Basics of Simple And Compound Interest

Simple Interest

Definition: Simple interest is calculated on the principal amount over a period of time.
Formula:

$I = P times R times T$ I=P×R×T

Where:
- $I$ I = Interest
- $P$ P = Principal amount
- $R$ R = Rate of interest per year (in decimal)
- $T$ 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:

$I = 1000 times 0.05 times 3 = 150$ I=1000×0.05×3=150

The total amount after 3 years will be:

$A = P + I = 1000 + 150 = 1150$ 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:

$A = P left(1 + frac{R}{n}right)^{nT}$ A=P(1+nR)nT

Where:
- $A$ A = Total amount after interest
- $P$ P = Principal amount
- $R$ R = Annual interest rate (in decimal)
- $n$ n = Number of times interest is compounded per year
- $T$ T = Time period (in years)
Example: For a $1000 investment at an interest rate of 5% per year compounded annually for 3 years:

$A = 1000 left(1 + frac{0.05}{1}right)^{1 times 3} = 1000 left(1.05right)^3 approx 1157.63$ A=1000(1+10.05)1×3=1000(1.05)3≈1157.63

The total interest earned will be:

$I = A – P = 1157.63 – 1000 = 157.63$ 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.

Basics of Simple And Compound Interest

🎥 Video Resources

Simple Interest || Introduction (Part-1) ||Quantitative Aptitude|| Common for all Competitive Exams