Questions: A house sells for 140,000 and a 20% down payment is made. A mortgage was secured at 4.3% for 25 years. Round to the nearest cent, if necessary. Part 1 of 4 Find the down payment. The down payment is 28,000. Part 2 of 4 Find the amount of the mortgage. The amount of the mortgage is 112,000 Part 3 of 4 Find the monthly payment. The monthly payment is

Solution Steps

To find the monthly payment for a mortgage, we can use the formula for a fixed-rate mortgage payment:

\[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \]

where:

• \( M \) is the monthly payment
• \( P \) is the loan principal (amount of the mortgage)
• \( r \) is the monthly interest rate (annual rate divided by 12)
• \( n \) is the number of payments (loan term in years multiplied by 12)

Given:

• The loan principal \( P \) is \$112,000
• The annual interest rate is 4.3%, so the monthly interest rate \( r \) is \( \frac{4.3}{100 \times 12} \)
• The loan term is 25 years, so the number of payments \( n \) is \( 25 \times 12 \)

The annual interest rate is given as \( 4.3\% \). To find the monthly interest rate \( r \), we convert it as follows:

\[ r = \frac{4.3}{100 \times 12} = 0.0035833333 \]

The loan term is \( 25 \) years. The total number of monthly payments \( n \) is calculated as:

\[ n = 25 \times 12 = 300 \]

Using the mortgage payment formula:

\[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \]

Substituting \( P = 112000 \), \( r = 0.0035833333 \), and \( n = 300 \):

\[ M = 112000 \frac{0.0035833333(1 + 0.0035833333)^{300}}{(1 + 0.0035833333)^{300} - 1} \]

Calculating this gives:

\[ M \approx 609.8866022 \]

Rounding to the nearest cent, we find:

\[ M \approx 609.89 \]

Final Answer