To determine the total mortgage for a \[tex]$190,000 purchase with a 20% down payment and specific closing costs, let's analyze and calculate each component step by step:
### Step 1: Calculate the Down Payment
The down payment percentage is 20%. Therefore:
\[ \text{Down payment} = \text{Purchase price} \times \text{Down payment percentage} \]
\[ \text{Down payment} = \$[/tex]190,000 \times 0.20 = \[tex]$38,000 \]
### Step 2: Calculate the Mortgage Amount
The mortgage amount is the portion of the purchase price financed through the mortgage, which is the purchase price minus the down payment:
\[ \text{Mortgage amount} = \text{Purchase price} - \text{Down payment} \]
\[ \text{Mortgage amount} = \$[/tex]190,000 - \[tex]$38,000 = \$[/tex]152,000 \]
### Step 3: Determine the Closing Costs
The closing costs comprise several fees:
#### a. Credit Report Cost
Given as:
[tex]\[ \text{Credit report cost} = \$500.00 \][/tex]
#### b. Loan Origination Fee
The loan origination fee is 1% of the mortgage amount:
[tex]\[ \text{Loan origination fee} = \text{Mortgage amount} \times \text{Loan origination fee percentage} \][/tex]
[tex]\[ \text{Loan origination fee} = \$152,000 \times 0.01 = \$1,520 \][/tex]
#### c. Attorney and Notary Fee
Given as:
[tex]\[ \text{Attorney and notary fee} = \$500.00 \][/tex]
#### d. Documentation Stamp Fee
The documentation stamp fee is 0.50% of the mortgage amount:
[tex]\[ \text{Documentation stamp fee} = \text{Mortgage amount} \times \text{Documentation stamp percentage} \][/tex]
[tex]\[ \text{Documentation stamp fee} = \$152,000 \times 0.005 = \$760 \][/tex]
#### e. Processing Fee
Given as:
[tex]\[ \text{Processing fee} = \$500.00 \][/tex]
### Step 4: Calculate the Total Closing Costs
Sum the closing cost components:
[tex]\[ \text{Closing costs} = \text{Credit report cost} + \text{Loan origination fee} + \text{Attorney and notary fee} + \text{Documentation stamp fee} + \text{Processing fee} \][/tex]
[tex]\[ \text{Closing costs} = \$500.00 + \$1,520.00 + \$500.00 + \$760.00 + \$500.00 = \$3,780.00 \][/tex]
### Step 5: Determine the Total Mortgage
The total mortgage is the sum of the mortgage amount and the closing costs:
[tex]\[ \text{Total mortgage} = \text{Mortgage amount} + \text{Closing costs} \][/tex]
[tex]\[ \text{Total mortgage} = \$152,000 + \$3,780 = \$155,780 \][/tex]
Thus, the total mortgage for a \[tex]$190,000 purchase with a 20% down payment and the given closing costs is:
\[ \$[/tex]155,780 \]
