Anna is buying a house selling for ​$265 comma 000. To obtain the​ mortgage, Anna is required to make a 20​% down payment. Anna obtains a 25​-year mortgage with an interest rate of 4​%.
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​a) Determine the amount of the required down payment.
​b) Determine the amount of the mortgage. 
​c) Determine the monthly payment for principal and interest.
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Part 1
​a) Determine the amount of the required down payment.
​$
  
53000
Part 2
​b) Determine the amount of the mortgage. 
​$
  
212000 
Part 3
​c) Determine the monthly payment for principal and interest.
​$
  
enter your response here ​(Round to the nearest​ cent.)

To solve this problem, let's break down each part step by step.

### Part 1: Determine the amount of the required down payment.
The down payment is 20% of the house price.

\[
\text{Down Payment} = 20\% \times 265,000 = 0.20 \times 265,000 = 53,000
\]

So, the required down payment is **$53,000**.

### Part 2: Determine the amount of the mortgage.
The amount of the mortgage is the total house price minus the down payment:

\[
\text{Mortgage Amount} = 265,000 - 53,000 = 212,000
\]

So, the mortgage amount is **$212,000**.

### Part 3: Determine the monthly payment for principal and interest.
For the monthly payment, we need to use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount (the mortgage),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of payments (loan term in years multiplied by 12).

Here:
- $P = 212,000$,
- The annual interest rate is 4%, so the monthly interest rate $r = \frac{4\%}{12} = \frac{0.04}{12} = 0.0033333$,
- The loan term is 25 years, so the number of payments $n = 25 \times 12 = 300$.

Now we can calculate the monthly payment.

I'll compute that for you.The monthly payment for principal and interest is approximately **$1,119.01**.

### Recap of answers:
- **a)** The required down payment is **$53,000**.
- **b)** The mortgage amount is **$212,000**.
- **c)** The monthly payment for principal and interest is **$1,119.01**.

Do you want more details on any part of this calculation?

Here are 5 related questions to expand your understanding:
1. How would the monthly payment change if the interest rate increased to 5%?
2. What would the total interest paid over the 25-year loan term be?
3. How does a shorter loan term, such as 15 years, affect the monthly payments?
4. If Anna made an additional payment each month, how much faster could she pay off the mortgage?
5. How does a change in the down payment percentage affect the total mortgage amount?

**Tip:** Making extra payments towards your mortgage principal can reduce the overall interest paid and shorten the loan term.

Anna is buying a house selling for $265,000. To obtain the mortgage, Anna is required to make a 20% down payment. Anna obtains a 25-year mortgage with an interest rate of 4%. a) Determine the amount of the required down payment. b) Determine the amount of the mortgage. c) Determine the monthly payment for principal and interest.

Learn how to calculate the down payment, mortgage amount, and monthly payments for a house priced at $265,000 with a 20% down payment and a 25-year mortgage at a 4% interest rate. Detailed step-by-step calculations and formulas provided. Suitable for Grades 10-12.

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