Final answer:
To calculate the woman's monthly mortgage payment and total interest paid, one can use the fixed-rate mortgage formula, which takes into account the principal after down payment, monthly interest rate, and total number of payments.
Step-by-step explanation:
The woman bought a house for $340,000, paid a $40,000 down payment, and took out a mortgage for the balance at a 5.7% interest rate for 20 years. To find her monthly payment and the total amount of interest she will pay, we can use the formula for fixed-rate mortgages:
M = P[r(1+r)^n] / [(1+r)^n - 1]
Where:
M = monthly payment
P = principal loan amount ($340,000 - $40,000 = $300,000)
r = monthly interest rate (5.7% annual rate / 12 months = 0.00475)
n = number of payments (20 years * 12 months = 240 payments)
Substituting the values, we calculate her monthly payment and then multiply by the number of payments to find the total cost of the mortgage. Subtracting the principal from the total cost gives us the total interest paid.