Richard Miyashiro purchased a condominium and obtained a 30-year loan of $194,000 at an annual interest rate of 8.45%. Find the amount of interest paid on the mortgage loan over the 30 years.

To find the amount of interest paid on the mortgage loan over 30 years, we can follow these steps:

### Step 1: Break down the loan terms
- Principal amount (loan): $ P = 194,000 $
- Annual interest rate: $ r = 8.45\% $ or $ 0.0845 $
- Loan term: $ t = 30 $ years
- Loan payments are typically made monthly, so the number of months is $ n = 30 \times 12 = 360 $.

### Step 2: Calculate the monthly interest rate
The monthly interest rate is:
\[
\text{Monthly interest rate} = \frac{0.0845}{12} = 0.00704167
\]

### Step 3: Use the formula for monthly mortgage payments
The formula to calculate the monthly mortgage payment is:
\[
M = \frac{P \cdot r_m \cdot (1 + r_m)^n}{(1 + r_m)^n - 1}
\]
Where:
- $ M $ is the monthly payment
- $ P $ is the loan amount
- $ r_m $ is the monthly interest rate
- $ n $ is the number of payments (360)

### Step 4: Calculate total paid and interest paid
Once we calculate the monthly payment, we can find the total amount paid over 30 years and subtract the principal to find the interest paid.

Let me calculate this for you.### Solution:

- The monthly mortgage payment is approximately **$1,484.82**.
- The total amount paid over the 30-year loan term is approximately **$534,536.33**.
- The total interest paid over the life of the loan is approximately **$340,536.33**.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How does changing the loan term affect the total interest paid?
2. What would the monthly payment be if the interest rate was reduced to 6%?
3. How much interest would be paid if the loan was repaid in 15 years instead of 30 years?
4. What would happen to the monthly payment if an additional $500 was paid each month?
5. How does the down payment size affect the overall interest on the loan?

**Tip:** Making extra payments early in the mortgage reduces the principal faster, lowering the overall interest paid.

Richard Miyashiro purchased a condominium and obtained a 30-year loan of $194,000 at an annual interest rate of 8.45%. Find the amount of interest paid on the mortgage loan over the 30 years.

Learn how to calculate the total interest paid on a 30-year mortgage loan of $194,000 at an annual interest rate of 8.45%. This problem involves calculating monthly payments, total loan amount, and the interest paid using the loan amortization formula. Suitable for advanced high school or college students.

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