Luka invests £1500.
At the end of the first year, 2% interest is added.
At the end of the second year, after interest has been added, the investment is worth £1606.50.

Find the interest (as a percentage) which has been added at the end of the second year.

Let's solve the problem step by step.

### Step 1: Calculate the value after the first year.
Luka invests £1500, and 2% interest is added at the end of the first year.

\[
\text{Interest for the first year} = 1500 \times \frac{2}{100} = 1500 \times 0.02 = £30
\]

\[
\text{Value at the end of the first year} = 1500 + 30 = £1530
\]

### Step 2: Determine the interest rate for the second year.
After the second year, the investment is worth £1606.50. Let the interest rate for the second year be \( r \% \).

\[
\text{Value at the end of the second year} = 1530 \times \left(1 + \frac{r}{100}\right) = 1606.50
\]

### Step 3: Solve for \( r \).
Now, solve the equation:

\[
1530 \times \left(1 + \frac{r}{100}\right) = 1606.50
\]

Divide both sides by 1530:

\[
1 + \frac{r}{100} = \frac{1606.50}{1530} = 1.05
\]

Subtract 1 from both sides:

\[
\frac{r}{100} = 0.05
\]

Multiply both sides by 100:

\[
r = 5
\]

### Conclusion:
The interest added at the end of the second year is **5%**.

Would you like any further details or have any questions? 

Here are 5 related questions you might find interesting:
1. How much would Luka's investment be worth after 3 years if the same interest rate of 5% is applied in the third year?
2. What would the total interest earned be after 2 years?
3. If the interest rate had been 3% in the second year instead of 5%, what would the investment be worth?
4. How does compound interest differ from simple interest in this context?
5. What is the formula to calculate the amount after n years with compound interest?

**Tip:** Always double-check your calculations when working with percentages and interest rates to ensure accuracy.

Learn how to calculate the interest added annually with a compound interest formula. Solve the problem where Luka invests £1500 and earns £1606.50 after 2 years with a 2% annual interest rate. Suitable for Grades 9-12.

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