Simple & Compound Interest
Simple & Compound Interest
Simple Interest adds the same fixed amount each period while Compound Interest reinvests earnings so the principal grows exponentially. Exams test your ability to switch between SI and CI formulas under time pressure. Master the CI\u2212SI difference shortcut and half-yearly compounding adjustment to handle the most frequently asked variants.
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
Apply this whenever the problem states simple interest or a flat rate with no compounding.
Compound Interest
A = P × (1 + R/100)ᵀ | CI = A − P
Use this when interest compounds annually and you need the final amount or total interest earned.
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.