A house sells for $ 175,000 and a 9% down payment is made. A mortgage is secured at 4% for 15 years. Do not round intermediate calculations. Round your answers in (a)-(d) to two decimal places, if necessary.
Use the formula below as needed. Find the monthly payment.

To find the monthly payment for the mortgage, we can use the standard formula for a fixed-rate mortgage:

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

Where:
- $M$ is the monthly mortgage payment
- $P$ is the principal loan amount (house price minus the down payment)
- $r$ is the monthly interest rate (annual interest rate divided by 12)
- $n$ is the total number of payments (loan term in years multiplied by 12)

### Step 1: Calculate the down payment
The house price is $175,000, and the down payment is 9%.

\[
\text{Down Payment} = 175,000 \times 0.09 = 15,750
\]

### Step 2: Calculate the loan amount (principal)
The principal loan amount $P$ is the house price minus the down payment.

\[
P = 175,000 - 15,750 = 159,250
\]

### Step 3: Calculate the monthly interest rate
The annual interest rate is 4%, so the monthly interest rate $r$ is:

\[
r = \frac{4\%}{12} = \frac{0.04}{12} = 0.0033333
\]

### Step 4: Calculate the total number of payments
The loan term is 15 years, so the total number of monthly payments $n$ is:

\[
n = 15 \times 12 = 180
\]

### Step 5: Plug into the mortgage formula
Now we substitute $P = 159,250$, $r = 0.0033333$, and $n = 180$ into the formula:

\[
M = 159,250 \times \frac{0.0033333(1 + 0.0033333)^{180}}{(1 + 0.0033333)^{180} - 1}
\]

Let's calculate this step-by-step to find the monthly mortgage payment.

I'll calculate this next.The monthly mortgage payment is approximately **$1,177.95**.

Would you like any further details or have additional questions?

Here are 5 related questions to extend this topic:
1. How much interest will be paid over the life of the loan?
2. What is the total cost of the house including interest?
3. How would a change in interest rate affect the monthly payment?
4. What would the monthly payment be for a 30-year mortgage?
5. How much equity is gained after 5 years of payments?

**Tip:** Making extra payments on a mortgage can reduce the total interest paid and shorten the loan term.

A house sells for $175,000 and a 9% down payment is made. A mortgage is secured at 4% for 15 years. Do not round intermediate calculations. Round your answers in (a)-(d) to two decimal places, if necessary. Find the monthly payment.

Learn how to calculate the monthly mortgage payment for a $175,000 home with a 9% down payment and a 4% interest rate over 15 years. This problem involves financial mathematics concepts such as down payment calculation, interest rate, and the mortgage payment formula. Step-by-step breakdown provided, suitable for 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