Simple interest and compound interest are two different methods of calculating the interest on a principal amount.
Simple Interest:
- Definition: Simple interest is calculated only on the principal amount, or the original amount of money invested or borrowed.
- Formula: The formula for calculating simple interest is:
\[
\text{Simple Interest} = P \times r \times t
\]
where:
- \( P \) = principal amount (the initial amount of money),
- \( r \) = annual interest rate (in decimal form),
- \( t \) = time (in years).
- Nature: The interest earned (or paid) remains the same each period.
Example: If you invest $1,000 at a simple interest rate of 5% for 3 years, the interest earned would be: \[ \text{Interest} = 1000 \times 0.05 \times 3 = 150 \] So, the total amount after 3 years would be $1,150.
Compound Interest:
- Definition: Compound interest is calculated on the principal amount and also on the interest that has been added to the principal from previous periods. This means that interest is earned on both the initial principal and the accumulated interest from prior periods.
- Formula: The formula for compound interest is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- \( A \) = the amount of money accumulated after n years, including interest,
- \( P \) = principal amount,
- \( r \) = annual interest rate (decimal),
- \( n \) = number of times that interest is compounded per year,
- \( t \) = time in years.
- Nature: The interest earned increases over time due to the compounding effect.
Example: If you invest $1,000 at a compound interest rate of 5% compounded annually for 3 years, the total amount would be calculated as: \[ A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \cdot 3} = 1000 \left(1.05\right)^3 \approx 1157.63 \] So, the total amount after 3 years would be approximately $1,157.63, earning around $157.63 in interest.
Summary of Key Differences:
-
Calculation Basis:
- Simple Interest: Only on the principal.
- Compound Interest: On principal plus accumulated interest.
-
Growth Over Time:
- Simple Interest: Linear growth (interest amount is constant).
- Compound Interest: Exponential growth (interest amount increases over time).
-
Total Earning:
- In general, with the same principal, interest rate, and time period, compound interest will result in a higher total amount compared to simple interest.