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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:

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

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