Bought a house for $140,000. Down payment 20%.30 year mortgage at 5 1/2% . What’s the total interest of the loan?

To calculate the total interest paid on a 30-year mortgage, we'll follow these steps:

1. **Find the loan amount**:
   Since the down payment is 20%, you'll finance the remaining 80% of the house price.

\[
\text{Loan Amount} = 140,000 \times (1 - 0.20) = 140,000 \times 0.80 = 112,000
\]

2. **Calculate the monthly interest rate**:
   The annual interest rate is 5.5%, so the monthly interest rate is:

\[
\text{Monthly Interest Rate} = \frac{5.5\%}{12} = \frac{0.055}{12} \approx 0.0045833
\]

3. **Find the number of payments**:
   For a 30-year mortgage, the number of monthly payments is:

\[
\text{Number of Payments} = 30 \times 12 = 360
\]

4. **Use the mortgage payment formula**:

\[
M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- $M$ is the monthly payment,
- $P$ is the loan amount (\$112,000),
- $r$ is the monthly interest rate (0.0045833),
- $n$ is the total number of payments (360).

Let's plug in the numbers:

\[
M = 112,000 \times \frac{0.0045833(1 + 0.0045833)^{360}}{(1 + 0.0045833)^{360} - 1}
\]

After calculating this:

\[
M \approx 635.57
\]

5. **Calculate the total amount paid over the life of the loan**:
   Multiply the monthly payment by the total number of payments:

\[
\text{Total Paid} = 635.57 \times 360 = 228,805.20
\]

6. **Find the total interest paid**:
   Subtract the original loan amount from the total paid:

\[
\text{Total Interest} = 228,805.20 - 112,000 = 116,805.20
\]

Thus, the total interest paid over the life of the loan is approximately **$116,805.20**.

Would you like more details or have any questions?

### Related Questions:
1. How would the total interest change if the down payment was 10% instead of 20%?
2. What if the interest rate was 4% instead of 5.5%?
3. How does shortening the loan term to 15 years impact the total interest?
4. How can extra monthly payments affect the total interest paid?
5. What is the benefit of making a larger down payment on the total interest?

**Tip**: Paying off your mortgage early by making extra payments can significantly reduce the total interest paid.

Bought a house for $140,000. Down payment 20%. 30 year mortgage at 5 1/2%. What’s the total interest of the loan?

Find out how to calculate the total interest on a $140,000 house with a 20% down payment and a 30-year mortgage at 5.5%. This detailed guide covers mortgage amortization, loan formulas, and interest calculations. Perfect for high school and college-level math students.

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