Step 1 :The total cost of the townhouse is \$2,900,000.
Step 2 :The required down payment is 19% of the total cost. So, the down payment is \(0.19 \times 2,900,000 = \$551,000\).
Step 3 :The amount of the mortgage can be calculated by subtracting the down payment from the total cost. So, the mortgage is \(2,900,000 - 551,000 = \$2,349,000\).
Step 4 :The monthly payment for principal and interest can be calculated using the formula for monthly mortgage payments: \(M = P[r(1+r)^n]/[(1+r)^n – 1]\), where M is the monthly payment, P is the principal loan amount, r is the monthly interest rate (calculated by dividing the annual interest rate by 12), and n is the number of payments (the number of months you will be paying the loan).
Step 5 :Substituting the given values into the formula, we get: \(M = 2,349,000[0.004583333333333333(1+0.004583333333333333)^300]/[(1+0.004583333333333333)^300 – 1] = \$14,424.92\).
Step 6 :So, the final answers are: a) The amount of the required down payment is \(\boxed{\$551,000}\). b) The amount of the mortgage is \(\boxed{\$2,349,000}\). c) The monthly payment for principal and interest is \(\boxed{\$14,424.92}\) (rounded to the nearest cent).