Suppose you obtain a 30-year home mortgage in the amount of $201,000 with an APR of 5.00%, compounded monthly. Find the total amount of interest paid over the term of the mortgage.

$228,331

$187,444

$164,208

$160,979

None of the above

To determine the total amount of interest paid over the term of the mortgage, we need to use the following mortgage formula:

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

Where:
- $ M $ is the monthly mortgage payment.
- $ P $ is the principal loan amount ($201,000).
- $ r $ is the monthly interest rate (APR divided by 12).
- $ n $ is the total number of payments (30 years × 12 months per year).

### Step 1: Find the monthly interest rate
The annual percentage rate (APR) is 5.00%, so the monthly interest rate is:
\[
r = \frac{5\%}{12} = \frac{0.05}{12} = 0.004167
\]

### Step 2: Find the total number of payments
The mortgage term is 30 years, and there are 12 months in a year, so the total number of payments is:
\[
n = 30 \times 12 = 360 \text{ payments}
\]

### Step 3: Calculate the monthly payment
Now we use the formula to calculate the monthly payment:
\[
M = \frac{201,000 \cdot 0.004167 \cdot (1 + 0.004167)^{360}}{(1 + 0.004167)^{360} - 1}
\]

Let me calculate this.The monthly mortgage payment $ M $ is approximately \$1,079.01.

### Step 4: Calculate the total amount paid over the 30 years
The total amount paid over the life of the mortgage is:
\[
\text{Total Paid} = M \times n = 1,079.01 \times 360
\]

Let me compute that.The total amount paid over the life of the mortgage is approximately \$388,444.13.

### Step 5: Calculate the total interest paid
The total interest paid is the difference between the total amount paid and the original loan amount:
\[
\text{Interest Paid} = \text{Total Paid} - P = 388,444.13 - 201,000
\]

Let me compute that.The total interest paid over the term of the mortgage is approximately \$187,444.13.

Thus, the correct answer is **\$187,444**, which matches one of the provided options.

Would you like further clarification or details on this process?

Here are 5 related questions to deepen your understanding:
1. How does the mortgage payment change with a higher interest rate?
2. What happens to the total interest if the loan term is shortened to 15 years?
3. How is the mortgage payment affected if the loan amount is increased to \$300,000?
4. What is the difference between APR and nominal interest rate?
5. How does bi-weekly payment scheduling affect total interest?

**Tip:** Always aim to pay extra towards the principal when possible to reduce the total interest paid over the life of the loan.

Learn how to calculate the total interest paid on a 30-year mortgage of $201,000 with a 5.00% APR compounded monthly. This detailed solution covers mortgage formulas, monthly payment calculation, and the total interest of $187,444. Suitable for advanced high school and college-level students.

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