Questions: Felix is purchasing a brownstone townhouse for 2,800,000. To obtain the mortgage, Felix is required to make a 16% down payment. Felix obtains a 30-year mortgage with an interest rate of 7.5%. 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. b) Determine the amount of the mortgage. c) Determine the monthly payment for principal and interest. (Round to the nearest cent.)

Felix is purchasing a brownstone townhouse for 2,800,000. To obtain the mortgage, Felix is required to make a 16% down payment. Felix obtains a 30-year mortgage with an interest rate of 7.5%. 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. b) Determine the amount of the mortgage. c) Determine the monthly payment for principal and interest. (Round to the nearest cent.)
Transcript text: Felix is purchasing a brownstone townhouse for $\$ 2,800,000$. To obtain the mortgage, Felix is required to make a $16 \%$ down payment. Felix obtains a 30 -year mortgage with an interest rate of $7.5 \%$. 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. \$ c) Determine the monthly payment for principal and interest. $\$ \square$ (Round to the nearest cent.)
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Solution

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Solution Steps

Step 1: Calculate the Down Payment

To calculate the down payment, multiply the purchase price (\$2800000) by the down payment percentage (16%): \[ \text{Down Payment} = 2800000 \times \frac{16}{100} = \$448000 \]

Step 2: Determine the Mortgage Amount

The mortgage amount is the difference between the purchase price and the down payment: \[ \text{Mortgage Amount} = 2800000 - 448000 = \$2352000 \]

Step 3: Calculate the Monthly Mortgage Payment

Using the formula for the monthly payment, where:

  • Monthly interest rate (r) = 7.5% / 12 / 100
  • Total number of payments (n) = 30 years \times 12 months/year The monthly payment (M) is calculated as follows: \[ M = 2352000 \times \frac{r(1 + r)^n}{(1 + r)^n - 1} = \$16445.53 \]

Final Answer:

The down payment is \$448000, the mortgage amount is \$2352000, and the monthly mortgage payment is \$16445.53.

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