What is the exact time when the total amount of money reache

To solve this problem, we need to track the growth of both the bank account and the amount in the safe-deposit box over each time period and determine when their total reaches 35,000 euros.

Bank Account

• Initial deposit: 4000 euros
• Interest rate: 5% per year, compounded annually

Safe-Deposit Box

• Annual addition: 5000 euros
• No interest is applied to the money here

Total Goal

• Reach a total of 35,000 euros.

Let's calculate year by year:

1. Year 1:
2. Bank Account: $4000\times 1.05=4200$
3. Safe-Deposit: 5000

4. Total: $4200+5000=9200$

5. Year 2:

6. Bank Account: $4200\times 1.05=4410$
7. Safe-Deposit: $5000\times 2=10,000$

8. Total: $4410+10,000=14,410$

9. Year 3:

10. Bank Account: $4410\times 1.05=4630.5$
11. Safe-Deposit: $5000\times 3=15,000$

12. Total: $4630.5+15,000=19,630.5$

13. Year 4:

14. Bank Account: $4630.5\times 1.05=4862.025$
15. Safe-Deposit: $5000\times 4=20,000$

16. Total: $4862.025+20,000=24,862.025$

17. Year 5:

18. Bank Account: $4862.025\times 1.05=5105.12625$
19. Safe-Deposit: $5000\times 5=25,000$

20. Total: $5105.12625+25,000=30,105.12625$

21. Year 6:

22. Bank Account: $5105.12625\times 1.05=5359.3825625$
23. Safe-Deposit: $5000\times 6=30,000$
24. Total: $5359.3825625+30,000=35,359.3825625$

Based on the above calculations, the total amount of money exceeds 35,000 euros between year 5 and 6, specifically at 6 years. If we are looking for an exact time, further refinement would be needed by solving the continuous equation, but the simplest integer number that first exceeds 35,000 in our calculations is at year 6.