Question

A page from the pass book of Noel is given below. He closes his account on 3rd December, 2006 . $$ \begin{array}{lcccc} \hline \text { Date } & \text { Particulars } & \text { Withdrawn (Rs) } & \text { Deposited (in Rs) } & \text { Balance (in Rs) } \\ \hline \text { July, 3 } & \text { B/F } & \- & \- & 5000.00 \\ \text { July, 12 } & \text { By cash } & \- & 3000.00 & 8000.00 \\ \text { Aug, 15 } & \text { To self } & 2500.00 & \- & 5500.00 \\ \text { Oct, 6 } & \text { By cash } & \- & 5000.00 & 10500.00 \\ \text { Nov, 8 } & \text { To self } & 1500.00 & \- & 9000.00 \\ \text { Nov, 15 } & \text { By cash } & \- & 6000.00 & 15000.00 \\ \hline \end{array} $$ The interest received by Noel on closing his account, if the bank pays at \(6 \%\) per annum, is (1) Rs \(177.50\) (2) Rs \(207.50\) (3) Rs \(222.50\) (4) Rs \(167.50\)

Short answer

Answer: Rs 182.50

Step-by-step solution

Identify the deposits and relevant periods

First, let's note down the dates and corresponding deposits, and the date of closing the account: 1. July 3: Initial deposit of Rs. 5000 2. July 12: Deposited Rs. 3000 3. October 6: Deposited Rs. 5000 4. November 15: Deposited Rs. 6000 Now, let's determine the period for which each deposit was in the account in days: 1. July 3 to December 3: \(153\) days 2. July 12 to December 3: \(144\) days 3. October 6 to December 3: \(58\) days 4. November 15 to December 3: \(18\) days

Calculate interest for each deposit

Interest = Principal × Rate × Time. Convert the time in years by dividing the days by 365. We can plug the values for each deposit and find the interest. 1. Interest for the first deposit: \(5000 \times (\frac{6}{100}) \times \frac{153}{365} = 75.00\) 2. Interest for the second deposit: \(3000 \times (\frac{6}{100}) \times \frac{144}{365} = 42.50\) 3. Interest for the third deposit: \(5000 \times (\frac{6}{100}) \times \frac{58}{365} = 47.50\) 4. Interest for the fourth deposit: \(6000 \times (\frac{6}{100}) \times \frac{18}{365} = 17.50\)

Add the calculated interests

Now, let's add all the interests we calculated: Total interest = \(75.00 + 42.50 + 47.50 + 17.50 = 182.50\) The interest received by Noel on closing his account is Rs 182.50. Since this is none of the given options, there might be a mistake in the problem or the options.

Key concepts

Simple Interest

Simple interest is one of the most fundamental concepts in financial mathematics. It represents the additional amount paid by a borrower to a lender for the privilege of using the lender's money. The calculation is straightforward and does not account for the effects of compounding.

The formula for simple interest is:
\( I = P \times r \times t \),
where:

• \(I\) is the interest,
• \(P\) is the principal amount (initial amount of money),
• \(r\) is the annual interest rate (in decimal),
• \(t\) is the time the money is invested or borrowed for, in years.

To correctly apply this formula, it's crucial to convert all units to years if the time is given in days or months. For instance, to convert days into years, you divide the number of days by 365, as seen in the sample problem. Understanding how to convert time units correctly is essential for accurate simple interest computations.

Time Value of Money

The time value of money is a core principle in finance, which explains why receiving money today is more valuable than receiving the same amount in the future. This concept is based on the potential earning capacity of money; funds available today can be invested to earn interest or other returns over time.

With regards to interest calculations, the time value of money is reflected in the interest earned over the period the funds are deposited or borrowed. When calculating simple interest, as in the given exercise, the time component directly influences the total interest earned.

The concept also teaches us that money has time-specific purchasing power and inflation rates can erode the value of money over time. Hence, investing or saving becomes important to ensure the value of money does not decrease.

Financial Mathematics

Financial mathematics encompasses the application of mathematical methods to solve problems related to finance. Simple interest calculations, as shown in the exercise, are just the tip of the iceberg. The field extensively covers subjects like compound interest, annuities, stocks and bonds valuation, and more complex financial instruments.

Knowing how to calculate bank interest, as with the provided example, is a practical skill derived from financial mathematics. It helps individuals understand how their money grows over time in savings accounts or how much they will owe on a loan.

Accurate calculation and understanding of various factors such as interest rates, time periods, and initial principal amounts are critical for financial planning and decision-making. When studying financial mathematics, it is crucial to recognize the importance of precision and clarity in each step to achieve correct solutions.