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? do the whole question

We are tasked with calculating the interest and principal components of the second month's mortgage payment, based on the following conditions:

- Purchase price: $185,000
- Down payment: 25%
- Mortgage term: 20 years
- Annual interest rate: 13.0%
- Mortgage payments are monthly.

### Step 1: Calculate the Loan Amount
Since you made a 25% down payment, the remaining 75% of the purchase price is financed through the mortgage.

\[
\text{Down payment} = 25\% \times 185,000 = 0.25 \times 185,000 = 46,250
\]

The loan amount (mortgage principal) is the remainder:

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

### Step 2: Monthly Interest Rate and Number of Payments
Since the interest rate is annual, we need to convert it to a monthly rate and calculate the total number of monthly payments.

\[
\text{Monthly interest rate} = \frac{13\%}{12} = \frac{0.13}{12} \approx 0.010833
\]

The number of monthly payments over 20 years is:

\[
\text{Total number of payments} = 20 \times 12 = 240
\]

### Step 3: Monthly Mortgage Payment (Using the Loan Amortization Formula)
The formula for the monthly mortgage payment $ M $ 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: $ 0.010833 $
- $ n $ is the number of payments: $ 240 $

Let's calculate $ M $.The monthly mortgage payment is approximately $ M = 1625.56 $.

### Step 4: Breakdown of the Second Month's Payment

For the second month, we will calculate:
1. The interest portion.
2. The amount applied to the principal.

#### Interest for the First Month:
The interest is calculated as the outstanding loan balance multiplied by the monthly interest rate.

At the beginning of the loan (before the first payment), the full principal of $138,750 is outstanding. The interest portion of the first month's payment is:

\[
\text{Interest (Month 1)} = 138,750 \times 0.010833 \approx 1503.13
\]

The remaining amount from the first payment is applied to the principal:

\[
\text{Principal applied (Month 1)} = 1625.56 - 1503.13 = 122.43
\]

Thus, the remaining loan balance after the first payment is:

\[
\text{Remaining balance} = 138,750 - 122.43 = 138,627.57
\]

#### Interest for the Second Month:
For the second month, the interest is based on the remaining balance of $138,627.57.

\[
\text{Interest (Month 2)} = 138,627.57 \times 0.010833 \approx 1501.75
\]

The amount applied to the principal in the second month is:

\[
\text{Principal applied (Month 2)} = 1625.56 - 1501.75 = 123.81
\]

### Final Answer:
- Interest for the second month: \$1501.75
- Principal applied in the second month: \$123.81

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the payment breakdown change if the interest rate were lower?
2. How does the down payment affect the total interest paid over the loan term?
3. What is the total amount of interest paid over the entire mortgage?
4. How does the length of the loan affect monthly payments?
5. How does early repayment of the principal affect the interest?

**Tip**: The earlier you make extra principal payments, the more you save on interest 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 breakdown of the second month's mortgage payment, including interest and principal, for a $185,000 cottage purchased with a 20-year fixed mortgage at a 13% interest rate and a 25% down payment. This step-by-step solution explains loan amortization and the formulas involved.

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