Simple & Compound Interest

SI is Interest on Principal ONLY. CI is Interest on Principal + Interest on Interest.

• SI: Rate $R$ per year. Total Interest for $T$ years = $R \times T \%$.
• CI: Successive % Change. Use $x+y+xy/100$ for 2 years.

Direct shortcut for Difference ($D$) between CI and SI.

• 2 Years: $D = P (R/100)^2$.
• 3 Years: $D = P (R/100)^2 (3 + R/100)$.

Sum becomes N times in T years.

• SI: Linear Growth. If it doubles (gain 100%) in 5 yrs, it triples (gain 200%) in 10 yrs.
• CI: Exponential Powers. If it doubles ($2^1$) in 5 yrs, it becomes 8 times ($2^3$) in $5 \times 3 = 15$ yrs.

Best for 2-3 years.

• 2 Years: $2R + R^2/100$. Example 10% $\to$ 21%.
• 3 Years: $3R.3R^2 R^3$ (Pascal's Triangle 3:3:1 logic). Example 10% $\to$ 33.1%.

Adjust Rate and Time.

• Half-Yearly: Rate becomes $R/2$, Time becomes $2T$.
• Quarterly: Rate becomes $R/4$, Time becomes $4T$.

Present Value Concept.

• SI Installment: Debt $A = x + (x + \text{int}) + ...$ (Reverse Order).
• CI Installment: $P = \frac{I}{(1+r)} + \frac{I}{(1+r)^2}$.