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 \(18^{\text {th }} 2007\). $$ \begin{array}{lllll} \hline \multicolumn{1}{c} {\text { Data }} & \multicolumn{1}{c} {\text { Particular }} & \text { Withdrawn } & \text { Deposited } & \multicolumn{1}{c} {\text { Balance }} \\ \hline \begin{array}{ll} \text { January } 2,07 \\ \text { January } 14,07 \end{array} & \text { B/F } & \- & \- & 4000 \\ \text { February } 14,07 & \text { By cash } & \- & 5000 & 9000 \\ \text { April 7, } 07 & \text { To self } & 3000 & & 6000 \\ \text { May } 8,07 & \text { By cash } & & 2000 & 8000 \\ \text { May } 18,07 & \text { To self } & 5500 & & 2500 \\ \hline \end{array} $$ If the bank paid Giri interest at \(8 \%\) p. a, then find the interest received by Giri on closing his account (in Rs) approximately. (1) 226 (2) 280 (3) 237 (4) 240

Short answer

Answer: 224 Rs.

Step-by-step solution

Calculate the number of days for each balance

To calculate the number of days for each balance, we will need to determine the period of time between each transaction and then add two extra months without transactions. Here's the breakdown: - January 14, 2007 - January 2, 2007: 12 days - February 14, 2007 - January 14, 2007: 31 days - April 7, 2007 - February 14, 2007: 52 days - May 8, 2007 - April 7, 2007: 31 days - May 18, 2007 - May 8, 2007: 10 days - July 2, 2007 - May 18, 2007: 45 days (2 extra months)

Calculate the interest for each balance period

Now that we have the number of days for each balance, we will calculate the interest for each period by using the following formula: Interest = (Principal * Rate * Time) / 365 Applying this formula for each balance period: - Interest for 12 days at Rs 4000: (4000 * 0.08 * 12) / 365 = 10.41 - Interest for 31 days at Rs 9000: (9000 * 0.08 * 31) / 365 = 74.85 - Interest for 52 days at Rs 6000: (6000 * 0.08 * 52) / 365 = 54.25 - Interest for 31 days at Rs 8000: (8000 * 0.08 * 31) / 365 = 54.52 - Interest for 10 days at Rs 2500: (2500 * 0.08 * 10) / 365 = 5.48 - Interest for 45 days at Rs 2500: (2500 * 0.08 * 45) / 365 = 24.66

Calculate the total interest

To calculate the total interest Giri received, we will add up all the interest amounts from each balance period: Total interest = 10.41 + 74.85 + 54.25 + 54.52 + 5.48 + 24.66 = 224.17 Since we are asked to approximate the interest received by Giri, we can round the total interest to the nearest whole number. In this case, the interest received by Giri is approximately 224 Rs. The closest answer choice to this number is (1) 226 Rs.

Key concepts

Bank Transactions

Bank transactions are movements of money into or out of a bank account. They include any action that impacts the balance, such as deposits, withdrawals, and transfers. In Giri's passbook, the transactions recorded are withdrawals and deposits which changed the account balance over time. Each transaction alters the available balance and affects the interest accrued. Understanding how these transactions work is crucial, as they are the basic activities in managing a bank account. They reflect the inflow and outflow of money, dictating how much interest one could potentially earn based on the bank's terms and conditions.

Interest Rate Calculation

Interest rate calculation involves determining the amount of money that will be earned or paid over time, based on the principal, which is the initial amount invested or borrowed. In Giri's case, the interest paid by the bank is calculated based on the balance of the account at different times and for different durations.The formula used is: \[ \text{Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{365} \]Here, the rate is the annual interest rate provided by the bank, which is 8% per annum for Giri. This formula helps in determining the exact interest accrued over specific periods, calculated in days, making it quite effective for precise financial assessments.

Passbook Ledger

A passbook ledger is like a financial diary for a bank account. It records all the transactions made, including deposits, withdrawals, and the resulting balance. For Giri, the passbook ledger contains several entries from January to May, each impacting the balance differently. The ledger outlines the history of transactions in order, facilitating easy tracking of financial activity.

• Every deposit increases the balance and thus the potential interest earnings.
• Withdrawals decrease the balance and limited potential interest accrual.

This document is crucial in maintaining accurate financial records, allowing for easy reference and verification of transactions at any point.

Time Duration in Interest Calculation

Time duration heavily influences interest calculation, as it determines how long a particular balance earns interest. In the exercise, different periods between transactions are calculated in days, reflecting the practical application of time in simple interest calculations. For each balance period, the duration varies, impacting the total interest earned. For example, the 52-day period between February and April greatly differs from the shorter 10-day period in May, showing how vital tracking time is in understanding interest. This concept reinforces the importance of closely monitoring timeframes, as even slight changes can significantly impact accrued interest.