Compare the monthly payment and total payment for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.
You need a ​$180 comma 000 loan.
Option​ 1: a​ 30-year loan at an APR of 9​%.
Option​ 2: a​ 15-year loan at an APR of 8​%.
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Part 1
Find the monthly payment for each option.
The monthly payment for option 1 is ​$
  
enter your response here.
The monthly payment for option 2 is ​$
  
enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To find the monthly payment for each loan option, we can use the standard formula for monthly mortgage payments:

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

Where:
- $M$ is the monthly payment,
- $P$ is the loan principal (in this case, $180,000),
- $r$ 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).

### Option 1: 30-year loan at 9% APR
- Annual interest rate: 9%, so the monthly interest rate $r = \frac{9\%}{12} = 0.0075$.
- Total number of payments $n = 30 \times 12 = 360$.

Now, let's calculate the monthly payment for option 1.

### Option 2: 15-year loan at 8% APR
- Annual interest rate: 8%, so the monthly interest rate $r = \frac{8\%}{12} = 0.00667$.
- Total number of payments $n = 15 \times 12 = 180$.

Let's calculate the monthly payment for option 2 as well. I'll now compute both monthly payments.The monthly payments for each option are:

- **Option 1 (30-year loan at 9% APR):** $1,448.32
- **Option 2 (15-year loan at 8% APR):** $1,720.17

Let me know if you want more details on how these were calculated or if you'd like to see the total payments over the life of each loan.

Here are five related questions:
1. What is the total payment for each option over the full loan term?
2. How much more in total interest is paid for the 30-year loan versus the 15-year loan?
3. How would the payments change if the APR for the 30-year loan decreased by 1%?
4. What would the monthly payment be for a 20-year loan at 7% APR?
5. What factors should be considered when choosing between a shorter and longer loan term?

**Tip:** A shorter loan term generally means less interest paid overall, but the trade-off is higher monthly payments.

Compare the monthly payment and total payment for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. You need a $180,000 loan. Option 1: a 30-year loan at an APR of 9%. Option 2: a 15-year loan at an APR of 8%. Find the monthly payment for each option.

This guide compares the monthly and total payments for two loan options: a 30-year loan at 9% APR and a 15-year loan at 8% APR. Using the loan amortization formula, we find that the 30-year loan's monthly payment is $1,448.32, while the 15-year loan's monthly payment is $1,720.17. Explore detailed calculations and insights on choosing the right loan term.

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