Questions: A 145,500 mortgage was financed with a 30 year fixed rate at 7.5%. a) What is the monthly payment? 1017.36 (Simplify your answer. Round to the nearest cent as needed.) b) What is the total of payments over 30 years? 366249.6 (Simplify your answer. Round to the nearest cent as needed.) c) What is the interest over the 30 years? 220749.60 (Simplify your answer. Round to the nearest cent as needed.) d) If the mortgage is reduced to 15 years, what would be the monthly payment? 1348.80 (Simplify your answer. Round to the nearest cent as needed.) e) How much would be saved in interest by choosing a 15 year mortgage? (Simplify your answer. Round to the nearest cent as needed.)

A 145,500 mortgage was financed with a 30 year fixed rate at 7.5%. a) What is the monthly payment? 1017.36 (Simplify your answer. Round to the nearest cent as needed.) b) What is the total of payments over 30 years? 366249.6 (Simplify your answer. Round to the nearest cent as needed.) c) What is the interest over the 30 years? 220749.60 (Simplify your answer. Round to the nearest cent as needed.) d) If the mortgage is reduced to 15 years, what would be the monthly payment? 1348.80 (Simplify your answer. Round to the nearest cent as needed.) e) How much would be saved in interest by choosing a 15 year mortgage? (Simplify your answer. Round to the nearest cent as needed.)
Transcript text: mylab.pearson.com Content / Winchester MA 111U: Contempo... Homework atics (4244_J201) Annuities Question Part 5 of 5 Watch the video and then solve the problem given below. Click here to watch the video. A \$145,500 mortgage was financed with a 30 year fixed rate at $7.5 \%$. a) What is the monthly payment? \$1017.36 (Simplify your answer. Round to the nearest cent as needed.) b) What is the total of payments over 30 years? \$ 366249.6 (Simplify your answer. Round to the nearest cent as needed.) c) What is the interest over the 30 years? $\$ 220749.60$ (Simplify your answer. Round to the nearest cent as needed.) d) If the mortgage is reduced to 15 years, what would be the monthly payment? $\$ 1348.80$ (Simplify your answer. Round to the nearest cent as needed.) e) How much would be saved in interest by choosing a 15 year mortgage? \$ $\square$ (Simplify your answer. Round to the nearest cent as needed.)
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Solution

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Solution Steps

To solve the given problem, we need to calculate the monthly payment, total payments, and interest for a mortgage. We will use the formula for monthly mortgage payments and then calculate the total payments and interest. For the 15-year mortgage, we will use the same formula with the adjusted term and then calculate the interest saved.

Step 1: Monthly Payment for 30 Years

To calculate the monthly payment for a mortgage of \( P = 145500 \) at an annual interest rate of \( r = 7.5\% \) over \( n = 30 \) years, we use the formula:

\[ M = P \cdot \frac{r/n}{1 - (1 + r/n)^{-n \cdot 12}} \]

Substituting the values, we find:

\[ M = 145500 \cdot \frac{0.075/12}{1 - (1 + 0.075/12)^{-30 \cdot 12}} \approx 1017.36 \]

Step 2: Total Payments Over 30 Years

The total payments over 30 years can be calculated as:

\[ \text{Total Payments} = M \cdot 12 \cdot n = 1017.36 \cdot 12 \cdot 30 \approx 366249.6 \]

Step 3: Interest Over 30 Years

The total interest paid over the 30 years is given by:

\[ \text{Interest} = \text{Total Payments} - P = 366249.6 - 145500 \approx 220749.6 \]

Step 4: Monthly Payment for 15 Years

For a 15-year mortgage, we use the same formula with \( n = 15 \):

\[ M_{15} = 145500 \cdot \frac{0.075/12}{1 - (1 + 0.075/12)^{-15 \cdot 12}} \approx 1348.8 \]

Step 5: Interest Saved by Choosing a 15-Year Mortgage

The total payments for the 15-year mortgage are:

\[ \text{Total Payments}_{15} = M_{15} \cdot 12 \cdot 15 = 1348.8 \cdot 12 \cdot 15 \approx 242784 \]

The interest paid over 15 years is:

\[ \text{Interest}_{15} = \text{Total Payments}_{15} - P = 242784 - 145500 \approx 97284 \]

The interest saved by choosing a 15-year mortgage is:

\[ \text{Interest Saved} = \text{Interest}_{30} - \text{Interest}_{15} = 220749.6 - 97284 \approx 123465.6 \]

Final Answer

  • Monthly payment for 30 years: \( \boxed{M_{30} = 1017.36} \)
  • Total payments over 30 years: \( \boxed{\text{Total Payments}_{30} = 366249.6} \)
  • Interest over 30 years: \( \boxed{\text{Interest}_{30} = 220749.6} \)
  • Monthly payment for 15 years: \( \boxed{M_{15} = 1348.8} \)
  • Interest saved by choosing a 15-year mortgage: \( \boxed{\text{Interest Saved} = 123465.6} \)
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