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Felix is purchasing a brownstone townhouse for $\$ 2,900,000$. To obtain the mortgage, Felix is required to make a $19 \%$ down payment. Felix obtains a 25 -year mortgage with an interest rate of $5.5 \%$.
Click the icon to view the table of monthly payments.
a) Determine the amount of the required down payment.
b) Determine the amount of the mortgage.
c) Determine the monthly payment for principal and interest.
a) Determine the amount of the required down payment.
$\$ \square$
b) Determine the amount of the mortgage.
$\$ \square$
c) Determine the monthly payment for principal and interest.
$\$ \square$ (Round to the nearest cent.)

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).