Connor invests £700 into an account that pays compound interest at a rate of

1% per year for 2 years
then 1.5% per year for 4 years.

Work out the value of Connor’s investment at the end of the 6 years.

To calculate the value of Connor's investment after 6 years with compound interest, we'll break it down into two parts based on the given interest rates:

### Step 1: Investment for the first 2 years at 1% interest per year

For compound interest, the formula is:

\[
A = P \times \left(1 + \frac{r}{100}\right)^n
\]

Where:
- \(A\) is the amount after interest.
- \(P\) is the initial principal.
- \(r\) is the annual interest rate.
- \(n\) is the number of years.

#### First 2 years:
- \(P = 700\)
- \(r = 1\%\)
- \(n = 2\)

\[
A = 700 \times \left(1 + \frac{1}{100}\right)^2
\]

\[
A = 700 \times \left(1.01\right)^2
\]

\[
A = 700 \times 1.0201 = 714.07
\]

At the end of 2 years, Connor's investment is worth **£714.07**.

### Step 2: Investment for the next 4 years at 1.5% interest per year

Now, we use the new principal of £714.07 and apply the new interest rate of 1.5% for 4 years.

#### Next 4 years:
- \(P = 714.07\)
- \(r = 1.5\%\)
- \(n = 4\)

\[
A = 714.07 \times \left(1 + \frac{1.5}{100}\right)^4
\]

\[
A = 714.07 \times \left(1.015\right)^4
\]

\[
A = 714.07 \times 1.0614 = 757.23
\]

At the end of the 6 years, Connor’s investment is worth **£757.23**.

### Final Answer:
The value of Connor's investment after 6 years is **£757.23**.

---

Would you like any more details on how this was calculated?

Here are some related questions:
1. What is the difference between compound and simple interest?
2. How does the interest rate affect the investment growth over time?
3. What is the formula for compound interest when interest is compounded monthly?
4. How does changing the number of compounding periods per year affect the final amount?
5. Can the interest rate be negative, and what does that mean for the investment?

**Tip:** Compound interest grows exponentially, so even small increases in the interest rate or investment period can significantly boost returns over time.

Connor invests £700 into an account that pays compound interest at a rate of 1% per year for 2 years then 1.5% per year for 4 years. Work out the value of Connor’s investment at the end of the 6 years.

Calculate the value of an investment with compound interest over 6 years, starting with £700. This problem uses the compound interest formula and features an interest rate of 1% for the first 2 years and 1.5% for the next 4 years. Suitable for Grades 9-10 students.

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