Time Required to Earn One-Third of 6 Simple Interest

Understanding the relationship between principal, interest rate, and time is crucial in finance. This article explores how long it takes for a principal to earn an interest equal to one-third of 6 simple interest, providing a detailed explanation and practical insights.

Introduction to Simple Interest

Simple interest is a method of calculating interest where the interest on a loan or mortgage is calculated as a percentage of the original principal. The formula for simple interest is:

I P × r × t

where:

I is the interest earned P is the principal amount (the initial amount of money) r is the rate of interest, expressed as a decimal t is the time in years

Calculating One-Third of 6 Simple Interest

To determine how long a principal will earn an interest equal to one-third of 6 simple interest, we follow these steps:

Step 1: Calculate One-Third of 6

One-third of 6 6 / 3 2

Step 2: Set Up the Simple Interest Formula

Using the simple interest formula, where we want the interest I to be equal to 0.02 times the principal P and the rate of interest is 0.06 (6% per annum), we can set up the equation:

0.02P P × 0.06 × t

Step 3: Simplify the Equation

By canceling out the principal P (assuming P ≠ 0), the equation simplifies to:

0.02 0.06 × t

Step 4: Solve for t

Dividing both sides by 0.06, we find:

t 0.02 / 0.06 1/3

Thus, it will take one-third of a year, or approximately 4 months, for the principal to earn an interest equal to one-third of 6 simple interest.

Alternative Method: Direct Calculation

Step 1: Let the Principal be P

Let the principal be P and let the time it takes be T.

P × 0.06 1/3P

Step 2: Set P 1

Setting P equal to 1 for simplicity, the equation becomes:

0.06T 1/3

Step 3: Solve for T

Dividing both sides by 0.06, we get:

T 1/3 / 0.06 5 5/9 years

This means it will take approximately 5.556 years to earn an interest equal to one-third of the principal as simple interest, but the original question was specifically about earning one-third of 6 simple interest in a shorter time frame.

Conclusion

In conclusion, understanding the simple interest formula allows us to accurately determine how long it takes to earn a specific amount of interest. Whether simplified to a few months or detailed over years, the calculations provide valuable insights into financial planning and investment strategies.