- Calculate the down payment: \(0.05 \times \$220,000 = \$11,000\).
- Determine the loan amount: \(\$220,000 - \$11,000 = \$209,000\).
- Sum the flat closing fees: \(\$500 + \$500 + \$600 = \$1,600\).
- Calculate the percentage fees: \(0.015 \times \$209,000 = \$3,135\).
- Compute the total mortgage: \(\$209,000 + \$1,600 + \$3,135 = \boxed{\$213,735}\).
Explanation
- Calculating the Base Loan Amount
The purchase price of the property is \(\$220,000\). The buyer makes a \(5\%\) down payment, which is calculated as:
\[0.05 \times \$220,000 = \$11,000.\]
The remaining amount to be financed, representing the base loan amount \(L\), is the purchase price minus the down payment:
\[L = \$220,000 - \$11,000 = \$209,000.\]
- Calculating Total Closing Costs
Closing costs include both flat fees and percentage-based fees. The flat fees are:
\[\$500 (\text{Credit Report}) + \$500 (\text{Attorney and notary}) + \$600 (\text{Processing Fee}) = \$1,600.\]
The percentage-based fees are applied to the loan amount \(L = \$209,000\). These are the loan origination fee (\(1\%\)) and the documentation stamp (\(0.50\%\)):
\[(0.01 + 0.005) \times \$209,000 = 0.015 \times \$209,000 = \$3,135.\]
Summing the flat fees and the percentage fees gives the total closing costs:
\[\$1,600 + \$3,135 = \$4,735.\]
- Determining the Total Mortgage Amount
The total mortgage amount \(M\) is the sum of the base loan amount \(L\) and the total closing costs:
\[M = \$209,000 + \$4,735 = \$213,735.\]
Thus, the total mortgage amount required for the purchase is \(\$213,735\).
Examples
Understanding mortgage calculations is essential for prospective homeowners when planning their finances. For example, when purchasing a house, buyers must account for not only the down payment but also various closing costs, such as loan origination fees and legal service charges. By correctly calculating the total mortgage, an individual can accurately estimate their monthly payments and evaluate the overall affordability of a property, ensuring they are prepared for the financial commitment of homeownership.