Final answer:
Using the mortgage payment formula, the monthly payment on a 30-year mortgage of $350,000 at 6% APR is $2,098.96. However, the total interest paid over the life of the loan is $405,625.60, not the amounts listed in the answer choices, making the provided options incorrect relating to the total interest.
Step-by-step explanation:
To find the monthly payment and total interest paid on a 30-year mortgage of $350,000 with an APR of 6%, we need to use the formula for the monthly payment of a fixed-rate mortgage, which is calculated using the loan amount, the monthly interest rate, and the number of payments.
For this loan:
Loan amount (P) = $350,000
Annual interest rate (r) = 6%
Monthly interest rate = 6% ÷ 12 months = 0.5%
Number of payments (n) = 30 years × 12 months/year = 360 payments
The formula for the monthly payment (M) is:
M = P × [i(1 + i)^n] ÷ [(1 + i)^n - 1]
Where i is the monthly interest rate in decimal form (0.5% = 0.005).
Plug the values into the formula:
M = $350,000 × [0.005(1 + 0.005)^360] ÷ [(1 + 0.005)^360 - 1]
This yields a monthly payment of approximately $2,098.96.
To find the total amount paid over the 30 years, you multiply the monthly payment by the number of payments.
Total amount paid = $2,098.96 × 360 = $755,625.60
The total interest paid is the total amount paid minus the original loan amount.
Total interest paid = $755,625.60 - $350,000 = $405,625.60
None of the answer choices provided has the correct total interest figure, but the correct monthly payment of $2,098.96 is provided in options A and B. Therefore, A) and B) are partially correct with the monthly payment, but the total interest figures are incorrect.