Jenelle bought a home for $360,000, paying 16% as a down payment, and financing the rest at 7% interest for 30 years. Round your answers to the nearest cent.

How much money did Jenelle pay as a down payment? $  

What was the original amount financed? $  

What is her monthly payment? $  

If Jenelle makes these payments every month for thirty years, determine the total amount of money she will spend on this home. Include the down payment in your answer. $  

Let's solve this step-by-step.

### 1. **Down Payment Calculation:**

Jenelle paid 16% as a down payment. We can calculate that using the formula:
\[
\text{Down Payment} = \text{Price of the Home} \times \text{Down Payment Percentage}
\]
\[
\text{Down Payment} = 360,000 \times 0.16 = 57,600
\]

So, **Jenelle paid $57,600 as a down payment**.

---

### 2. **Original Amount Financed:**

The amount financed is the cost of the home minus the down payment:
\[
\text{Amount Financed} = 360,000 - 57,600 = 302,400
\]

So, **the original amount financed is $302,400**.

---

### 3. **Monthly Payment Calculation:**

To calculate Jenelle's monthly mortgage payment, we use the formula for a fixed-rate mortgage payment (using the amortization formula):
\[
M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- $M$ is the monthly payment,
- $P$ is the principal (amount financed = $302,400),
- $r$ is the monthly interest rate (annual interest rate ÷ 12 months = 0.07 ÷ 12 = 0.0058333),
- $n$ is the total number of payments (30 years × 12 months = 360 months).

Substituting the values:
\[
M = \frac{302,400 \times 0.0058333 \times (1 + 0.0058333)^{360}}{(1 + 0.0058333)^{360} - 1}
\]

Calculating this step-by-step:

\[
M \approx \frac{302,400 \times 0.0058333 \times 9.4097}{9.4097 - 1}
\]
\[
M \approx \frac{302,400 \times 0.0548778}{8.4097}
\]
\[
M \approx \frac{16,598.24}{8.4097} \approx 1,973.17
\]

So, **Jenelle's monthly payment is approximately $1,973.17**.

---

### 4. **Total Amount Spent on the Home:**

The total amount Jenelle will spend over 30 years is the sum of her monthly payments over 360 months plus the down payment:
\[
\text{Total Amount Spent} = (\text{Monthly Payment} \times 360) + \text{Down Payment}
\]
\[
\text{Total Amount Spent} = (1,973.17 \times 360) + 57,600
\]
\[
\text{Total Amount Spent} = 710,341.20 + 57,600 = 767,941.20
\]

So, **Jenelle will spend a total of $767,941.20 on her home** over 30 years, including the down payment.

---

### Summary of Results:
1. **Down Payment**: $57,600
2. **Amount Financed**: $302,400
3. **Monthly Payment**: $1,973.17
4. **Total Amount Spent**: $767,941.20

---

Would you like more details or have any questions?

Here are five related questions to consider:
1. How much interest will Jenelle pay over the life of the loan?
2. What if the interest rate was 6% instead of 7%? How would that affect her monthly payment?
3. How much would she save if she made an extra monthly payment of $500?
4. What is the total amount of interest paid if Jenelle refinances her loan after 10 years?
5. What is the impact of a 20% down payment instead of 16%?

**Tip**: Making extra payments towards your mortgage principal can reduce the total interest paid over the life of the loan.

Jenelle bought a home for $360,000, paying 16% as a down payment, and financing the rest at 7% interest for 30 years. Round your answers to the nearest cent. How much money did Jenelle pay as a down payment? What was the original amount financed? What is her monthly payment? If Jenelle makes these payments every month for thirty years, determine the total amount of money she will spend on this home. Include the down payment in your answer.

Learn how to calculate the down payment, financed amount, monthly mortgage payments, and total cost over 30 years for a $360,000 home with a 16% down payment and 7% interest. Step-by-step explanation using finance and loan amortization formulas, perfect for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation