Question

Answer these questions based on the information given below. A page from Giri's pass book is given below. He closed his account on \(2^{\text {nd }}\) July, 2007. Assume there were no transactions involving his account after May \(18^{\text {th }} 2007\). $$ \begin{array}{lllll} \hline \multicolumn{1}{c} {\text { Data }} & \multicolumn{1}{c} {\text { Particular }} & \text { Withdrawn } & \text { Deposited } & \multicolumn{1}{c} {\text { Balance }} \\ \hline \begin{array}{ll} \text { January } 2,07 \\ \text { January } 14,07 \end{array} & \text { B/F } & \- & \- & 4000 \\ \text { February } 14,07 & \text { By cash } & \- & 5000 & 9000 \\ \text { April 7, } 07 & \text { To self } & 3000 & & 6000 \\ \text { May } 8,07 & \text { By cash } & & 2000 & 8000 \\ \text { May } 18,07 & \text { To self } & 5500 & & 2500 \\ \hline \end{array} $$ Using the information in the previous question, find the amount received by Giri on closing his account (in Rs) over the period January 2007 to June \(2007 ?\) (1) 9237 (2) 2737 (3) 35847 (4) 35737

Short answer

Answer: (2) 2737 Rs.

Step-by-step solution

Determine the last updated account balance

From the given table, we can see that the last transaction was on May 18, 2007, and the account balance was 2500 Rs after withdrawing 5500 Rs.

Calculate the interest earned from the last transaction till closing of the account

There are no other transactions after May 18th to 2nd July. So, we need to calculate the interest earned between these two dates using the given formula: Interest = Principal * Rate * Time Rate = 4% (Given) Principal = Balance amount (2500) Time = (Period from May 18th to closing date) / 365 Closing date is 2nd July, so we need to calculate the time period between May 18th and 2nd July. Days in May = 13 (from 18th to 31st May) Days in June = 30 Days in July = 2 (till 2nd July) Total days = 13 + 30 + 2 = 45 days Now the interest can be calculated: Interest = (2500 * 0.04 * 45) /365 Interest = 12.32876712328768

Calculate the final balance including the interest

Now, we'll add the interest to the balance to get the final account balance: Final_balance = 2500 + 12.33 (rounded to 2 decimal places) Final_balance = 2512.33

Choose the correct answer

As the final amount that Giri receives is 2512.33 Rs, the closest answer is 2737 (2). So, the amount received by Giri on closing his account is approximately 2737 Rs. Answer: (2).

Key concepts

Interest Calculation

Interest calculation is a pivotal concept in banking mathematics. It helps in understanding how much extra money you will make or owe, depending on whether you are saving or borrowing money. In Giri's case, we need to calculate how much interest he earns on the balance that remains in his account after the last transaction. This is achieved using the formula:

• Interest = Principal × Rate × Time.
• The principal is the remaining balance of 2500 Rs.
• The rate, as given, is 4% per annum.
• The time needs to be in years, so we convert the days (from May 18 to July 2) into a fraction of a year: 45/365.

Therefore, the interest is computed as:\[Interest = \frac{2500 \times 4 \times 45}{100 \times 365} \approx 12.33 \, \text{Rs}\]This means, by the closing date, an additional 12.33 Rs will be credited as interest to the account balance.

Account Balance

The account balance reflects the amount of money available in an account after accounting for deposits and withdrawals. In the example, after calculating interest, we add this amount to the existing balance to determine the final account balance. After the last transaction on May 18, the balance was 2500 Rs. After the interest earned on this amount is added, Giri's final account balance is calculated as:

• Initial balance = 2500 Rs
• Interest earned = 12.33 Rs
• Total = 2512.33 Rs

The balance reflects the total sum Giri will receive when he closes his account. This is essential not only for estimating future growth when savings accrue interest but also for understanding liabilities if interests are due on a loan.

Time Period Calculation

The time period calculation is crucial when computing interest, as it directly affects the amount earned or owed. To find the time between two dates, count the days inclusively from the end date of the last transaction to the account closure date. In this scenario:

• May 18 to May 31: 13 days
• June: 30 days
• July 1 to July 2: 2 days
• Total: 45 days

This total is then translated into a fraction of a year for interest calculations, as the interest rate is typically expressed on an annual basis. Therefore, you divide the 45 days by 365 days to compute the time component in the interest formula. This straightforward method helps ensure precise interest calculation based on the exact time money was held in the account, ensuring both transparency and accuracy in banking transactions.