If a $10,000 Investment Earns Interest of $500 in One Year, What Is Its Rate of Return?[Solved] (2024)

As an expert in finance and mathematics, I have a deep understanding of concepts related to simple interest, rates of return, and the calculations involved in these financial formulas. I have both practical experience in applying these concepts and a theoretical understanding backed by education and professional expertise.

Regarding the concept of simple interest, it is the interest calculated solely on the initial principal amount. It does not take into account the compounding of interest over time. In the scenario provided, where a $10,000 investment yields an interest of $500 in one year, the rate of return can be determined using the formula for simple interest:

[ \text{Simple Interest} = \left( \frac{P \times R \times T}{100} \right) ]

Here, 'P' represents the principal amount, 'R' denotes the rate of interest, and 'T' signifies the time period. By substituting the given values into the formula—$10,000 as the principal, 1 year as the time period, and $500 as the interest earned—the rate of interest ('R') can be calculated.

[ 500 = \left( \frac{10000 \times R \times 1}{100} \right) ] [ 500 \times 100 = 10000 \times R ] [ R = \frac{50000}{10000} = 5 ]

Hence, the rate of interest is found to be 5%.

This example showcases the direct application of the simple interest formula to compute the rate of return on an investment. It highlights how understanding the relationship between principal, time, and interest rate is crucial in determining financial returns in straightforward interest scenarios.

In essence, the article provides a step-by-step breakdown of the simple interest formula and its application to solve a specific problem. The key components covered include:

1. Simple Interest Formula: ( \text{Simple Interest} = \left( \frac{P \times R \times T}{100} \right) )
2. Variables: 'P' for principal amount, 'R' for rate of interest, 'T' for time period.
3. Calculation Process: Substituting known values into the formula to solve for the unknown variable (rate of interest in this case).
4. Rate of Return Determination: Using the calculated rate of interest to determine the rate of return on the investment, which, in this instance, is 5%.

Understanding such basic financial concepts empowers individuals to make informed decisions regarding investments and loans, enabling them to calculate potential returns or interest payments accurately.