The Difference Between Compound Interest and Simple Interest:

Simple interest and compound interest are two different methods used to calculate the interest on a loan or investment. The main difference between the two lies in how the interest is calculated and added to the principal amount.

Simple Interest:
- Simple interest is calculated only on the principal amount of the loan or investment.
- It is a linear calculation, where the interest remains constant throughout the duration of the loan or investment.
- The formula for calculating simple interest is:
Simple Interest = (Principal Amount * Rate of Interest * Time) / 100

Compound Interest:
- Compound interest is calculated on both the principal amount and the accumulated interest from previous periods.
- It is a compounding calculation, where the interest is added to the principal at regular intervals, such as annually, semi-annually, quarterly, or monthly.
- The formula to calculate compound interest is:
Compound Interest = Principal Amount * (1 + (Rate of Interest / n))^(n * Time) - Principal Amount

Where:
- Principal Amount is the initial amount of the loan or investment.
- Rate of Interest is the annual interest rate (in percentage).
- Time is the duration of the loan or investment (in years).
- n represents the number of compounding periods per year.

Calculating the Rate of Interest:
In this scenario, the difference between the compound interest and simple interest is given as Rs 96 for an amount of Rs 15000 over a period of 2 years. We need to find the rate of interest per annum.

Let's assume the rate of interest per annum as 'r'.

Using the given information, we can set up the following equations:

Compound Interest = Simple Interest + Difference
(Principal Amount * (1 + (r/100))^2) - Principal Amount = (Principal Amount * r * 2) / 100 + 96

Simplifying the equation:

(15000 * (1 + (r/100))^2) - 15000 = (15000 * r * 2) / 100 + 96

Now, we can solve this equation to find the value of 'r', which represents the rate of interest per annum.