The Difference between CI and SI on a Certain Sum of Money Invested for Three Years at 6%:

Introduction:
In this question, we are given that a certain sum of money is invested for three years at a 6% rate of interest. The difference between the Compound Interest (CI) and Simple Interest (SI) earned on this investment is given as Rs. 110.16. We need to calculate the principal amount.

Understanding the Concepts of CI and SI:
Before we proceed with the calculation, let's first understand the concepts of Compound Interest (CI) and Simple Interest (SI).

- Simple Interest (SI): Simple Interest is calculated on the principal amount only. It remains constant over the investment period. The formula to calculate SI is: SI = (P * R * T) / 100, where P is the principal, R is the rate of interest, and T is the time period.

- Compound Interest (CI): Compound Interest is calculated on both the principal amount and the interest earned over previous periods. It keeps increasing with each compounding period. The formula to calculate CI is: CI = P * (1 + R/100)^T - P, where P is the principal, R is the rate of interest, and T is the time period.

Now, let's proceed with the calculation to find the principal amount.

Calculation:
Given:
Difference between CI and SI = Rs. 110.16
Rate of interest (R) = 6%
Time period (T) = 3 years

Let's assume the principal amount to be P.

Step 1: Calculate the SI using the SI formula.
SI = (P * R * T) / 100

Step 2: Calculate the CI using the CI formula.
CI = P * (1 + R/100)^T - P

Step 3: Find the difference between CI and SI.
Difference = CI - SI

According to the given question, the difference between CI and SI is Rs. 110.16. Hence, we can write the equation as:
Difference = CI - SI = Rs. 110.16

Step 4: Substitute the values in the equation and solve for P.
110.16 = P * (1 + 6/100)^3 - P - (P * 6 * 3) / 100

Simplifying the equation,
110.16 = P * (1.06)^3 - P - (P * 18) / 100

Step 5: Solve the equation to find the value of P.
110.16 = 1.191016 P - P - 0.18P

Combining like terms,
0.191016P = 110.16

Dividing both sides by 0.191016,
P = 110.16 / 0.191016

Calculating the value of P,
P ≈ Rs. 577.40

Hence, the principal amount is approximately Rs. 577.40.

Conclusion:
The principal amount that was invested for three years at a 6% rate of interest, resulting in a difference of Rs. 110.16 between Compound Interest

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