Introduction
Simple Interest (SI) is calculated only on the original principal for the entire loan/investment period —
making it a straightforward, linear (as opposed to Compound Interest's exponential) calculation.
Basic Formula
| Formula |
|---|
| SI = (P × R × T) / 100 |
| Amount (A) = P + SI |
| P = (SI × 100) / (R × T) |
| R = (SI × 100) / (P × T) |
| T = (SI × 100) / (P × R) |
Where P = Principal, R = Rate of interest per annum (%), T = Time in years.
Q. Find the SI on ₹8,000 at 6% per annum for 3 years.
SI = (8000 × 6 × 3) / 100 = 144000/100 = ₹1,440
Key Property — Equal Annual Interest
💡 Core Insight: Since SI is calculated only on the original principal, the interest earned is exactly the same every year — this is the fundamental difference from Compound Interest, where interest grows each year.
Ratio of Principal to Amount Shortcut
Q. A sum becomes ₹1,200 in 3 years and ₹1,320 in 5 years at simple interest. Find the sum and the rate of interest.
SI for 2 years (5−3) = 1320 − 1200 = 120 → SI per year = 60
SI for 3 years = 60 × 3 = 180 → Principal = 1200 − 180 = ₹1,020
Rate = (60 × 100) / (1020 × 1) = ≈5.88%
"Sum Becomes n Times" Pattern
Flowchart — Time to Reach a Multiple of the Principal
If a sum becomes "n" times itself in "T" years at SI
↓
Rate % = [(n−1) × 100] / T
Q. At what rate of simple interest will a sum become 3 times itself in 10 years?
Rate = [(3−1) × 100] / 10 = 200/10 = 20%
Splitting a Sum for Equal Interest
Q. A sum of ₹1,500 is divided into two parts such that the interest on the first part for 5 years at 6% equals the interest on the second part for 4 years at 5%. Find the two parts.
Let parts be x and (1500−x)
x×5×6 = (1500−x)×4×5 → 30x = 30000 − 20x → 50x = 30000 → x = 600
Parts = ₹600 and ₹900
✅ Practice Focus: Core SI formula and its rearrangements · Constant-annual-interest property · "Amount at two different times" difference method · "Sum becomes n times" rate shortcut.