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.