To calculate the total amount of money in your bank account at the end of 3 years, we need to consider the deposits, withdrawals, and the interest rate applied annually. Let's break this down step-by-step:

Year 1

1. Initial deposit on 13th birthday: $100
2. Interest for Year 1:
   • Interest rate: 4% per annum
   • Interest earned = $100 * 4% = $4
3. Total amount at the end of Year 1: $100 + $4 = $104

Year 2

1. Deposit on 14th birthday: $100
   • New balance before withdrawal: $104 (from Year 1) + $100 = $204
2. Withdrawal immediately after deposit: $50
   • New balance after withdrawal: $204 - $50 = $154
3. Interest for Year 2:
   • Interest earned = $154 * 4% = $6.16
4. Total amount at the end of Year 2: $154 + $6.16 = $160.16

Year 3

1. Deposit on 15th birthday: $100
   • New balance before interest: $160.16 + $100 = $260.16
2. Interest for Year 3:
   • Interest earned = $260.16 * 4% = $10.4064 (rounded to $10.41)
3. Total amount at the end of Year 3: $260.16 + $10.41 = $270.57

Therefore, the total amount in your bank account at the end of year 3 is $270.57.

If you have any further questions or need more details, feel free to ask.

Here are some related questions to expand your understanding:

1. How does compounding interest differ from simple interest in long-term savings?
2. What would be the total amount if no withdrawals were made?
3. How would the total change if the interest rate were compounded monthly instead of annually?
4. What impact does a different interest rate (e.g., 5% p.a.) have on the final amount?
5. How do different withdrawal amounts affect the overall interest earned?
6. What would be the impact of depositing more money each year?
7. How can you calculate the future value of an account with regular deposits and variable interest rates?
8. What strategies can maximize the interest earned in a savings account?

Tip: Keeping withdrawals to a minimum and allowing interest to compound can significantly increase the amount of money earned in a savings account over time.