Step 1: We need to calculate the interest earned over 5 years.
We will use the formula for compound interest: A = P \left(1 + \frac{r}{100}\right)^n
Where:
A = amount after n years
P = starting principal amount (10 000 € in this case)
r = annual interest rate (3% in this case)
n = number of years (5 years in this case)
Plugging in the values:
A = 10 000 \left(1 + \frac{3}{100}\right)^5
Step 2: Calculate the amount after 5 years without tax.
A = 10 000 \times (1 + 0.03)^5 = 10 000 \times 1.15927 \approx 11 592.70
Step 3: Calculate the interest earned:
11 592.70 - 10 000 = 1 592.70 \text{ euros}
Step 4: Calculate the withholding tax on the interest earned at 30%.
0.30 \times 1 592.70 = 477.81
Step 5: Calculate the final amount left after deducting the withholding tax:
11 592.70 - 477.81 = 11 114.89
\boxed{11 114.89 \text{ euros}}
Answer: After 5 years, Matilda will have approximately 11 114.89 euros in her savings account.