the problem step by step:

1. **Find the down payment**:
   The down payment is 25% of the cottage price.

   \[
   \text{Down payment} = 185,000 \times 0.25 = 46,250
   \]

2. **Find the loan amount**:
   The loan amount is the total price of the cottage minus the down payment.

   \[
   \text{Loan amount} = 185,000 - 46,250 = 138,750
   \]

3. **Calculate the monthly interest rate**:
   The annual interest rate is 13%, so the monthly interest rate is:

   \[
   \text{Monthly interest rate} = \frac{13\%}{12} = 0.01083 \text{ (rounded to 5 decimal places)}
   \]

4. **Use the loan amount and monthly interest rate to calculate the monthly mortgage payment**:

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

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

   Where:
   - $P$ is the loan amount = 138,750
   - $r$ is the monthly interest rate = 0.01083
   - $n$ is the total number of payments = 20 years × 12 months = 240

   Let's compute this step next.The monthly mortgage payment is approximately \$1,625.56.

Now, let's calculate the interest and principal portions of the second month's payment:

5. **Interest for the first month**:
   The interest for the first month is calculated on the entire loan amount (since no principal has been paid yet):

   \[
   \text{First month's interest} = 138,750 \times 0.01083 \approx 1,502.31
   \]

   The remainder of the first payment goes toward the principal:

   \[
   \text{Principal payment in the first month} = 1,625.56 - 1,502.31 \approx 123.25
   \]

6. **Loan balance after the first month**:
   After the first month's payment, the remaining balance on the loan is reduced by the amount applied to the principal:

   \[
   \text{New loan balance} = 138,750 - 123.25 = 138,626.75
   \]

7. **Interest for the second month**:
   The interest for the second month is calculated on the new loan balance:

   \[
   \text{Second month's interest} = 138,626.75 \times 0.01083 \approx 1,501.10
   \]

8. **Principal payment for the second month**:
   The remainder of the second month's payment goes toward the principal:

   \[
   \text{Principal payment in the second month} = 1,625.56 - 1,501.10 \approx 124.46
   \]

Thus, for the second month's payment:
- The interest portion is approximately \$1,501.10.
- The principal portion is approximately \$124.46.

Would you like more details on any step or clarifications? 

Here are 5 related questions:
1. How would the monthly payment change with a lower interest rate?
2. How much total interest would you pay over the life of the loan?
3. What is the loan balance after 1 year?
4. How would additional principal payments affect the loan term?
5. What happens if the interest rate changes on an adjustable-rate mortgage?

**Tip**: Making extra payments on the principal can significantly reduce the total interest you pay over the life of the loan.

You purchase a cottage for $185,000. You obtain a 20-year, fixed rate mortgage loan at 13.0% 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 second month's interest and principal payment on a $185,000 cottage, given a 20-year, fixed-rate mortgage at 13.0% interest. Includes a breakdown of key mortgage formulas and steps to determine how much goes toward interest versus the principal.

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