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Part 1

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.

You need a ​$100,000 loan.

Option​ 1: a​ 30-year loan at an APR of 9.5​%.

Option​ 2: a​ 15-year loan at an APR of 9.05​%.

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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 payments for each loan option, we will use the **loan amortization formula**:

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

Where:
- $ M $ is the monthly payment,
- $ P $ is the loan amount,
- $ r $ is the monthly interest rate (annual 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 9.5% APR
- $ P = 100,000 $
- Annual interest rate = 9.5% or 0.095, so monthly interest rate $ r = \frac{0.095}{12} = 0.00791667 $
- Loan term = 30 years, so total number of payments $ n = 30 \times 12 = 360 $

### Option 2: 15-year loan at 9.05% APR
- $ P = 100,000 $
- Annual interest rate = 9.05% or 0.0905, so monthly interest rate $ r = \frac{0.0905}{12} = 0.00754167 $
- Loan term = 15 years, so total number of payments $ n = 15 \times 12 = 180 $

Now, I will calculate the monthly payments for both options.The monthly payments for each loan option are as follows:

- **Option 1 (30-year loan at 9.5% APR)**: \$840.85
- **Option 2 (15-year loan at 9.05% APR)**: \$1017.24

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How does the total interest paid differ between the two loan options?
2. What is the total loan cost (principal + interest) for each option?
3. How does changing the interest rate impact monthly payments?
4. What are the benefits of choosing a shorter loan term despite higher monthly payments?
5. How would an extra monthly payment towards the principal affect each loan's term and total cost?

**Tip:** Paying more than the required monthly payment can significantly reduce the overall loan cost by reducing the principal faster.

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.
You need a $100,000 loan.
Option 1: a 30-year loan at an APR of 9.5%.
Option 2: a 15-year loan at an APR of 9.05%.
Find the monthly payment for each option.

Compare the monthly payments for a $100,000 loan with two different options: a 30-year loan at 9.5% APR and a 15-year loan at 9.05% APR. Learn how to use the loan amortization formula to calculate monthly payments and understand the financial implications of each loan term.

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