You want to buy a $236,000 home. You plan to pay 20% 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 6%?

$

c) What will your monthly payments be if the interest rate is 7%?

Let's break down each part of the problem.

### a) Loan amount

The loan amount will be the purchase price of the home minus the down payment. You are paying 20% as a down payment, so:

\[
\text{Down payment} = 0.20 \times 236,000 = 47,200
\]

The loan amount will then be:

\[
\text{Loan amount} = 236,000 - 47,200 = 188,800
\]

So, the loan amount is **$188,800**.

### b) Monthly payments at a 6% interest rate

We can calculate the monthly payments using the **loan amortization formula**:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan amount (188,800)
- $ r $ = monthly interest rate (annual rate / 12) = $ \frac{6\%}{12} = 0.005 $
- $ n $ = number of payments (30 years * 12 months = 360 months)

Now, plugging the values into the formula:

\[
M = 188,800 \times \frac{0.005(1+0.005)^{360}}{(1+0.005)^{360} - 1}
\]

Let's calculate that.The monthly payment for the loan with a 6% interest rate is approximately **$1,131.95**.

### c) Monthly payments at a 7% interest rate

Now, we'll use the same amortization formula but with a 7% interest rate. The monthly interest rate will be:

\[
r = \frac{7\%}{12} = 0.0058333
\]

Let's calculate the new monthly payment.The monthly payment for the loan with a 7% interest rate is approximately **$1,256.09**.

### Summary:

a) The loan amount will be **$188,800**.

b) With a 6% interest rate, the monthly payments will be **$1,131.95**.

c) With a 7% interest rate, the monthly payments will be **$1,256.09**.

Would you like further details or have any questions? Here are some related questions:

1. How does changing the interest rate affect the total amount paid over the life of the loan?
2. How much total interest would you pay with a 6% interest rate over the 30-year period?
3. How would the monthly payments change if the loan term were only 15 years?
4. What is the effect of making extra payments on the principal each month?
5. How does the size of the down payment impact the monthly payments?

Tip: Even small changes in interest rates can significantly affect your total loan payments over time.

You want to buy a $236,000 home. You plan to pay 20% 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 6%?
c) What will your monthly payments be if the interest rate is 7%?

Learn how to calculate the loan amount and monthly payments for a $236,000 home with a 20% down payment. This step-by-step solution explains how to use the loan amortization formula for interest rates of 6% and 7%. Suitable for high school students and home buyers.

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