Simple Interest and Compound Interest Formulas for CAT 2026 + 12 PYQs
Every simple interest and compound interest formula CAT 2026 aspirants need, with the 30-second CI-to-SI approximation trick, successive-year ratio identity, and 12 CAT previous year questions solved using shortcuts. Covers the 8 core formulas, half-yearly and quarterly compounding, depreciation analogues, and the three repeatable CAT question patterns to spot in under 8 seconds.
Simple Interest and Compound Interest Formulas for CAT 2026 + 12 PYQs
Most CAT aspirants memorise the simple interest formula in week one of prep and never look at it again until a mock test traps them on a two-year CI-minus-SI difference question. The result is predictable: 4 to 6 marks lost on questions that the syllabus officially calls easy. Simple interest and compound interest show up in 1 to 2 problems on every recent CAT paper, but the formulas tested are not the textbook ones. They are the shortcut identities that turn a 90-second computation into a 20-second mental calculation.
This guide collects every simple interest and compound interest formula for CAT 2026, the 30-second CI-to-SI approximation trick, the successive-year ratio identity, and 12 CAT previous year questions solved using the shortcuts rather than the long form.
SI is linear, CI is exponential, but for two years they collapse to one identity: CI − SI = PR² / 100². Memorise eight formulas: the SI base, the CI base, two-year and three-year CI−SI differences, half-yearly and quarterly CI, depreciation, and the equal-installment present value. The 30-second trick: compute SI mentally, then add SI×R/200 for the two-year CI estimate. CAT 2020 to CAT 2024 featured at least one SI/CI question every year. The 12 PYQs at the end show exactly which shortcut works on which pattern.
Why Simple Interest and Compound Interest Stay on CAT Every Year
The CAT setter loves SI and CI because the topic tests three skills in one question: percentage manipulation, equation setup, and number sense. A well-built SI/CI problem can be solved in 20 seconds by the aspirant who knows the shortcut and in 90 seconds by the aspirant who builds the equation from scratch. That time gap is exactly the kind of differentiation the test wants between 90th and 99th percentile scorers.
Across CAT 2020 to CAT 2024, at least one SI or CI problem appeared in every cycle, with two cycles featuring two questions. The pattern is consistent enough that aspirants targeting a Quant percentile above 90 should treat SI/CI as a non-skippable formula family alongside percentages, ratio and proportion, and profit and loss. The CAT 2026 marking scheme guide covers the +3/-1/0 scoring math that makes a 20-second SI/CI question one of the highest-ROI attempts on the paper.
The Eight Core Formulas (Memorise These)
The list below covers every SI/CI variant CAT has tested in the last decade. Memorise the form, then memorise one example for each. When the mock test shows up, the pattern recognition is faster than the derivation.
Simple Interest on Principal P at rate R for time T
SI = (P × R × T) / 100R is in percent per year, T is in years. Amount A = P + SI. The interest is constant each year because it is always computed on the same P.
Compound Interest compounded annually
A = P × (1 + R/100)^T CI = A − PEach year's interest is added to the principal before the next year's interest is computed. For T = 1, CI equals SI. For T = 2 or higher, CI exceeds SI by the compounding effect.
The most-tested CAT shortcut for two-year problems
CI − SI (for 2 years) = P × (R/100)² = PR² / 10000This single identity solves roughly half of all CAT SI/CI questions. If the question gives the difference and the rate, the principal pops out in one step. If the question gives the difference and the principal, the rate solves in one square root.
The three-year extension of Formula 3
CI − SI (for 3 years) = P × R² × (300 + R) / 100³For most CAT-style rates (R between 5 and 15 percent), the 300 + R term is approximately 300, so the difference is approximately 3PR²/100² — that is, three times the two-year difference. Use the approximation for elimination, the exact form for computation.
Half-yearly, quarterly, monthly compounding
Half-yearly: A = P × (1 + R/200)^(2T)Quarterly: A = P × (1 + R/400)^(4T)
Monthly: A = P × (1 + R/1200)^(12T)
Divide the annual rate by the number of compoundings per year. Multiply the time T in the exponent by the same factor. For CAT, half-yearly and quarterly are the only variants worth memorising; monthly is rarely tested.
Compound depreciation analogue
A = P × (1 − R/100)^TReplace the plus with a minus. Depreciation appears in CAT under disguised wording: a car loses 10 percent of its value each year; a population shrinks at a fixed rate. The formula is the CI formula with a sign flip.
Same form as compound interest
P_final = P_initial × (1 + R/100)^TPopulation growth, bacteria multiplication, and revenue compounding all use the same identity. CAT 2022 featured a question phrased as population growth that collapsed to a two-year CI problem in disguise.
Loans repaid in N equal compound installments
P = X / (1 + R/100) + X / (1 + R/100)² + … + X / (1 + R/100)^NX is the equal installment, N is the number of installments. For CAT, the N = 2 case is the most common; expand the sum and solve a quadratic in X. The trick: convert the rate into a fraction (e.g., 10 percent = 11/10) to keep arithmetic clean.
Aspirants apply the two-year CI−SI identity to three-year problems and get the wrong answer. The identity changes with T. Memorise the 2-year and 3-year forms separately. For T = 4 and above, build the difference from A_CI − A_SI directly; the shortcut breaks down.
Compute SI mentally first. Then add half the SI times R-over-100. For P = 10,000 at R = 10 percent for 2 years: SI = 2,000. Add 2,000 × 10 / 200 = 100. So CI ≈ 2,100. The exact CI = 2,100. The approximation is exact for two years.
For three years, the approximation becomes CI ≈ SI + 3 × SI × R / 200. This is accurate within 1 to 2 marks for CAT-style rates and saves 30 to 45 seconds per question.
The SI vs CI Side-by-Side Reference
The table below is the cheatsheet you want loaded into mental cache before the CAT exam. It maps the variable to the SI formula to the CI formula in one row each, so the comparison is one glance instead of a mental retrieval.
| Variable | Simple Interest | Compound Interest (Annual) |
|---|---|---|
| Interest formula | PRT / 100 | P[(1 + R/100)^T − 1] |
| Amount | P + PRT/100 | P(1 + R/100)^T |
| Interest in year 1 | PR/100 | PR/100 |
| Interest in year 2 | PR/100 (same as year 1) | PR/100 + PR²/10000 |
| Ratio year2/year1 | 1 : 1 | (1 + R/100) : 1 |
| Equivalent annual rate | R (always) | Effective rate = (1 + R/100)^T − 1 |
| Effect of doubling time | Interest doubles | Interest more than doubles |
For CI problems with rate R that fits a clean fraction (10 percent = 11/10, 20 percent = 6/5, 25 percent = 5/4, 12.5 percent = 9/8), convert R into the fraction before multiplying. A = P(1 + R/100)^T becomes a product of fractions, which compounds in two or three multiplications without long decimal arithmetic.
How SI and CI Connect to the Wider CAT Arithmetic Family
Simple interest and compound interest belong to the percentage-applications family, alongside profit and loss, ratio and proportion, and time-and-work. The skill that transfers across the family is the ability to convert a percentage into a fraction, recognise the multiplier, and chain multipliers without losing track of the base. The profit and loss formulas for CAT 2026 guide covers the successive discount identity, which is structurally identical to the successive CI compounding identity — same math, different wrapper.
For a wider view of the formula cluster that CAT keeps testing every cycle, the ratio and proportion formulas guide covers partnership problems where SI/CI rates are split between two investors. The crossover questions in CAT 2023 and CAT 2024 specifically targeted aspirants who knew SI/CI in isolation but could not chain it with a partnership ratio.
Want a personalised CAT 2026 arithmetic plan with daily SI/CI drills and a paced PYQ track?
Build My CAT Arithmetic Plan12 CAT PYQs on Simple Interest and Compound Interest
The 12 questions below cover the three patterns CAT keeps testing: pure SI computation with a twist, pure CI with non-annual compounding, and the CI−SI difference identity. Each solution uses the shortcut from the formula list, not the long-form derivation.
The 2-Year Difference Anchor
The difference between compound interest and simple interest on a sum at 10 percent per annum for 2 years is Rs. 50. Find the principal.
The 3-Year Difference Anchor
The difference between CI and SI on a sum of Rs. 8,000 at 10 percent per annum for 3 years is _____.
Rate from Difference
If the difference between CI and SI on a sum of Rs. 1,000 for 2 years is Rs. 10, find the annual rate.
Half-Yearly Compounding
Find the compound interest on Rs. 10,000 at 20 percent per annum compounded half-yearly for 1 year.
Equal Installment Two-Year Loan
A sum of Rs. 7,260 is borrowed at 10 percent CI and is to be repaid in 2 equal annual installments. Find the installment amount.
Pure CI Growth
Rs. 6,250 amounts to Rs. 7,290 in 2 years at compound interest. Find the rate.
SI Doubling
A sum of money at simple interest doubles itself in 10 years. In how many years will it triple?
CI Tripling
A sum becomes triple itself in 5 years at compound interest. In how many years will it become 27 times?
Mixed SI + CI Comparison
A sum of Rs. 10,000 is invested in two parts. The first part at 10 percent SI and the second at 10 percent CI, both for 2 years, return the same interest. Find the ratio of the two parts.
Depreciation
A car worth Rs. 5,00,000 depreciates at 10 percent per annum compounded annually. What is its value after 3 years?
Variable Rate SI
A sum of Rs. 5,000 is lent at 5 percent SI for the first year, 6 percent for the second, and 7 percent for the third. Find the total interest.
Population Growth (CI in Disguise)
The population of a town increases at 10 percent per annum. After 2 years, the population is 12,100. Find the original population.
The Three Patterns CAT Keeps Testing
Across 25-plus CAT papers, SI and CI questions cluster into three repeatable patterns. Pattern recognition is faster than computation, so spend the first 8 seconds of every SI/CI question deciding which pattern it is before writing a single equation.
- Pattern A — Difference identity. The question gives CI−SI for 2 or 3 years and asks for P or R. Apply Formula 3 or 4 directly. Solve in one or two steps.
- Pattern B — Compounding frequency. The question switches from annual to half-yearly or quarterly. Apply Formula 5; rewrite the rate per period and adjust the exponent.
- Pattern C — Disguised wrapper. The question reads as population growth, depreciation, bacterial multiplication, or revenue compounding. Spot the underlying CI identity (Formula 2 or 6 or 7) and reduce to the standard form.
For aspirants who feel the SI/CI section is weak even after the formula list, the gap is almost always in pattern recognition, not in formula memorisation. The fix: drill 30 mixed SI/CI questions across the three patterns over five days, tagging each one by pattern before solving. By Day 5, the recognition step takes under 8 seconds. The CAT exam overview covers the broader Quant section context, and the CAT 2026 waitlist includes a paced arithmetic drill track with pattern-tagged PYQs.
- Memorise 8 formulas: SI, CI, 2-year and 3-year CI−SI, non-annual, depreciation, growth, installment.
- Apply the 2-year CI−SI identity PR²/10000 first — it solves half of CAT SI/CI problems.
- Convert R into a fraction (10% = 11/10, 25% = 5/4) before computing CI by hand.
- Spot Pattern A (difference), B (compounding frequency), or C (disguised wrapper) in under 8 seconds.
- The CI-to-SI approximation: CI ≈ SI + SI×R/200 for 2 years — exact, not an estimate.
- For T = 1, SI equals CI. The compounding effect starts at T = 2.
- Half-yearly halves the rate and doubles the periods. Quarterly quarters the rate and quadruples the periods.
CAT does not reward memory. It rewards pattern recognition built on memorised structure. SI/CI is the cleanest topic to prove that to yourself.
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