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.