 Find the monthly mortgage payment on the following mortgages.


 $153,000 at 4.5% interest amortized over 30 years. 

To calculate the monthly mortgage payment, we use the formula for a fixed-rate mortgage:

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

Where:  
- $M$ is the monthly payment  
- $P$ is the loan amount (\$153,000)  
- $r$ 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)

### Given:
- $P = 153,000$
- Annual interest rate = $4.5\%$ ($0.045$ as a decimal)
- Loan term = $30$ years

### Step 1: Convert the interest rate to a monthly rate
\[
r = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375
\]

### Step 2: Calculate the total number of payments
\[
n = 30 \cdot 12 = 360
\]

### Step 3: Plug the values into the formula
\[
M = 153,000 \cdot \frac{0.00375(1 + 0.00375)^{360}}{(1 + 0.00375)^{360} - 1}
\]

### Step 4: Calculate step-by-step:
1. $1 + r = 1 + 0.00375 = 1.00375$
2. $(1 + r)^{360} = 1.00375^{360} \approx 3.8503$
3. $r(1 + r)^{360} = 0.00375 \cdot 3.8503 \approx 0.014439$
4. $(1 + r)^{360} - 1 = 3.8503 - 1 = 2.8503$
5. $\frac{0.014439}{2.8503} \approx 0.005068$

### Step 5: Calculate the monthly payment:
\[
M = 153,000 \cdot 0.005068 \approx 775.41
\]

### Final Answer:
The monthly mortgage payment is approximately **\$775.41**.

Would you like me to expand on any steps or assumptions? 

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### Related Questions:
1. What would the monthly payment be for a 15-year term instead of 30 years?
2. How does changing the interest rate to 5% affect the monthly payment?
3. What is the total interest paid over the life of this mortgage?
4. Can you calculate the remaining balance after 10 years of payments?
5. How would a larger down payment impact the monthly payment?

### Tip:
Double-check your calculations using an online mortgage calculator to verify results quickly!

Find the monthly mortgage payment on the following mortgages: $153,000 at 4.5% interest amortized over 30 years.

Learn how to calculate the monthly mortgage payment for a $153,000 loan at 4.5% interest over 30 years. This detailed solution explains key concepts in financial mathematics, including the fixed-rate mortgage payment formula. Suitable for high school students and financial beginners.

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