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### Problem:
You want to buy a $228,000 home, with the following information:
- You plan to pay 20% as a down payment.
- The loan will be for 30 years at a 6.15% interest rate.

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

The home price is $228,000, and the down payment is 20%. The loan amount is the remaining 80% of the home's value:

\[
\text{Loan Amount} = 228,000 \times 0.80 = 182,400
\]

#### b) What will your monthly payments be?

Using the formula for a monthly payment of a fixed-rate mortgage:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan amount ($182,400)
- $ r $ = monthly interest rate (annual rate divided by 12)
- $ n $ = total number of payments (loan term in months)

Here, the annual interest rate is 6.15%, so the monthly interest rate is:

\[
r = \frac{6.15}{100 \times 12} = 0.005125
\]

The loan term is 30 years, so the total number of payments is:

\[
n = 30 \times 12 = 360
\]

Let's calculate the monthly payment $ M $.

#### c) How much total interest do you pay?

The total interest paid over the life of the loan is the difference between the total of all payments and the original loan amount:

\[
\text{Total Interest} = M \times n - P
\]

We will calculate this after determining the monthly payment.

#### d) Monthly payment if paid off in 15 years?

The only change here is that the number of payments becomes $ n = 15 \times 12 = 180 $. We will recalculate $ M $ using this adjusted $ n $.

#### e) Interest saved by financing for 15 years instead of 30?

We will compare the total interest paid in 15 years to the total interest paid in 30 years.

I'll now calculate these values step by step.Here are the calculated results based on the given information:

- **a) Loan Amount**: \$182,400
- **b) Monthly Payment for 30 Years**: \$1,111.23
- **c) Total Interest Paid over 30 Years**: \$217,643.58
- **d) Monthly Payment for 15 Years**: \$1,554.02
- **e) Interest Saved by Financing for 15 Years instead of 30 Years**: \$120,320.79

Let me know if you want further details or have any questions.

Here are some follow-up questions to explore:
1. How does changing the interest rate affect the monthly payment for 30 years?
2. What happens to the total interest if the down payment is increased to 30%?
3. How would a shorter loan term, such as 10 years, impact the total interest?
4. What effect does making an extra payment each year have on the total interest?
5. How much principal is paid off after 5 years in both the 15-year and 30-year scenarios?

**Tip:** Increasing your down payment reduces the amount you need to borrow, which significantly decreases both monthly payments and total interest.

You want to buy a $228,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan at 6.15% interest for the rest. a) How much is the loan amount going to be? b) What will your monthly payments be? c) How much total interest do you pay? d) Suppose you want to pay off the loan in 15 years rather than 30. What will your monthly payment be? e) How much money in interest will you save if you finance for 15 years instead of 30 years?

Calculate the monthly payments, total interest, and loan amount for a $228,000 home with 20% down and a 6.15% interest rate for 30 years. Also explore the impact of a 15-year loan term and the interest savings.

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