Question

What is the rate of simple interest at which Rs. 14,000 gives interest of Rs. 1960 in two years? (a) $4\mathrm{\%}$ (b) $5\mathrm{\%}$ (c) $7\mathrm{\%}$ (d) $10\mathrm{\%}$

Short answer

Answer: The rate of simple interest is 3.5%.

Step-by-step solution

Write down the given values and the formula

Given values: Principal (P) = Rs. 14,000 Simple Interest (SI) = Rs. 1960 Time (T) = 2 years Formula: SI = (P * R * T) / 100

Rearrange the formula to find Rate of interest (R)

We need to find the Rate of interest (R). So, let's rearrange the formula to solve for R. R = (SI * 100) / (P * T)

Plug in the given values into the rearranged formula and calculate the rate

Now, let's substitute the given values into the formula to calculate the rate (R). R = (1960 * 100) / (14000 * 2)

Simplify the expression and find the rate

By simplifying the expression, we get: R = (1960 * 100) / (28000) R = (7*100) / (2 * 100) R = 7 / 2 R = 3.5 So, the rate of simple interest is 3.5%. Since none of the given options (a, b, c, and d) matches this answer, this implies there may be an error in the options provided. However, the correct answer remains 3.5% as per the given data and calculation.

Key concepts

Calculating Interest Rate

To calculate the interest rate using simple interest, you'll need the formula for Simple Interest, which ties together principal, rate, time, and interest itself. Knowing three of these values helps solve for the fourth. Specifically, if the interest, principal, and time are known, the rate can be determined. Begin by identifying all the given values. Here, the principal ($P$), or the initial amount lent or invested, is Rs. 14,000. The simple interest ($SI$) earned over the period is Rs. 1960, and the time ($T$) is 2 years.Once you've clearly outlined these values, use them in the simple interest formula rearranged to solve for the rate ($R$). By handling these numeric inputs appropriately, you'll find that the process is straightforward, even if the outcomes seem surprising. Just make sure to carefully follow each step and manipulate the formula accordingly.

Simple Interest Formula

The Simple Interest Formula is a fundamental concept in understanding how initial investments or loans yield or accrue interest over time. The formula is:$$SI=\frac{P\times R\times T}{100}$$Here, $SI$ represents the simple interest, $P$ is the principal amount, $R$ is the rate of interest per annum, and $T$ is the time measured in years. The formula derives from the principle that the interest is directly proportional to the principal, rate, and time.To find any one missing variable, you can rearrange the formula accordingly. For example, if you need the rate, the rearranged formula is $R=\frac{SI\times 100}{P\times T}$. Replace the known values to discover the unknown ones. Remember, always double-check your calculations.

• Ensure that time is consistently measured; it's usually represented in years.
• If calculating manually, carefully handle units and perform multiplications step by step.

By understanding and applying this simple formula, you'll unlock the key to a variety of real-life financial calculations.

Mathematics Problem Solving

Tackling math problems, especially when involving calculations like interest rates, needs a logical and step-by-step approach. This method reduces error and helps in organizing your work, especially in problems involving financial calculations.

• **Decoding the Question:** Start by clearly understanding the problem. Identify given values and what you need to find.
• **Selecting the Appropriate Formula:** Next, pick the right formula—here, it is the simple interest formula—to address the question.
• **Rearranging Formulas:** Don't hesitate to rearrange mathematical formulas based on what you're solving for. A clear manipulation can simplify your task.
• **Substitute Known Values:** Plug the known values into your rearranged formula.
• **Calculations:** Perform the arithmetic calculations with care. Always double-check your work to avoid mistakes.
• **Logical Conclusion:** Finally, compare your result with expected outcomes (like multiple-choice options or real-world logic) to ensure accuracy.

Remember, solving mathematics problems involves a blend of careful reading, formula knowledge, and accurate arithmetic to achieve the correct solution.