Activity › Discussion › Math › what is the difference between compound and simple interest ? › Reply To: what is the difference between compound and simple interest ?

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Simple interest and compound interest are two methods used to calculate the interest on a principal amount over a given period. The main difference between the two lies in how the interest is calculated and added to the principal.

Simple Interest: Simple interest is calculated only on the initial principal amount. It does not take into account any accumulated interest from previous periods. The formula for calculating simple interest is:
Simple Interest = Principal × Interest Rate × Time
Here, the interest rate is usually expressed as an annual percentage rate (APR), and the time is the duration for which the interest is calculated.
For example, if you invest $1,000 at a simple interest rate of 5% per year for 3 years, the interest earned would be:
Simple Interest = $1,000 × 0.05 × 3 = $150
After 3 years, the total amount would be the principal plus the interest: $1,000 + $150 = $1,150.
 Compound Interest:
Compound interest takes into account the accumulated interest from previous periods along with the initial principal amount. The interest is added to the principal at regular intervals, such as annually, semiannually, quarterly, or monthly, and subsequent interest calculations are based on the updated amount.
The formula for calculating compound interest is:
Compound Interest = Principal × (1 + Interest Rate)^Time – Principal
Here, the interest rate is also usually expressed as an annual percentage rate, and the time is the duration for which the interest is calculated.
For example, if you invest $1,000 at a compound interest rate of 5% per year compounded annually for 3 years, the interest earned would be:
Compound Interest = $1,000 × (1 + 0.05)^3 – $1,000 = $157.63 (approximately)
After 3 years, the total amount would be the principal plus the compound interest: $1,000 + $157.63 = $1,157.63.
In summary, the key difference between simple interest and compound interest is that simple interest is calculated only on the principal amount, while compound interest takes into account the accumulated interest from previous periods, resulting in interest being earned on both the principal and the interest itself. Compound interest tends to grow faster than simple interest over time, making it a more common method for longterm investments or loans.
Hope, it helps 🙂
