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Let's break down the problem step by step:

Sarah invested £12,000 in a unit trust five years ago.

1. For the first two years, the price of the unit trust decreased by 3% per annum.
2. For the last three years, the price increased by 7% per annum.

### Step 1: Calculate the value after the first two years (3% annual decrease)
The formula for depreciation is:
\[
\text{New Value} = \text{Initial Value} \times (1 - \text{Rate of Decrease})^n
\]
Where:
- Initial Value = £12,000
- Rate of Decrease = 3% = 0.03
- n = 2 years

\[
\text{Value after 2 years} = 12,000 \times (1 - 0.03)^2
= 12,000 \times 0.97^2
\]
\[
\text{Value after 2 years} = 12,000 \times 0.9409 = 11,290.8
\]

### Step 2: Calculate the value after the next three years (7% annual increase)
The formula for appreciation is:
\[
\text{New Value} = \text{Initial Value} \times (1 + \text{Rate of Increase})^n
\]
Where:
- Initial Value = £11,290.8
- Rate of Increase = 7% = 0.07
- n = 3 years

\[
\text{Value after 5 years} = 11,290.8 \times (1 + 0.07)^3
= 11,290.8 \times 1.07^3
\]
\[
= 11,290.8 \times 1.225043
= 13,823.57
\]

### Final Answer:
The current price of the unit trust is approximately **£13,824** (rounded to the nearest whole number).

Would you like further details or have any other questions?

Here are some related questions:
1. How does compound interest work with annual percentage changes?
2. How would the answer change if the rate of increase were different for each year?
3. What is the difference between linear and compound growth in investment returns?
4. How can investment risks be factored into these calculations?
5. How do financial calculators simplify these compound interest problems?

**Tip:** For compound growth, small changes in the percentage rate can have significant impacts over multiple years, so always account for compounding effects when planning investments.

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 experiencing 3% annual depreciation for 2 years, followed by 7% annual appreciation for 3 years. This problem demonstrates the application of compound interest for both percentage decrease and increase. Suitable for Grades 9-12.

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