Find the monthly house payments necessary to amortize the following loan. Then calculate the total payments and the total amount of interest paid.

198,000 

at 

6.93%

for 

15

years




Let's calculate the monthly house payments, total payments, and the total interest paid using the amortization formula.

### Given:
- Principal $ P = 198,000 $
- Annual interest rate $ r = 6.93\% $
- Loan term $ n = 15 $ years

### Step 1: Calculate the Monthly Interest Rate
The annual interest rate needs to be converted to a monthly interest rate:
\[
\text{Monthly Interest Rate} = \frac{6.93}{100 \times 12} = \frac{6.93}{1200} = 0.005775
\]

### Step 2: Calculate the Number of Monthly Payments
The number of monthly payments is:
\[
n = 15 \times 12 = 180 \text{ payments}
\]

### Step 3: Use the Amortization Formula
The formula to calculate the monthly payment $ M $ is:
\[
M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\]

### Step 4: Calculate Total Payments and Interest
Once we have the monthly payment, we can calculate the total payments as:
\[
\text{Total Payments} = M \times n
\]
And the total interest paid is:
\[
\text{Total Interest} = \text{Total Payments} - P
\]

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Calculate the monthly house payments, total payments, and total interest paid for a $198,000 loan at 6.93% interest over 15 years using the amortization formula. Understand the financial mathematics behind loan amortization with a detailed step-by-step solution.

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