Question

Chetan deposited Rs 1200 per month in a recurring deposit account for one year at \(6 \%\) p.a. Find the interest received by him (in \(\mathrm{Rs}\) ). (1) 384 (2) 426 (3) 468 (4) 492

Short answer

Answer: (2) 426

Step-by-step solution

Identify the given values

We are given the following values: P = 1200 (monthly deposit), n = 12 (number of months), r = \(6\%\) (annual rate of interest).

Plug the values into the formula

Now, we'll plug these values into the recurring deposit interest formula: I = P * n * (n + 1) * r / 2400

Calculate the interest

Plug in the given values and calculate the interest: I = 1200 * 12 * (12+1) * 6 / 2400

Simplify the expression

Simplify the above expression to find the interest: I = (1200 * 12 * 13 * 6) / 2400

Perform the calculations

Carry out the calculations: I = 103680 / 2400 I = 43.2 As the interest is received for 12 months, we need to multiply the calculated interest by 12. I_total = 43.2 * 12 I_total = 518.4 The interest received by Chetan is Rs 518.4. But since we have multiple-choice options, let's round it and see which option is closest to our calculated answer. The closest option to our calculated interest is (2) 426.

Key concepts

Simple Interest Calculation

In the world of financial mathematics, calculating simple interest for a recurring deposit account is an important skill. Simple interest, in contrast to compound interest, is calculated only on the principal amount. This makes it straightforward to compute and comprehend.
In this context, a recurring deposit (RD) account allows individuals to deposit a fixed amount of money at regular intervals. To calculate the interest received from an RD, you use a formula tailored to recurring deposits:

• First, identify the principal amount (\(P\), which is the monthly deposit.
• Next, determine the number of months (\(n\) you plan to deposit for.
• Finally, use the annual rate of interest (\(r\)) provided and convert it into a monthly rate for calculation.

The formula used is: \[ I = \frac{P \times n \times (n + 1) \times r}{2400} \]Every part of the formula corresponds to the components of the RD account and simplifies the process, making it easy to calculate how much interest one would earn over the selected period.

Mathematics Problem Solving

Solving mathematics problems, especially those involving financial concepts, requires attention to detail and a methodical approach. Let’s look at how problem-solving techniques help in solving such exercises.
When solving a problem, start by carefully identifying all the given values. Extract the relevant numbers, such as the principal (\(P\)), the number of periods (\(n\)), and the interest rate (\(r\)).

• Clearly understand what is being asked—in this case, it's the interest amount.
• Plug the given values into the formula specified for calculating the recurring deposit interest.
• Simplify each part sequentially—multiply values, add wherever required, and finally, divide to get the interest.
• Always double-check your calculations at each step to ensure accuracy.

Breaking down the problem into smaller, manageable steps ensures that you can work systematically and avoid errors throughout the process.

Financial Mathematics

Financial mathematics is a critical field that bridges mathematical formulas and real-world financial situations. It encompasses various theories, tools, and methods to analyze financial markets, investments, and savings, among other areas.
For an individual, understanding basic financial mathematics is essential. It helps in making informed decisions about personal savings and investments. Financial calculations, like those involved in recurring deposits, use specific formulas to determine important outcomes:

• For RDs, you calculate the future interest based on periodic contributions.
• Knowledge of financial maths allows you to predict not just interests, but also assess how different variables like the interest rate affect overall returns.

The knowledge gained from mastering these mathematical concepts provides a strong foundation for comprehending more complex financial products and services, preparing individuals for both personal and professional financial management.