Question 15, 4.D.37 Part 1 of 3 HW Score: $0 \%, 0$ of 16 points Points: 0 of 1 Save 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 $\$ 120,000$ loan. Option 1: a 30 -year loan at an APR of $10 \%$. Option 2: a 15 -year loan at an APR of $9.5 \%$. Find the monthly payment for each option. The monthly payment for option 1 is $\$ \square$. The monthly payment for option 2 is $\$ \square$. (Do not round until the final answer. Then round to the nearest cent as needed.)

Step 1 ：We are given a loan of $120,000 and asked to calculate the monthly payment for two options: a 30-year loan at an APR of 10% and a 15-year loan at an APR of 9.5%.

Step 2 ：We use the formula for the monthly payment on a mortgage: \[M = P\left[\frac{r(1+r)^n}{(1+r)^n – 1}\right]\] where: M is the monthly payment, P is the principal loan amount, r is the monthly interest rate (annual interest rate divided by 12), and n is the number of payments (the number of months you will be paying the loan).

Step 3 ：For the first option, we substitute the given values into the formula: \[M = 120000\left[\frac{0.00833(1+0.00833)^{360}}{(1+0.00833)^{360} – 1}\right]\] This simplifies to approximately $1054.01.

Step 4 ：For the second option, we substitute the given values into the formula: \[M = 120000\left[\frac{0.00792(1+0.00792)^{180}}{(1+0.00792)^{180} – 1}\right]\] This simplifies to approximately $1237.09.

Step 5 ：\(\boxed{\text{Final Answer:}}\) The monthly payment for the first option is approximately $1054.01. The monthly payment for the second option is approximately $1237.09.