Calculating Simple Interest Rate with Given Principal and Time Period

When dealing with financial problems, it is essential to understand how to calculate the rate of simple interest given the principal amount, interest earned, and the time period. This article will walk you through the process using the example where the simple interest on a principal amount of 1300 is 292.50 over a period of 108 months, or 9 years. We will derive the rate of interest and explore the formula and steps involved.

Understanding the Simple Interest Formula

The formula for calculating simple interest is:

Simple Interest (SI) Principal (P) × Rate (R) × Time (T) / 100

Given the problem, the principal (P) is 1300, the simple interest (SI) is 292.50, and the time (T) is 108 months, which is equivalent to 9 years. We need to find the rate (R).

Step-by-step Explanation

We can rearrange the formula to solve for the rate (R):

Rate (R) (Simple Interest (SI) × 100) / (Principal (P) × Time (T))

Substituting the given values into the formula:

Rate (R) (292.50 × 100) / (1300 × 9)

Rate (R) 29250 / 11700

Rate (R) 2.5%

Thus, the rate of interest is 2.5%. This calculation can be verified through several methods, demonstrating the consistency of the rate calculation.

Additional Example

Another way to verify this result is by breaking down the monthly interest into an annual rate:

108 months is 9 years, and the interest earned per annum would be:

Interest per annum 292.50 / 9 32.5

Then, calculating the rate per 1300 principal amount:

Rate 32.5 / 1300 0.025 or 2.5%

This confirms that the rate of interest for the given scenario is 2.5%.

Formulas and Derivations

The simple interest calculation can also be expressed as:

Simple Interest (SI) P × R × T / 100

Solving for the rate (R), we have:

R (SI × 100) / (P × T)

Given:

P 1300, SI 292.50, T 108 months (or 9 years)

R (292.50 × 100) / (1300 × 9)

R 292.5000 / 11700

R 2.5

This confirms that the rate of interest is indeed 2.5%, and this method aligns with the initial calculation.

In conclusion, the rate of interest for a principal of 1300 earning a simple interest of 292.50 over 108 months (9 years) is 2.5%. Understanding and applying the simple interest formula effectively can help in various financial calculations, making it a valuable tool for students, professionals, and financial planners alike.