Principal, Rate & Time
Every simple-interest problem revolves around four quantities: Principal (P, the money lent or borrowed), Rate (R, percent per annum), Time (T, in years) and the Interest itself (SI). They are tied by one equation, SI = PRT/100, so if you know any three you can solve for the fourth by rearranging. The CAT skill is fast rearrangement and unit discipline: rate is per annum, so 8 months must become 8/12 year and 146 days becomes 146/365 year. A second habit worth building is treating the yearly interest as a fixed building block — since P×R/100 is the same every year under SI, multiplying it by the number of years is often quicker than the full formula. Always read whether the question asks for interest alone or for the amount (principal plus interest); mixing the two is the single biggest source of careless errors here.
✅ Solved examples
✏️ Practice — try these, take hints as needed
📝 Topic test — 8 questions
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Formula Reference Sheet
Core simple-interest relations
| Simple interest | SI = P × R × T / 100 |
|---|---|
| Amount (maturity value) | A = P + SI = P(1 + RT/100) |
| Principal from SI | P = 100 × SI / (R × T) |
| Rate from SI | R = 100 × SI / (P × T) |
| Time from SI | T = 100 × SI / (P × R) |
CAT power-tools
| Sum becomes n times in T years | R × T = (n − 1) × 100 |
|---|---|
| Yearly interest (a constant) | I per year = P × R / 100 |
| Equal annual instalment (loan, SI) | See instalment formula in SI Applications |
| Two amounts ⇒ principal & rate | Yearly interest = (A₂ − A₁)/(T₂ − T₁) |
| Average rate over split sums | Total SI / (Total P × Total T) × 100 |