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We are asked to calculate the current price of Sarah's unit trust after investing £12,000 five years ago. Here's a step-by-step breakdown of how we can solve this:

1. **Initial Investment**: £12,000 five years ago.
2. **Annual Decrease (Years 1 and 2)**: The price decreased by 3% per annum for the first 2 years.
3. **Annual Increase (Years 3, 4, and 5)**: The price increased by 7% per annum for the last 3 years.

### Step 1: Calculate the value after the first 2 years (3% decrease)
For each year of decrease:
\[
\text{Value after year 1} = 12,000 \times (1 - 0.03)
\]
\[
\text{Value after year 2} = \text{Value after year 1} \times (1 - 0.03)
\]

### Step 2: Calculate the value after the next 3 years (7% increase)
For each year of increase:
\[
\text{Value after year 3} = \text{Value after year 2} \times (1 + 0.07)
\]
\[
\text{Value after year 4} = \text{Value after year 3} \times (1 + 0.07)
\]
\[
\text{Value after year 5} = \text{Value after year 4} \times (1 + 0.07)
\]

Let me calculate the final value using these steps.The current price of Sarah's unit trust, after five years, is approximately **£13,832**.

Would you like further details or have any questions about the solution? 

Here are some related questions you might want to explore:
1. How would the result change if the initial decrease was 5% instead of 3%?
2. What is the total percentage change over the five-year period?
3. How would the final value differ if the annual increase was 10%?
4. Can you reverse this process to find the original investment from a current value?
5. How does compounding affect the result in comparison to simple interest calculations?

**Tip:** When dealing with percentage increases and decreases, always apply them step-by-step to ensure accuracy in cumulative changes.

Sarah invested £12,000 in a unit trust five years ago. The value of the unit trust has increased by 7% per annum for each of the last 3 years. Before this, the price had decreased by 3% per annum. Calculate the current price of the unit trust. Give your answer to the nearest whole number of pounds.

Learn how to calculate the current price of a unit trust after percentage decreases followed by increases. This problem focuses on compound interest formulas and percentage change calculations. Suitable for students in Grades 10-12.

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