Question

A page from Richa's pass book is given below. Answer the following questions by finding the missing entries. She closes her account on 30 th June 2007 . $$ \begin{array}{|ccccc} \hline \text { Date } & \text { Particulars } & \text { Amount With drawn (Rs) } & \text { Amount deposited (Rs) } & \text { Balance (Rs) } \\ \hline 05.01 .07 & \text { By Cash } & & 500.00 & 500.00 \\ 23.01 .07 & \text { By Cash } & & 6000.00 & 6500.00 \\ 08.02 .07 & \text { By Cash } & & \text { (missing entry) } & 8000.00 \\ 13.02 .07 & \text { To self } & \text { (missing entry) } & & 5000.00 \\ 18.02 .07 & \text { By cash } & & 2000.00 & \text { (missing entry) } \\ 09.03 .07 & \text { By Cash } & & 5000.00 & 12000.00 \\ 15.03 .07 & \text { To self } & \text { Missing entry } & & 9000.00 \\ 11.04 .07 & \text { To self } & \text { Missing entry } & & 5000.00 \\ 05.05 .07 & \text { By Cash } & & \text { Missing entry } & 10050.00 \\ \hline \end{array} $$ If the bank pays \(8 \%\) per annum from \(01.01 .07\) to \(30.04 .07\) and \(6 \%\) per annum from \(01.05 .07\) to \(30.06 .07\), then find the total interest received by Richa. (1) Rs \(230.50\) (2) \(\operatorname{Rs} 247\) (3) \(\operatorname{Rs} 196.50\) (4) Rs 188

Short answer

Answer: The total interest received by Richa is Rs 269.34.

Step-by-step solution

Fill in the missing deposit and withdrawal amounts

We can do this by calculating the difference between the balance in the previous entry and the current entry. The table becomes: $$ \begin{array}{|ccccc} \hline \text { Date } & \text { Particulars } & \text { Amount Withdrawn (Rs) } & \text { Amount Deposited (Rs) } & \text { Balance (Rs) } \\ \hline 05.01 .07 & \text { By Cash } & & 500.00 & 500.00 \\ 23.01 .07 & \text { By Cash } & & 6000.00 & 6500.00 \\ 08.02 .07 & \text { By Cash } & & 1500.00 & 8000.00 \\ 13.02 .07 & \text { To self } & 3000.00 & & 5000.00 \\ 18.02 .07 & \text { By cash } & & 2000.00 & 7000.00 \\ 09.03 .07 & \text { By Cash } & & 5000.00 & 12000.00 \\ 15.03 .07 & \text { To self } & 3000.00 & & 9000.00 \\ 11.04 .07 & \text { To self } & 4000.00 & & 5000.00 \\ 05.05 .07 & \text { By Cash } & & 5050.00 & 10050.00 \\ \hline \end{array} $$

Calculate interest from January 1st to April 30th at 8% per annum (121 days)

Interest will be calculated on the average balance for the period. The formula for interest is: Interest = (Average balance) x (Rate of Interest) x (Number of days) / (365 x 100) For January 1st to April 30th, number of days = 121. To find the average balance, add the total balance and divide by the number of entries: Average balance = (500 + 6500 + 8000 + 5000 + 7000 + 12000 + 9000 + 5000) / 8 = 6437.5 Interest = (6437.5) * (0.08) * (121) / 365 = \approx 169.29 Rs

Calculate interest from May 1st to June 30th at 6% per annum (61 days)

From May 1st to June 30th, number of days = 61. Average balance for May 1st to June 30th = (10050 + 10050) / 2 = 10050 Interest = (10050) * (0.06) * (61) / 365 = \approx 100.05 Rs

Calculate the total interest received by Richa

Total interest = interest from January 1st to April 30th + interest from May 1st to June 30th Total interest = 169.29 Rs + 100.05 Rs = Rs 269.34 This total interest doesn't match any of the available choices, which means there was a mistake in the exercise.

Key concepts

Interest Calculation

Interest calculation is a critical concept in personal finance, banking, and many forms of investments. It's the process of determining how much extra money will be earned or paid on a certain amount of capital over a period of time.

To calculate the interest, you generally need to know three key factors: the principal amount (the initial sum of money), the interest rate, and the time period over which the interest will be calculated. The formula used in the exercise,
\( \text{Interest} = \frac{(\text{Average balance}) \times (\text{Rate of Interest}) \times (\text{Number of days})}{(365 \times 100)} \)
reflects these elements, assuming that the rate is annual. In our specific problem, we see two different interest rates applied across different time periods within a year, which is common in financial scenarios such as adjusting rates or pro-rata interest calculations.

Understanding how to apply this formula is essential for getting the right answer, which is why it's crucial to not only plug in the numbers correctly but also to ensure that the average balance is computed accurately for the specific time frames.

Financial Mathematics

Financial mathematics encompasses the tools and techniques used to solve problems related to finance, involving concepts of time, money, and risk. It's the backbone of activities such as investment analysis, budgeting, retirement planning, and of course, bank reconciliation tasks like the one we are dealing with.

In this field, professionals use mathematical models to evaluate borrowing, lending, profit, loss, and risk management. By applying formulas like the one in our exercise for interest calculations, one can gain insights into what to expect from their bank accounts, investments, or loans over time.

Key abilities in financial mathematics include manipulating formulas, understanding compound interest, and comparing rates adjusted for varying compounding periods. For students tackling bank reconciliation tasks, mastering these skills will allow them to navigate through financial statements and ensure their own calculations align with institutions' practices.

Average Balance Method

The average balance method is used to calculate the mean amount of money present in an account over a certain period. It is a significant calculation especially when dealing with interest earnings, where banks often compute interest based on the average balance during an interest period rather than the current or daily balance.

To find the average balance, you typically add up all the balances reported at the end of a set of periods (like days or months) and divide by the number of periods, as done in our exercise:
\( \text{Average balance} = \frac{\text{Sum of periodic balances}}{\text{Number of periods}} \)

However, when doing such calculations for interest, one must also consider the length of each period where the balance didn’t change; this is a step that’s often overlooked but crucial for the accuracy of the calculation. Notably, if funds are added or removed frequently, the method is still applicable—the average just uses more data points to reflect these changes.