A 20-year fixed-rate mortgage has monthly payments of €700 per month and a quoted interest rate of 5.97 per cent per year compounded monthly. 
Required:

If a buyer purchases a home with the cash proceeds of the mortgage loan plus an additional deposit that equals 25 per cent of the mortgage loan, what is the purchase price of the home?

To determine the purchase price of the home, we can follow these steps:

1. **Calculate the loan amount (mortgage loan):**
   We are given the monthly mortgage payments, interest rate, and loan term. Using the formula for the monthly payment of a fixed-rate mortgage, we can solve for the mortgage loan amount.

The formula for the monthly payment \( P \) is:
\[
P = \frac{L \cdot r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- \( P \) is the monthly payment (€700),
- \( L \) is the loan amount (what we need to find),
- \( r \) is the monthly interest rate,
- \( n \) is the total number of payments (loan term in months).

### Step 1: Find the monthly interest rate:
The quoted annual interest rate is 5.97% compounded monthly, so the monthly interest rate \( r \) is:
\[
r = \frac{5.97\%}{12} = \frac{0.0597}{12} = 0.004975
\]

### Step 2: Calculate the number of payments:
The loan term is 20 years, so the total number of monthly payments \( n \) is:
\[
n = 20 \times 12 = 240 \text{ months}
\]

### Step 3: Rearrange the monthly payment formula to solve for the loan amount \( L \):
Rearranging the formula, we get:
\[
L = \frac{P \cdot \left( (1 + r)^n - 1 \right)}{r \cdot (1 + r)^n}
\]

### Step 4: Substitute the known values into the formula:
\[
L = \frac{700 \cdot \left( (1 + 0.004975)^{240} - 1 \right)}{0.004975 \cdot (1 + 0.004975)^{240}}
\]

Now, let's calculate the loan amount \( L \).The mortgage loan amount \( L \) is approximately €97,943.

### Step 5: Calculate the total purchase price of the home:
We are told that the buyer also contributes an additional deposit that equals 25% of the mortgage loan. Therefore, the purchase price \( \text{Purchase Price} \) is:

\[
\text{Purchase Price} = L + 0.25 \times L = 1.25 \times L
\]

Now, let's calculate the total purchase price.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the total purchase price manually. Simply multiply the loan amount by 1.25:

\[
\text{Purchase Price} = 1.25 \times 97,943 = 122,428.75
\]

So, the total purchase price of the home is approximately €122,429.

Would you like more details or have any questions?

Here are some related questions you may find interesting:
1. How would the total cost change with a different interest rate?
2. What is the impact of a longer mortgage term on monthly payments?
3. How would the loan amount change if the down payment percentage increased?
4. How is the amortization schedule of the mortgage calculated?
5. What happens to the total interest paid if you make extra payments?

**Tip**: Making extra payments on a mortgage early on reduces the total interest significantly over the life of the loan!

A 20-year fixed-rate mortgage has monthly payments of €700 per month and a quoted interest rate of 5.97 per cent per year compounded monthly. If a buyer purchases a home with the cash proceeds of the mortgage loan plus an additional deposit that equals 25 per cent of the mortgage loan, what is the purchase price of the home?

Find out how to calculate the total purchase price of a home given a 20-year fixed-rate mortgage with monthly payments of €700 and a 5.97% interest rate compounded monthly. This problem covers financial math concepts such as mortgage payments, loan amortization, and interest rates. Suitable for college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation