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This is a compound interest problem. Let's go through each part step by step.

### Given Information
- Principal (initial deposit), \( P = £2000 \)
- Annual interest rate, \( r = 2.5\% = 0.025 \)
- Time, \( t = 7 \) years

The formula for compound interest is:
\[
A = P \times (1 + r)^t
\]
where:
- \( A \) is the amount in the account after \( t \) years,
- \( P \) is the initial principal,
- \( r \) is the interest rate per period (in decimal form),
- \( t \) is the time in years.

### Part (a) - Total Amount After 7 Years
Using the formula:
\[
A = 2000 \times (1 + 0.025)^7
\]

Calculating this step-by-step:
1. \( 1 + 0.025 = 1.025 \)
2. \( 1.025^7 \approx 1.1857 \)
3. \( A \approx 2000 \times 1.1857 = 2371.40 \)

So, Megan will have approximately **£2371.40** in the account after 7 years.

### Part (b) - Interest Earned Over 7 Years
The interest earned is the total amount after 7 years minus the initial deposit:
\[
\text{Interest} = A - P = 2371.40 - 2000 = 371.40
\]

So, the interest Megan will have earned from the account after 7 years is approximately **£371.40**.

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Would you like further details or have any questions?

Here are some related questions to deepen your understanding:
1. How would the answer change if the interest was compounded quarterly?
2. What if the interest rate was increased to 3% per year?
3. How much would Megan have if she withdrew the interest every year?
4. How long would it take for the initial amount to double with this interest rate?
5. What is the difference between compound and simple interest?

**Tip:** Compound interest grows faster than simple interest because it includes interest on both the initial principal and the accumulated interest.

Megan opens a savings account which gives compound interest of 2.5% per year. She puts £2000 into it.

a) How much money will Megan have in the account after 7 years?

b) How much interest will Megan have earned from this account after 7 years?

Give your answers in pounds (£) to the nearest 1p.

This example demonstrates how to calculate compound interest on an initial deposit of £2000 with an annual rate of 2.5% over 7 years. Learn to use the compound interest formula and determine both the total amount and the interest earned. Perfect for students in Grades 9-11.

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