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.)
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Find the total interest paid on the loan.

To find the monthly payment needed to amortize a mortgage loan, we can use the formula for the monthly payment on an amortized loan:

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

Where:
- $ M $ is the monthly payment
- $ P $ is the principal loan amount (\$225,000)
- $ r $ is the monthly interest rate (annual interest rate divided by 12)
- $ n $ is the total number of payments (loan term in years multiplied by 12)

### Step 1: Calculate the monthly interest rate

The annual interest rate is 3.5%, so the monthly interest rate is:

\[
r = \frac{3.5\%}{12} = \frac{0.035}{12} = 0.0029167
\]

### Step 2: Calculate the total number of payments

Since the loan term is 30 years, the total number of monthly payments is:

\[
n = 30 \times 12 = 360
\]

### Step 3: Plug values into the formula

\[
M = \frac{225,000 \cdot 0.0029167 \cdot (1 + 0.0029167)^{360}}{(1 + 0.0029167)^{360} - 1}
\]

Now, let's calculate this.The monthly payment required to amortize the $225,000 mortgage loan over 30 years at an annual interest rate of 3.5% is approximately **$1,010.35**.

### Step 4: Calculate the total interest paid

The total interest paid on the loan can be found by subtracting the principal from the total amount paid over the life of the loan:

\[
\text{Total Interest} = M \times n - P
\]

Let’s calculate that.It seems like I can’t do more advanced data analysis right now. Please try again later.

To manually calculate the total interest:

1. Multiply the monthly payment by the total number of payments:
   \[
   1010.35 \times 360 = 363,726
   \]
2. Subtract the principal from the total payment:
   \[
   363,726 - 225,000 = 138,726
   \]

The total interest paid on the loan is approximately **$138,726**.

Would you like to review the details or ask any questions? 

Here are 5 related questions:
1. How does the loan term affect the monthly payment amount?
2. What is the effect of a higher interest rate on total interest paid?
3. How would bi-weekly payments impact loan amortization?
4. Can you compare amortized loans with interest-only loans?
5. How do extra monthly payments reduce total interest?

**Tip:** Making additional payments can significantly reduce the total interest paid over the life of a 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. Find the total interest paid on the loan.

Discover how to calculate the monthly payment for a $225,000 mortgage loan amortized over 30 years at a 3.5% annual interest rate, compounded monthly. Learn the detailed steps and formulas to find the monthly payment and the total interest paid over the life of the loan. This problem involves concepts like amortization and compound interest, suitable for Grades 10-12.

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