Simple Interest
Definition: Simple interest is calculated on the principal amount over a period of time.
Formula:
I=P×R×TWhere:
- I = Interest
- P = Principal amount
- R = Rate of interest per year (in decimal)
- T = Time period (in years)
Example: If you invest $1000 at an interest rate of 5% per year for 3 years, the simple interest is:
I=1000×0.05×3=150The total amount after 3 years will be:
A=P+I=1000+150=1150
Compound Interest
Definition: Compound interest is calculated on the principal amount and also on the accumulated interest from previous periods.
Formula:
A=P(1+nR)nTWhere:
- A = Total amount after interest
- P = Principal amount
- R = Annual interest rate (in decimal)
- n = Number of times interest is compounded per year
- T = Time period (in years)
Example: For a $1000 investment at an interest rate of 5% per year compounded annually for 3 years:
A=1000(1+10.05)1×3=1000(1.05)3≈1157.63The total interest earned will be:
I=A−P=1157.63−1000=157.63
Summary: Simple interest is straightforward, calculated directly on the principal. Compound interest, however, includes interest on both the principal and accumulated interest, leading to higher total interest earned over time.