On World Savings Day (October 31, 2023) you open a savings account with 550 euros. In the following two months, an interest rate of 3% p.a. applies with monthly interest On January 1st, 2024, the bank announces a change to quarterly interest at 2.7% p.a. On April 1st, 2024 you pay 400 euros into the savings account. On June 30th, 2024 you withdraw 100 euros. What is the balance in your savings account on October 1st, 2024? a) 868.77 b) 910.34 c) 860.77 d) 862.54 e) 409.03

To calculate the balance in your savings account on October 1st, 2024, we need to break down the timeline and compute the balance step by step: 1. Initial deposit on October 31, 2023: 550 euros. 2. November 2023: - Interest: (550 * 0.03) / 12 = 1.375 euros. - Total: 550 + 1.375 = 551.375 euros. 3. December 2023: - Interest: (551.375 * 0.03) / 12 = 1.3784375 euros. - Total: 551.375 + 1.3784375 = 552.7534375 euros. 4. January 2024: - Change to quarterly interest at 2.7% p.a. - Interest for the quarter: (552.7534375 * 0.027) / 4 = 3.73142974219 euros. - Total: 552.7534375 + 3.73142974219 = 556.48486724219 euros. 5. February 2024: - Interest for the quarter: (556.48486724219 * 0.027) / 4 = 3.77287077833 euros. - Total: 556.48486724219 + 3.77287077833 = 560.25773802052 euros. 6. March 2024: - Interest for the quarter: (560.25773802052 * 0.027) / 4 = 3.81456694733 euros. - Total: 560.25773802052 + 3.81456694733 = 564.07230496785 euros. 7. April 1, 2024: - Deposit of 400 euros. - Total: 564.07230496785 + 400 = 964.07230496785 euros. 8. May 2024: - Interest for the quarter: (964.07230496785 * 0.027) / 4 = 6.53536642742 euros. - Total: 964.07230496785 + 6.53536642742 = 970.60767139527 euros. 9. June 2024: - Withdrawal of 100 euros. - Total: 970.60767139527 - 100 = 870.60767139527 euros. The final balance on October 1st, 2024 is approximately 870.61 euros. So, the closest answer from the options provided is: a) 868.77