Quantitative Aptitude
Simple & Compound Interest
Simple & Compound Interest
Simple Interest grows linearly — same amount every period. Compound Interest grows exponentially — interest is added to principal each period. Knowing the difference between them is key to all SI/CI problems.
Key Idea
The extra amount in CI over SI for 2 years = P(R/100)². This shortcut directly gives the CI−SI difference without computing both separately.
Core Formulas
Simple Interest
SI = P × R × T / 100 | Amount = P + SI
For linear interest problems — same interest earned every period.
Compound Interest
A = P × (1 + R/100)ᵀ | CI = A − P
When interest is compounded annually — principal grows each period.
CI − SI Difference (2 years)
CI − SI = P × (R/100)²
To directly find the difference between CI and SI for 2 years without computing each.
Compounding Frequency Adjustment
Half-yearly: A = P(1 + R/200)^(2T) | Quarterly: A = P(1 + R/400)^(4T)
When interest is compounded more than once per year — adjust rate and time.
Rule of 72 (Doubling Time)
Years to double ≈ 72 / R (for CI) | 100 / R (for SI)
To quickly estimate how long it takes for money to double at a given rate.
Relevant Exams
SI/CI questions are guaranteed in every banking exam (IBPS PO, SBI PO) and appear regularly in SSC CGL. The CI−SI difference and half-yearly compounding variants are high-frequency.