Questions: Complete the following: Note: Do not round intermediate calculations. Round your answers to the nearest cent. Selling price Down payment Amount mortgage Rate Years Monthly payment First Payment Broken Down Into: Interest Principal Balance at end of month --- --- --- --- --- --- --- --- --- S 149,000 30,000 7.50% 30

Complete the following:
Note: Do not round intermediate calculations. Round your answers to the nearest cent.

Selling price Down payment Amount mortgage Rate Years Monthly payment First Payment Broken Down Into: Interest Principal Balance at end of month
--- --- --- --- --- --- --- --- ---
S 149,000 30,000 7.50% 30

Transcript text: Complete the following: Note: Do not round intermediate calculations. Round your answers to the nearest cent. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{2}{|r|}{Selling price} & \multicolumn{2}{|l|}{\multirow[t]{2}{*}{Down payment}} & \multirow[t]{2}{*}{Amount mortgage} & \multirow[t]{2}{*}{Rate} & \multirow[t]{2}{*}{Years} & \multirow[t]{2}{*}{Monthly payment} & \multicolumn{2}{|l|}{First Payment Broken Down Into} & \multirow[t]{2}{*}{Balance at end of month} \\ \hline & & & & & & & & Interest & Principal & \\ \hline S & 149,000 & \$ & 30,000 & & 7.50\% & 30 & & & & \\ \hline \end{tabular}

Solution

Solution Steps

Solution Approach

To solve the problem, we need to calculate the monthly mortgage payment and break down the first payment into interest and principal components. We will use the formula for monthly mortgage payments, which involves the principal amount, interest rate, and loan term. The principal amount is the selling price minus the down payment. The interest component of the first payment can be calculated using the monthly interest rate applied to the principal, and the principal component is the remainder of the monthly payment after subtracting the interest.

Step 1: Calculate the Loan Amount

The loan amount is calculated by subtracting the down payment from the selling price: \[ \text{Loan Amount} = \text{Selling Price} - \text{Down Payment} = 149000 - 30000 = 119000 \]

Step 2: Calculate the Monthly Interest Rate

The monthly interest rate is derived from the annual interest rate: \[ \text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12} = \frac{0.075}{12} \approx 0.00625 \]

Step 3: Calculate the Number of Payments

The total number of payments over the loan term is: \[ \text{Number of Payments} = \text{Years} \times 12 = 30 \times 12 = 360 \]

Step 4: Calculate the Monthly Payment

The monthly payment can be calculated using the formula for an amortizing loan: \[ M = \frac{P \cdot r}{1 - (1 + r)^{-n}} \] where $ P = 119000 $, $ r = 0.00625 $, and $ n = 360 $: \[ M \approx \frac{119000 \cdot 0.00625}{1 - (1 + 0.00625)^{-360}} \approx 832.0653 \]

Step 5: Calculate the First Month's Interest

The interest for the first month is calculated as: \[ \text{First Month Interest} = \text{Loan Amount} \cdot \text{Monthly Interest Rate} = 119000 \cdot 0.00625 \approx 743.75 \]

Step 6: Calculate the First Month's Principal Payment

The principal portion of the first payment is: \[ \text{First Month Principal} = \text{Monthly Payment} - \text{First Month Interest} \approx 832.0653 - 743.75 \approx 88.3153 \]

Step 7: Calculate the Balance at the End of the First Month

The remaining balance after the first payment is: \[ \text{Balance at End of Month} = \text{Loan Amount} - \text{First Month Principal} \approx 119000 - 88.3153 \approx 118911.6847 \]