Question: User: Jenelle bought a home for $350,000, paying 12% as a down payment, and financing the rest at 5.4% interest for 30 years. Round your answers to the nearest cent.
How much money did Jenelle pay as a down payment? $Question 7 Part 1 of 4$
What was the original amount financed? $Question 7 Part 2 of 4$
What is her monthly payment?
1. **State the problem:** Jenelle bought a home for $350,000$ and paid $12\%$ as a down payment. She financed the rest at $5.4\%$ annual interest for $30$ years. We need to find:
- The down payment amount.
- The original amount financed.
- The monthly payment.
2. **Calculate the down payment:**
The down payment is $12\%$ of $350,000$.
$$\text{Down payment} = 0.12 \times 350,000 = 42,000$$
3. **Calculate the amount financed:**
The amount financed is the home price minus the down payment.
$$\text{Amount financed} = 350,000 - 42,000 = 308,000$$
4. **Calculate the monthly payment:**
Use the mortgage payment formula:
$$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$
where:
- $M$ is the monthly payment
- $P = 308,000$ is the loan principal
- $r = \frac{5.4\%}{12} = \frac{0.054}{12} = 0.0045$ is the monthly interest rate
- $n = 30 \times 12 = 360$ is the total number of payments
5. **Calculate $(1+r)^n$:**
$$ (1 + 0.0045)^{360} = 1.0045^{360} \approx 5.349$$
6. **Calculate numerator and denominator:**
Numerator:
$$0.0045 \times 5.349 = 0.02407$$
Denominator:
$$5.349 - 1 = 4.349$$
7. **Calculate monthly payment $M$:**
$$M = 308,000 \times \frac{0.02407}{4.349} = 308,000 \times 0.00553 = 1703.24$$
8. **Final answers:**
- Down payment: $42,000$
- Amount financed: $308,000$
- Monthly payment: $1703.24$