Calculating Simple Interest Rate

The question asks us to find the rate of simple interest given that the simple interest for five years is 35% of the principal amount. Let's break down the problem using the simple interest formula.

The formula for simple interest is:

\( SI = \frac{P \times R \times T}{100} \)

Where:

• \( SI \) is the Simple Interest
• \( P \) is the Principal amount
• \( R \) is the Rate of interest (per annum)
• \( T \) is the Time period (in years)

From the problem statement, we are given two pieces of information:

1. The time period (\( T \)) is five years.
2. The simple interest (\( SI \)) for these five years is equal to 35% of the principal (\( P \)).

We can write the second statement as an equation:

\( SI = 35\% \text{ of } P \)

To use this in our formula, we convert the percentage to a decimal or fraction:

\( 35\% = \frac{35}{100} = 0.35 \)

So, \( SI = 0.35 \times P \).

Now, let's substitute the given values into the simple interest formula:

\( 0.35 \times P = \frac{P \times R \times 5}{100} \)

Our goal is to find the rate \( R \). We can rearrange the equation to solve for \( R \).

First, let's simplify the right side of the equation:

\( 0.35 \times P = \frac{5P \times R}{100} \)

\( 0.35 \times P = \frac{5}{100} \times P \times R \)

\( 0.35 \times P = 0.05 \times P \times R \)

Now, we can isolate \( R \). Since the principal \( P \) is on both sides of the equation (and assuming \( P \neq 0 \), which must be true for interest to be calculated), we can divide both sides by \( P \):

\( 0.35 = 0.05 \times R \)

To find \( R \), divide both sides by 0.05:

\( R = \frac{0.35}{0.05} \)

To perform this division, we can multiply the numerator and denominator by 100 to remove decimals:

\( R = \frac{0.35 \times 100}{0.05 \times 100} = \frac{35}{5} \)

\( R = 7 \)

The rate of interest is 7. Since \( R \) in the formula is typically the percentage rate, the rate is 7% per annum.

Step-by-Step Calculation

1. Identify the given information: Time \( T = 5 \) years, Simple Interest \( SI = 35\% \) of Principal \( P \).
2. Convert the percentage of interest to a decimal: \( SI = 0.35P \).
3. Write down the simple interest formula: \( SI = \frac{P \times R \times T}{100} \).
4. Substitute the known values into the formula: \( 0.35P = \frac{P \times R \times 5}{100} \).
5. Simplify the equation: \( 0.35P = \frac{5PR}{100} \implies 0.35P = 0.05PR \).
6. Divide both sides by P (assuming P > 0): \( 0.35 = 0.05R \).
7. Solve for R: \( R = \frac{0.35}{0.05} = \frac{35}{5} = 7 \).
8. The rate of interest is 7% per annum.

Revision Table: Simple Interest Calculation Key Points

Additional Information on Simple Interest

Simple interest is the easiest method to calculate interest on a principal amount. It is fixed over the entire period of the loan or investment. This is different from compound interest, where interest is calculated on the principal amount plus the accumulated interest from previous periods.

Key characteristics of simple interest:

• Interest is earned or paid only on the original principal amount.
• The amount of interest earned or paid each year is constant, assuming the principal and rate remain unchanged.
• It is often used for short-term loans or investments.

Understanding the relationship between simple interest, principal, rate, and time is crucial for solving problems like the one discussed. In this problem, the simple interest was given as a percentage of the principal, which allowed us to set up an equation where the principal term cancels out, letting us solve for the rate directly.