https://file.aiquickdraw.com/mathbot/file/172582526779126iqdx36.jpg

Let me transcribe the math content from the image and provide assistance with the calculations and answers.

---

### Transcription of the question from the image:

#### Question 1
The price of a house in a particular area has been increasing over a number of years. The value of the house increases by 9% each year.

At the start of 2020, the value of the house was **€240,000**.

(a) Work out the price of the house at the start of 2021 and the price at the start of 2023.

---

### Handwritten Work Analysis:

The handwritten solution shows the following steps:

1. **Price at the start of 2021**:
   - 240,000 × (1 + 0.09) = 240,000 × 1.09 = €261,600.

2. **Price at the start of 2023**:
   - For the price in 2022: 261,600 × 1.09 = €285,144.
   - Then, for 2023: 285,144 × 1.09 = €310,807.68.

Thus, the price at the start of 2021 is **€261,600** and the price at the start of 2023 is **€310,807.68**.

---

**(b)** Another house was valued at **€469,933**. After one year, the value of this house had gone up to **€477,000**. 

Work out the percentage increase in the value of this house over the year. Give your answer correct to 1 decimal place.

---

### Let's solve part (b):

To calculate the percentage increase:

\[
\text{Percentage Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100
\]

Substituting the values:

\[
\text{Percentage Increase} = \left( \frac{477,000 - 469,933}{469,933} \right) \times 100 = \left( \frac{7,067}{469,933} \right) \times 100
\]

Let me calculate that.The percentage increase in the value of the house over the year is **1.5%**, correct to 1 decimal place.

---

Do you want more details or have any questions? Here are some related questions you might consider:

1. What formula is used for compound interest when calculating house price increases over multiple years?
2. How can we model future house price growth over a period of time using exponential functions?
3. What would happen to the house price if the annual increase were compounded monthly instead of yearly?
4. How does percentage increase differ from percentage points when calculating price changes?
5. How can inflation affect the real value of house prices over time?

**Tip:** When calculating the percentage change, ensure that the numerator (the difference) and denominator (the initial value) are clearly understood to avoid errors in interpretation.

The price of a house in a particular area has been increasing over a number of years. The value of the house increases by 9% each year. At the start of 2020, the value of the house was €240,000. (a) Work out the price of the house at the start of 2021 and the price at the start of 2023. (b) Another house was valued at €469,933. After one year, the value of this house had gone up to €477,000. Work out the percentage increase in the value of this house over the year. Give your answer correct to 1 decimal place.

This problem involves calculating the price increase of a house valued at €240,000 with a 9% annual growth rate. It also involves determining the percentage increase for another house, growing from €469,933 to €477,000. The problem covers compound growth and percentage change calculations. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation