You want to buy a $233,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest.

a) How much is the loan amount going to be?

$

b) What will your monthly payments be if the interest rate is 5%?

$

c) What will your monthly payments be if the interest rate is 6%?

Let's break this problem into steps:

### Part (a): Loan Amount Calculation
You plan to pay 10% as a down payment. To calculate the loan amount, we subtract the down payment from the home's price.

1. **Home price** = $233,000  
2. **Down payment** = 10% of $233,000 = $ 0.10 \times 233,000 $
3. **Loan amount** = $ 233,000 - \text{Down payment} $

\[
\text{Loan amount} = 233,000 - (0.10 \times 233,000)
\]
\[
\text{Loan amount} = 233,000 - 23,300 = 209,700
\]

So, the loan amount will be **$209,700**.

### Part (b): Monthly Payments with a 5% Interest Rate
The formula for monthly payments on a loan is given by:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan amount = $209,700
- $ r $ = monthly interest rate (annual interest rate divided by 12) = $ \frac{5\%}{12} = \frac{0.05}{12} $
- $ n $ = total number of payments = $ 30 \times 12 = 360 $

Substituting the values into the formula, we can calculate the monthly payment.

### Part (c): Monthly Payments with a 6% Interest Rate
For the interest rate of 6%, we can use the same formula, but with $ r = \frac{6\%}{12} = \frac{0.06}{12} $.

Let me calculate both payments for you.### Results:

- **Part (a)**: The loan amount will be **$209,700**.
- **Part (b)**: The monthly payment at a 5% interest rate will be **$1,125.71**.
- **Part (c)**: The monthly payment at a 6% interest rate will be **$1,257.26**.

Let me know if you'd like more details or further explanations.

Here are some related questions you might find helpful:
1. How much total interest will be paid over the loan's 30-year term at 5%?
2. How much total interest will be paid over the loan's 30-year term at 6%?
3. What happens to monthly payments if the loan term is shortened to 15 years at 5%?
4. How does making extra payments affect the overall interest paid?
5. What if the interest rate decreases to 4%? How much will the new monthly payment be?

**Tip**: Reducing the loan term (e.g., from 30 to 15 years) increases monthly payments but decreases the total interest paid significantly!

You want to buy a $233,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest. a) How much is the loan amount going to be? b) What will your monthly payments be if the interest rate is 5%? c) What will your monthly payments be if the interest rate is 6%?

Learn how to calculate the loan amount for a $233,000 home with a 10% down payment. Discover the monthly payments for 5% and 6% interest rates over a 30-year mortgage. Detailed step-by-step breakdown of the loan and payment calculation.

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