In simple interest, we calculate interest on the sum borrowed but in compound interest, we add the interest and the principal amount in a regular period of time and then calculate the interest.

Simple Interest vs Compound Interest

Simple Interest:
- Simple interest is calculated only on the principal amount of a loan or investment.
- The interest amount remains constant throughout the period of investment.
- The formula for calculating simple interest is: I = P * R * T, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.
- The total amount after a certain period can be calculated by adding the principal amount and the interest: A = P + I.

Compound Interest:
- Compound interest is calculated on both the principal amount and the accumulated interest from previous periods.
- The interest amount increases over time as it is calculated on the total amount in each period.
- The formula for calculating compound interest is: A = P(1 + r/n)^(nt), where A is the total amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
- Compound interest helps in accelerating the growth of an investment due to the interest being reinvested.

Differences:
- Simple interest is calculated only on the principal amount, while compound interest is calculated on both the principal and accumulated interest.
- In simple interest, the interest amount remains constant, whereas in compound interest, it increases over time.
- Compound interest leads to higher returns compared to simple interest due to the compounding effect.
In conclusion, the key difference between simple interest and compound interest lies in how interest is calculated and the impact it has on the total amount over time. Understanding these differences is crucial for making informed decisions regarding investments and loans.