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Interest
CAT'26 QUANT CHEATSHEET
Every interest formula and CAT shortcut you need for CAT 2026 — on one page.
Interest questions on CAT rarely stay in their own lane — the same compound interest formula quietly reappears as population growth, depreciation, and reverse-compounding problems dressed up in different words. The habit that saves the most time is spotting which of the two flavours you are dealing with, Simple or Compound, and then reaching for the right shortcut instead of expanding everything by hand. This sheet lays out every formula you need for the CAT quant section: SI and CI basics, compounding frequency, the memorised growth factors, the CI − SI difference shortcuts, and the population, depreciation and reverse-compounding variants that all secretly reuse the same formula, each with a worked example in real numbers. Keep it open while you practise, and after a mock check where you stand on the CAT score predictor to see which idea is costing you marks.
Dev note: the canonical route
/cheatsheets/optima-learn-interest-cheatsheet is not live yet
(no /cheatsheets hub in the current sitemap). Built production-ready as a drop-in once it ships.Interest: every formula you need
1Core Idea
Extra money earned or paid on a principal.
Amount = Principal + Interest
Example: P = ₹5000 at R = 10% for T = 2 years builds toward an Amount above the principal.
CAT Hack: Always identify whether a question is Simple or Compound Interest before picking a formula.
2Simple Interest
Interest grows in a straight line, on the principal alone.
SI = (P × R × T) / 100
Example: P = ₹5000, R = 10%, T = 2 → SI = (5000·10·2)/100 = ₹1000.
3Amount in Simple Interest
Two equivalent ways to reach the same amount.
Amount = P + SI or Amount = P × (1 + RT/100)
Example: P = ₹1000, SI = ₹200 → Amount = ₹1200.
4Compound Interest
Interest earns interest, so growth is multiplicative.
A = P × (1 + R/100)T | CI = A − P
Example: P = ₹1000, R = 10%, T = 2 → A = 1000·(1.1)2 = ₹1210, CI = ₹210.
5Compounding Frequency
The rate and time both scale with how often interest compounds.
Half-yearly: A = P(1+R/200)2T | Quarterly: A = P(1+R/400)4T
Example: ₹1000 at 10% p.a., compounded half-yearly for 1 year → A = 1000(1+5/100)2 = ₹1102.50.
CAT Favourite: A CAT favourite: rate divides and time multiplies by the same factor (2 for half-yearly, 4 for quarterly).
6Common Growth Factors
The multiplier a rate turns into, memorised once.
10% → 1.10 | 20% → 1.20 | 25% → 1.25 | 50% → 1.50 | 100% → 2.00
Example: ₹2000 growing at 25% for one year → 2000 · 1.25 = ₹2500.
CAT Hack: Memorise these factors so you can multiply straight through instead of computing 1 + R/100 each time.
7CI − SI Difference (2 Years)
A direct shortcut — no need to compute both separately.
CI − SI = P × (R/100)2
Example: P = ₹1000, R = 10% → difference = 1000 · (0.1)2 = ₹10.
8CI − SI Difference (3 Years)
The 3-year version of the same shortcut.
CI − SI = P × (R/100)2 × (3 + R/100)
Example: P = ₹1000, R = 10% → 1000 · 0.01 · 3.1 = ₹31.
CAT Favourite: One of the most reused CAT shortcuts — worth memorising both the 2-year and 3-year forms.
9Doubling Time
A quick estimate for how long money takes to double.
Time ≈ 100 / Rate (approximation)
Example: at 20% p.a., doubling time → 100/20 = 5 years (approx.).
CAT Insight: This is an approximation, not exact CI math — useful for quick estimation-based questions, not precise ones.
10Depreciation
Value falls the way compound interest grows, just in reverse.
Value = Original × (1 − R/100)T
Example: ₹10,000 depreciating at 10% for 2 years → 10000 · (0.9)2 = ₹8100.
11Population Growth
Growing population follows the compound interest formula exactly.
Population = Initial × (1 + R/100)T
Example: a town of 10,000 growing at 10% for 2 years → 10000 · (1.1)2 = 12,100.
12Reverse Compounding
Work backward from the amount to find the principal.
Principal = Amount ÷ (1 + R/100)T
Example: Amount = ₹1210, R = 10%, T = 2 → P = 1210 ÷ (1.1)2 = ₹1000.
Common Mistake: Don't confuse this with subtracting interest directly — you must divide by the growth factor, not subtract a percentage.
CAT exam shortcuts, traps & revision
13
CAT Exam Shortcuts
- Convert percentages into growth-factor multipliers up front
- CI − SI (2 yrs) = P(R/100)2; (3 yrs) = P(R/100)2(3+R/100)
- Population and depreciation both reuse the compound interest formula
- Doubling time ≈ 100/Rate (approximation only)
- Half-yearly: R/2 and 2T; Quarterly: R/4 and 4T
- Reverse compounding: divide by the growth factor, don't subtract
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Most Common CAT Traps
- Applying the SI formula to a compound interest question.
- Forgetting to adjust rate and time for the compounding frequency.
- Adding percentages directly instead of multiplying growth factors.
- Skipping the CI − SI shortcut and computing both fully.
- Confusing the Amount with the Interest earned.
15
30-Second Revision Box
- SI = (P×R×T)/100; Amount = P + SI
- CI = Amount − Principal; A = P(1+R/100)^T
- Half-yearly → R/2 and 2T; Quarterly → R/4 and 4T
- CI − SI (2 yrs) = P(R/100)2
- Population = CI formula; Depreciation = reverse-sign CI formula
- Principal = Amount ÷ growth factor
Interest rewards pattern recognition over long computation — once you see that population growth, depreciation and reverse compounding are all the same formula wearing a different label, the question stops being new. Drill this sheet until the growth factors and the CI − SI shortcuts are reflex, then test them on full sets and track progress with the CAT score predictor. For more topic guides, browse the Optima Learn blog or explore every study guide, and work through the full CAT exam hub for section-wise strategy. When you want structured, mentor-led prep, the team at Optima Learn can map out your plan — book a free CAT 2026 call and line up your next eight weeks.
