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 ​$1190,000 loan.

Option​ 1: a​ 30-year loan at an APR of 8.5​%.

Option​ 2: a​ 15-year loan at an APR of 7..5​%.

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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 use the formula for calculating the monthly payment on a fixed-rate mortgage:

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

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

Let's calculate the monthly payments for each option.

### Option 1: 30-year loan at an APR of 8.5%
- Loan amount $P = 1,190,000$
- Annual interest rate = 8.5%, so the monthly interest rate $r = \frac{8.5\%}{12} = \frac{0.085}{12} = 0.007083$
- Loan term = 30 years, so $n = 30 \times 12 = 360$ months.

### Option 2: 15-year loan at an APR of 7.5%
- Loan amount $P = 1,190,000$
- Annual interest rate = 7.5%, so the monthly interest rate $r = \frac{7.5\%}{12} = \frac{0.075}{12} = 0.00625$
- Loan term = 15 years, so $n = 15 \times 12 = 180$ months.

I'll calculate the monthly payments for both options.The monthly payments for the two loan options are as follows:

- **Option 1** (30-year loan at 8.5% APR): \$9,150.07
- **Option 2** (15-year loan at 7.5% APR): \$11,031.45

Would you like to proceed with calculating the total payments or ask about anything else?

### Related Questions:
1. What is the total interest paid for each loan?
2. How do shorter loan terms impact the total interest paid?
3. What would the monthly payment be if the APR was reduced by 0.5%?
4. How do different loan terms affect affordability over time?
5. What happens if you pay extra towards principal each month?

### Tip:
Shorter loan terms often lead to lower overall interest costs, but the monthly payments are higher.

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 ​$1,190,000 loan. Option​ 1: a​ 30-year loan at an APR of 8.5​%. Option​ 2: a​ 15-year loan at an APR of 7.5​%. Find the monthly payment for each option.

Calculate and compare the monthly payments for a $1,190,000 loan at 8.5% APR over 30 years and 7.5% APR over 15 years. Understand the formulas behind fixed-rate mortgage calculations and how loan terms affect monthly payments. Suitable for Grades 10-12.

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