Spencer and Camilla bought a modest home right after their wedding (Spencer did not want to live with his in-laws). The price of the home was $120,000, and they took out a $100,000 15-year mortgage with an interest rate of 3.33% on the home. If they take the full 15-year term to pay off the loan, how much total interest will they end up paying on the loan?
(Round payment to two decimal places.)

To determine the total interest Spencer and Camilla will pay on their 15-year mortgage, we need to calculate the monthly mortgage payment and then find the total payment over the 15-year period.

### Step 1: Calculate the Monthly Mortgage Payment

The formula for the monthly mortgage payment $ M $ is given by:
\[
M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]
where:
- $ P $ is the loan principal ($100,000)
- $ r $ is the monthly interest rate (annual rate divided by 12)
- $ n $ is the total number of payments (number of years times 12)

First, we convert the annual interest rate to a monthly rate:
\[
r = \frac{3.33\%}{12} = \frac{0.0333}{12} = 0.002775
\]

Next, we find the total number of payments:
\[
n = 15 \times 12 = 180
\]

Now, we plug these values into the formula for $ M $:
\[
M = 100,000 \times \frac{0.002775(1 + 0.002775)^{180}}{(1 + 0.002775)^{180} - 1}
\]

### Step 2: Compute the Value Inside the Formula

1. Compute $(1 + r)^{180}$:
\[
(1 + 0.002775)^{180} \approx 1.600327
\]

2. Compute the numerator:
\[
0.002775 \times 1.600327 \approx 0.004442
\]

3. Compute the denominator:
\[
1.600327 - 1 = 0.600327
\]

4. Now, compute $ M $:
\[
M = 100,000 \times \frac{0.004442}{0.600327} \approx 100,000 \times 0.007397 \approx 739.70
\]

### Step 3: Calculate the Total Payment Over the Loan Period

The total amount paid over the 15-year period is:
\[
\text{Total Payment} = M \times n = 739.70 \times 180 = 133,146
\]

### Step 4: Calculate the Total Interest Paid

The total interest paid is the total payment minus the principal:
\[
\text{Total Interest} = \text{Total Payment} - P = 133,146 - 100,000 = 33,146
\]

Therefore, Spencer and Camilla will pay **$33,146** in total interest over the 15-year period.

Would you like further details or have any questions? 

Here are some related questions you might find useful:
1. How would the total interest change if the interest rate were 4% instead of 3.33%?
2. What would the monthly payment be for a 30-year mortgage at the same interest rate?
3. How much interest is paid in the first year of the mortgage?
4. How does the principal balance decrease over the first five years?
5. What is the impact of making an extra payment of $100 per month on the total interest paid?
6. How would refinancing to a lower interest rate after 5 years affect the total interest?
7. What is the remaining balance after 10 years?
8. How do property taxes and insurance typically affect monthly mortgage payments?

**Tip:** Understanding how to calculate mortgage payments and interest can help you make better financial decisions when buying a home.

Learn how to calculate the total interest paid on a mortgage with a detailed example. This problem involves mortgage calculations and compound interest concepts. Suitable for adults interested in financial planning.

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