you want to buy a 256,000 home. you plan to pay 5% as a down payment, and take out a 30 year loan for the rest. how much is the loan amount going to be ? what will your monthly payments be if the interest rate is 5% ? what will you monthly payments be if the interest rate is 6%?

Let's break down the problem step-by-step:

### Step 1: Calculate the Down Payment
The down payment is 5% of the home's price.

\[
\text{Down Payment} = 256,000 \times 0.05 = 12,800
\]

### Step 2: Calculate the Loan Amount
The loan amount is the home's price minus the down payment.

\[
\text{Loan Amount} = 256,000 - 12,800 = 243,200
\]

### Step 3: Calculate Monthly Payments

The formula for monthly mortgage payments is given by:

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

where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount.
- $ 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).

#### Case 1: Interest Rate of 5%
- Annual interest rate = 5% = 0.05
- Monthly interest rate, $ r = \frac{0.05}{12} \approx 0.004167 $
- Loan term = 30 years
- Total number of payments, $ n = 30 \times 12 = 360 $

Let's calculate $ M $.

#### Case 2: Interest Rate of 6%
- Annual interest rate = 6% = 0.06
- Monthly interest rate, $ r = \frac{0.06}{12} = 0.005 $
- Loan term = 30 years
- Total number of payments, $ n = 30 \times 12 = 360 $

Let's calculate $ M $.### Summary of Results:

1. **Down Payment**: $12,800
2. **Loan Amount**: $243,200

#### Monthly Payments:
- **At 5% Interest Rate**: $1,305.55
- **At 6% Interest Rate**: $1,458.11

Do you want more details or have any questions?

### Related Questions:
1. How much total interest will you pay over the 30 years at each interest rate?
2. How does the total cost of the loan differ between the two interest rates?
3. What would be the impact of making an additional monthly payment of $100?
4. How much would the monthly payment change if you put a 10% down payment instead?
5. What is the break-even point if you consider refinancing the loan?

**Tip:** Always aim to make a larger down payment if possible; it reduces the loan amount and monthly payments, and can significantly decrease the total interest paid over time.

Find out how to calculate the loan amount and monthly mortgage payments for a $256,000 home with a 5% down payment. Compare payments at interest rates of 5% and 6% over 30 years. This step-by-step solution includes the amortization formula and relevant financial concepts.

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