Brad decides to purchase a $190,000
 house. He wants to finance the entire balance. He has received an APR of 3.7%
 for a 15
-year mortgage. Over the course of the loan, how much interest will Brad pay? Round your answer to the nearest hundredth.
 

To calculate the total interest Brad will pay over the life of the loan, we need to follow these steps:

### Step 1: Calculate the monthly interest rate
The annual percentage rate (APR) is 3.7%. We need to convert it into a monthly interest rate.
\[
\text{Monthly interest rate} = \frac{3.7\%}{12} = \frac{0.037}{12} = 0.0030833
\]

### Step 2: Calculate the number of monthly payments
Since Brad is financing the house with a 15-year mortgage, the total number of monthly payments is:
\[
\text{Total number of payments} = 15 \times 12 = 180 \text{ months}
\]

### Step 3: Calculate the monthly payment using the loan payment formula
The mortgage formula is:
\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- $M$ is the monthly payment
- $P$ is the principal loan amount ($190,000)
- $r$ is the monthly interest rate (0.0030833)
- $n$ is the number of payments (180)

Substitute the values into the formula:
\[
M = 190,000 \times \frac{0.0030833(1+0.0030833)^{180}}{(1+0.0030833)^{180} - 1}
\]

Let me calculate the monthly payment and the total interest Brad will pay.Brad's monthly mortgage payment will be approximately \$1,377.01. Over the course of the 15-year loan, the total interest he will pay is approximately **\$57,862.58**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the total amount Brad will pay, including the house price and interest?
2. How would the interest change if the mortgage term were 30 years instead of 15?
3. What if Brad made extra payments each month — how would that affect the total interest?
4. How much would Brad save if he received an APR of 3.0% instead of 3.7%?
5. How can refinancing the mortgage after 5 years impact the total interest?

**Tip:** Making additional payments toward the principal can significantly reduce the total interest paid over the life of a loan.

Brad decides to purchase a $190,000 house. He wants to finance the entire balance. He has received an APR of 3.7% for a 15-year mortgage. Over the course of the loan, how much interest will Brad pay? Round your answer to the nearest hundredth.

Find out how much interest Brad will pay on a $190,000 loan with a 15-year mortgage at 3.7% APR. This step-by-step guide uses the loan amortization formula to calculate monthly payments and total interest. Suitable for Grades 10-12 students learning finance and exponential functions.

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