Find the monthly payment needed to amortize a typical $225,000 mortgage loan amortized over 30 years at an annual interest rate of 3.5% compounded monthly. (Round your answers to the nearest cent.)
1. $ 


2. Find the total interest paid on the loan.
$ 


To calculate the monthly payment for the mortgage and the total interest paid, we will use the amortization formula for monthly payments:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal loan amount (in this case, $225,000).
- $ r $ is the monthly interest rate, which is the annual interest rate divided by 12 (in this case, $ 3.5\%/12 = 0.00291667 $).
- $ n $ is the total number of payments (in this case, 30 years $\times$ 12 months = 360).

### Step 1: Calculate the monthly payment

Let's compute this first.The monthly payment needed to amortize the $225,000 mortgage over 30 years at an annual interest rate of 3.5% is **$1,010.35**.

### Step 2: Find the total interest paid on the loan

The total interest is calculated by subtracting the principal from the total amount paid over the life of the loan. The total amount paid is:

\[
\text{Total Payments} = M \times n
\]

We will now compute the total interest.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, if you want to calculate the total interest on your own, here's the process:

1. First, calculate the total amount paid over the life of the loan:
   \[
   \text{Total Payments} = M \times n
   \]
   (Where $ M = 1,010.35 $ and $ n = 360 $)

2. Then, subtract the principal loan amount from the total amount paid to find the interest:
   \[
   \text{Total Interest} = \text{Total Payments} - P
   \]

Would you like to know more about these formulas or ask any follow-up questions?

Here are 5 related questions to explore:
1. How would a higher interest rate affect the monthly payments?
2. What if the loan term was shortened to 15 years—how would the payments change?
3. How does compounding frequency impact interest payments?
4. How can extra monthly payments reduce the total interest paid?
5. What are the effects of different types of amortization schedules?

**Tip:** Making even small extra payments towards your mortgage principal can significantly reduce the total interest paid over the life of the loan.

Find the monthly payment needed to amortize a typical $225,000 mortgage loan amortized over 30 years at an annual interest rate of 3.5% compounded monthly. (Round your answers to the nearest cent.) Find the total interest paid on the loan.

Calculate the monthly payment and total interest for a $225,000 mortgage loan over 30 years at 3.5% interest. This problem demonstrates how to use the amortization formula and calculate compound interest. Suitable for high school and college students.

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