Consider a home mortgage of $\$ 150,000$ at a fixed APR of $6 \%$ for 30 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Step 1 ：Given a home mortgage of $150,000 at a fixed APR of 6% for 30 years, we are asked to calculate the monthly payment, determine the total amount paid over the term of the loan, and find out what percentage is paid toward the principal and what percentage is paid for interest.

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

Step 3 ：Substituting the given values into the formula, we get: \[M = 150000\left[\frac{0.005(1+0.005)^{360}}{(1+0.005)^{360} – 1}\right]\] which simplifies to approximately $899.33.

Step 4 ：To find the total amount paid over the term of the loan, we multiply the monthly payment by the number of payments: \[total = M \times n = 899.33 \times 360\] which equals approximately $323,757.28.

Step 5 ：To find the percentage paid toward the principal and the percentage paid for interest, we subtract the principal from the total amount paid to find the total interest paid. Then, we divide the principal and the total interest by the total amount paid and multiply by 100 to get the percentages.

Step 6 ：Calculating the total interest paid, we get: \[total\_interest = total\_paid - P = 323757.28 - 150000\] which equals approximately $173,757.28.

Step 7 ：Calculating the percentages, we get: \[principal\_percentage = \frac{P}{total\_paid} \times 100 = \frac{150000}{323757.28} \times 100\] which equals approximately 46.33%, and \[interest\_percentage = \frac{total\_interest}{total\_paid} \times 100 = \frac{173757.28}{323757.28} \times 100\] which equals approximately 53.67%.

Step 8 ：\(\boxed{\text{Final Answer:}}\) a. The monthly payment is approximately $899.33. b. The total amount paid over the term of the loan is approximately $323,757.28. c. Of the total amount paid, approximately 46.33% is paid toward the principal and approximately 53.67% is paid for interest.