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Nisha deposits Rs. 3,000 in her RD account once every 3 months and never withdraws the amount. The bank pays a simple interest of 5% per annum on the amount deposited. The interest is deposited every three months- on 1st January, 1st April, 1st July and 1st October every year. If Nisha opened this RD account on 1st January 2022 with the first deposit of Rs.3,000, then what will be her account balance on 1st January 2024 after the bank has deposited the interest and Nisha has deposited Rs.3,000 due on that day ?Rs. 24,000Rs. 25,350Rs. 27,000Rs. 28,350

Question

Nisha deposits Rs. 3,000 in her RD account once every 3 months and never withdraws the amount. The bank pays a simple interest of 5% per annum on the amount deposited. The interest is deposited every three months- on 1st January, 1st April, 1st July and 1st October every year. If Nisha opened this RD account on 1st January 2022 with the first deposit of Rs.3,000, then what will be her account balance on 1st January 2024 after the bank has deposited the interest and Nisha has deposited Rs.3,000 due on that day ?Rs. 24,000Rs. 25,350Rs. 27,000Rs. 28,350

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Solution

To calculate Nisha's account balance on 1st January 2024, we need to consider the deposits she makes every 3 months and the interest deposited by the bank.

  1. First, let's calculate the interest earned on Nisha's deposits. The bank pays a simple interest of 5% per annum, which is divided into four equal parts and deposited every three months.

  2. Nisha opened the RD account on 1st January 2022 with a deposit of Rs. 3,000. The first interest deposit will be made on 1st April 2022.

  3. From 1st April 2022 to 1st January 2024, there will be a total of 8 interest deposits made by the bank. Each deposit will be 5% of the previous balance.

  4. To calculate the interest earned on each deposit, we can use the formula: Interest = Principal * Rate * Time. Here, the principal is the previous balance, the rate is 5% (0.05), and the time is 3 months (0.25 years).

  5. We can calculate the interest earned on each deposit and add it to the previous balance to get the new balance after each deposit.

  6. After the 8th interest deposit on 1st January 2024, Nisha will also deposit Rs. 3,000 due on that day.

  7. Finally, we can add up all the deposits and interest earned to find Nisha's account balance on 1st January 2024.

Let's calculate the account balance step by step:

  1. Initial deposit on 1st January 2022: Rs. 3,000

  2. Interest deposit on 1st April 2022: Interest = Rs. 3,000 * 0.05 * 0.25 = Rs. 37.50 New balance = Rs. 3,000 + Rs. 37.50 = Rs. 3,037.50

  3. Interest deposit on 1st July 2022: Interest = Rs. 3,037.50 * 0.05 * 0.25 = Rs. 37.97 New balance = Rs. 3,037.50 + Rs. 37.97 = Rs. 3,075.47

  4. Interest deposit on 1st October 2022: Interest = Rs. 3,075.47 * 0.05 * 0.25 = Rs. 38.44 New balance = Rs. 3,075.47 + Rs. 38.44 = Rs. 3,113.91

  5. Interest deposit on 1st January 2023: Interest = Rs. 3,113.91 * 0.05 * 0.25 = Rs. 38.92 New balance = Rs. 3,113.91 + Rs. 38.92 = Rs. 3,152.83

  6. Interest deposit on 1st April 2023: Interest = Rs. 3,152.83 * 0.05 * 0.25 = Rs. 39.41 New balance = Rs. 3,152.83 + Rs. 39.41 = Rs. 3,192.24

  7. Interest deposit on 1st July 2023: Interest = Rs. 3,192.24 * 0.05 * 0.25 = Rs. 39.90 New balance = Rs. 3,192.24 + Rs. 39.90 = Rs. 3,232.14

  8. Interest deposit on 1st October 2023: Interest = Rs. 3,232.14 * 0.05 * 0.25 = Rs. 40.40 New balance = Rs. 3,232.14 + Rs. 40.40 = Rs. 3,272.54

  9. Interest deposit on 1st January 2024: Interest = Rs. 3,272.54 * 0.05 * 0.25 = Rs. 40.91 New balance = Rs. 3,272.54 + Rs. 40.91 = Rs. 3,313.45

  10. Additional deposit on 1st January 2024: Rs. 3,000

  11. Final account balance on 1st January 2024: Total balance = Rs. 3,313.45 + Rs. 3,000 = Rs. 6,313.45

Therefore, Nisha's account balance on 1st January 2024 will be Rs. 6,313.45.

This problem has been solved

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