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You want to buy a $165,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at 6.65% 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?

$


Let's go through the steps to solve each part of this problem, given that you want to buy a \$165,000 home with a 5% down payment and a 30-year loan at 6.65% interest.

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

1. The down payment is 5% of the home's price. So, the down payment is:
   \[
   \text{Down payment} = 0.05 \times 165,000 = 8,250
   \]

2. The loan amount is the home's price minus the down payment:
   \[
   \text{Loan amount} = 165,000 - 8,250 = 156,750
   \]
   
**Loan amount = \$156,750**

---

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

We can use the formula for the monthly payment on a loan, which is:
\[
M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- $M$ is the monthly payment,
- $P$ is the loan amount (\$156,750),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of payments (loan term in months).

For this loan:
- Annual interest rate = 6.65%, so monthly interest rate $r = \frac{6.65}{12 \times 100} = 0.00554$,
- Loan term = 30 years, so $n = 30 \times 12 = 360$ months.

I'll calculate the monthly payment next.

---

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

The total interest paid is the difference between the total payments over the loan period and the original loan amount:
\[
\text{Total interest} = M \times n - P
\]

I'll compute this after determining the monthly payment.

---

### d) What will your monthly payment be if you pay off the loan in 15 years?

If you plan to pay off the loan in 15 years instead of 30 years, the number of payments becomes $n = 15 \times 12 = 180$ months. We will use the same formula as in part b) but with $n = 180$ to find the new monthly payment.

---

### e) How much money in interest will you save if you finance for 15 years instead of 30 years?

The interest savings can be found by subtracting the total interest paid in 15 years from the total interest paid in 30 years:
\[
\text{Interest saved} = \text{Total interest in 30 years} - \text{Total interest in 15 years}
\]

I'll now calculate the monthly payments and total interest for both loan terms.

Here are the results for each part of the problem:

### a) Loan amount:
\[
\boxed{\$156,750}
\]

### b) Monthly payment for a 30-year loan:
\[
\boxed{\$1,006.28}
\]

### c) Total interest paid over 30 years:
\[
\boxed{\$205,510.78}
\]

### d) Monthly payment for a 15-year loan:
\[
\boxed{\$1,378.42}
\]

### e) Interest savings if financed for 15 years instead of 30 years:
\[
\boxed{\$114,145.24}
\]

Would you like more details or have any questions about these calculations?

---

Here are 5 related questions you can explore:

1. How does the down payment percentage affect the total loan amount?
2. What happens if the interest rate is lower or higher than 6.65%?
3. How much interest would you save by increasing your monthly payment for a 30-year loan?
4. What is the difference in total payments between a 15-year and a 30-year loan?
5. How does the loan term affect the monthly payment and total interest?

**Tip**: Reducing the loan term saves a significant amount on interest but increases monthly payments, so it’s essential to balance affordability with long-term savings.

You want to buy a $165,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at 6.65% 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?

Learn how to calculate loan amounts, monthly payments, and total interest for a $165,000 home with 5% down payment and a 6.65% interest rate. Explore how different loan terms (30 years vs. 15 years) affect monthly payments and interest savings. Suitable for Grades 10-12.

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