Consider a home mortgage of ​$125 comma 000 at a fixed APR of 4.5​% for 15 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.  ​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

We can solve this problem step by step using the standard mortgage formula for monthly payments and then calculate the total amount paid and interest-related percentages.

### Part (a): Monthly Payment Calculation

The formula to calculate the monthly payment for a fixed-rate mortgage is:

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

Where:
- $M$ = monthly payment
- $P$ = loan principal (\$125,000)
- $r$ = monthly interest rate (APR divided by 12)
- $n$ = total number of payments (loan term in months, 15 years = 180 months)

Let's calculate:

1. The monthly interest rate $r$ is the annual rate (4.5%) divided by 12.
   \[
   r = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375
   \]

2. The total number of payments $n$ is:
   \[
   n = 15 \times 12 = 180 \text{ months}
   \]

Now, we can calculate the monthly payment $M$. 

### Part (b): Total Amount Paid

The total amount paid over the life of the loan is simply the monthly payment $M$ multiplied by the total number of payments $n$:
\[
\text{Total Amount Paid} = M \times 180
\]

### Part (c): Percentage Paid Toward Principal and Interest

1. The amount paid toward the principal is simply the original loan amount $P = 125,000$.

2. The amount paid toward interest is the difference between the total amount paid and the principal:
   \[
   \text{Interest Paid} = \text{Total Amount Paid} - P
   \]

3. The percentage paid toward the principal is:
   \[
   \text{Percentage toward Principal} = \frac{P}{\text{Total Amount Paid}} \times 100
   \]

4. The percentage paid toward interest is:
   \[
   \text{Percentage toward Interest} = \frac{\text{Interest Paid}}{\text{Total Amount Paid}} \times 100
   \]

Let's now calculate these values step-by-step.### Results:

**(a)** The monthly payment is approximately **\$956.24**.

**(b)** The total amount paid over the term of the loan is approximately **\$172,123.49**.

**(c)** 
- Percentage paid toward the principal: **72.62%**.
- Percentage paid toward interest: **27.38%**.

Would you like more details on any part of the calculations? 

Here are five related questions to deepen your understanding:
1. How would the monthly payment change with a 30-year mortgage term?
2. What happens to the monthly payment if the interest rate increases to 6%?
3. How much interest would be saved if the loan term were reduced to 10 years?
4. How does making additional monthly payments affect the loan term and total interest?
5. What is the effect of an adjustable-rate mortgage compared to a fixed-rate one?

**Tip**: Always aim to pay a little extra each month to reduce your overall interest over time.

Consider a home mortgage of $125,000 at a fixed APR of 4.5% for 15 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest? (Do not round until the final answer. Then round to the nearest cent as needed.)

Learn how to calculate the monthly payment, total amount paid, and the percentage of interest and principal for a $125,000 mortgage at a 4.5% APR over 15 years. Includes step-by-step instructions for using the loan amortization formula and percentage calculations.

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