Questions: As one of the loan officers for Grove Gate Bank, calculate the monthly principal and interest, PI (in ), using this table and the monthly PITI (in ) for the mortgage. (Round dollars to the nearest cent.) Amount Financed Interest Rate Term of Loan (years) Monthly PI Annual Property Tax Annual Insurance Monthly PITI --- --- --- --- --- --- --- 280,000 3.50% 25 6,573 2,156

As one of the loan officers for Grove Gate Bank, calculate the monthly principal and interest, PI (in ), using this table and the monthly PITI (in ) for the mortgage. (Round dollars to the nearest cent.) Amount Financed Interest Rate Term of Loan (years) Monthly PI Annual Property Tax Annual Insurance Monthly PITI --- --- --- --- --- --- --- 280,000 3.50% 25 6,573 2,156
Transcript text: As one of the loan officers for Grove Gate Bank, calculate the monthly principal and interest, PI (in \$), using this table and the monthly PITI (in \$) for the mortgage. (Round dollars to the nearest cent.) \begin{tabular}{|c|c|c|c|c|c|c|} \hline \begin{tabular}{c} Amount \\ Financed \end{tabular} & \begin{tabular}{c} Interest \\ Rate \end{tabular} & \begin{tabular}{c} Term \\ of Loan \\ (years) \end{tabular} & \begin{tabular}{c} Monthly \\ PI \end{tabular} & \begin{tabular}{c} Annual \\ Property \\ Tax \end{tabular} & \begin{tabular}{c} Annual \\ Insurance \end{tabular} & \begin{tabular}{c} Monthly \\ PITI \end{tabular} \\ \hline$\$ 280,000$ & $3.50 \%$ & 25 & $\$ \square$ & $\$ 6,573$ & $\$ 2,156$ & $\square$ \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Calculate Monthly Interest Rate

The monthly interest rate is calculated from the annual interest rate: \[ \text{monthly interest rate} = \frac{0.035}{12} = 0.0029166667 \]

Step 2: Calculate Number of Payments

The total number of payments over the loan term of 25 years is: \[ \text{number of payments} = 25 \times 12 = 300 \]

Step 3: Calculate Monthly Principal and Interest (PI)

Using the loan amortization formula, the monthly principal and interest payment is calculated as follows: \[ \text{monthly PI} = \frac{280000 \times 0.0029166667}{1 - (1 + 0.0029166667)^{-300}} \approx 1401.75 \]

Step 4: Calculate Monthly Property Tax and Insurance

The monthly property tax and insurance are calculated from their annual values: \[ \text{monthly property tax} = \frac{6573}{12} \approx 547.75 \] \[ \text{monthly insurance} = \frac{2156}{12} \approx 179.67 \]

Step 5: Calculate Monthly PITI

The total monthly payment including principal, interest, taxes, and insurance (PITI) is: \[ \text{monthly PITI} = 1401.75 + 547.75 + 179.67 \approx 2129.16 \]

Final Answer

The monthly principal and interest payment is approximately \( \boxed{1401.75} \) and the monthly PITI is approximately \( \boxed{2129.16} \).

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