31 questions from actual AFCAT papers · all shown free · click option to reveal solution
COMPOUND INTEREST — COMPLETE EXAM GUIDE ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
CORE CONCEPT — WHAT IS COMPOUND INTEREST? ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
In Simple Interest, you earn interest only on the original amount (principal). In Compound Interest (CI), you earn interest on the principal PLUS the interest already earned. This is called 'interest on interest.' Think of it like a snowball rolling downhill — it keeps getting bigger. Example in plain English: You deposit Rs 1000 at 10% per year CI. After Year 1, interest = Rs 100. Now in Year 2, interest is calculated on Rs 1100 (not Rs 1000). So CI always gives more than SI for the same rate and time (when time > 1 year).
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CI > SI always (for same P, R, T when T is more than 1 year)
For 1 year, CI = SI (no difference)
Compounding can be annual, half-yearly, quarterly, or monthly
When compounding is half-yearly: Rate becomes R/2, Time becomes 2T
When compounding is quarterly: Rate becomes R/4, Time becomes 4T
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For half-yearly compounding:
For quarterly compounding:
Difference between CI and SI for 2 years:
Difference between CI and SI for 3 years:
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— WHAT GETS ASKED ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ SSC CGL regularly asks: - Find CI or Amount after 2-3 years - Difference between CI and SI (very common!) - Half-yearly or quarterly compounding questions - Find Principal when CI and Rate/Time are given - Population growth and depreciation problems (same CI formula) - Find rate of interest when Amount and Principal are given ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ SHORTCUTS AND TRICKS ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ TRICK 1 — Effective Rate Method for 2 years: If rate = R%, then for 2 years, effective CI rate = 2R + R^2/100 percent Example: R = 10%, Effective rate = 20 + 100/100 = 21% So CI on Rs 1000 for 2 years at 10% = 21% of 1000 = Rs 210 TRICK 2 — Ratio Method: If A:B are amounts in consecutive years, growth ratio is constant. Useful when finding CI for different time periods using given data. TRICK 3 — Quick Difference Formula (2 years): CI - SI = P x (R/100)^2 This is one of the most tested shortcuts in SSC. Memorise it cold. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Use A = P x (1 + R/100)^T A = 8000 x (1 + 15/100)^2 A = 8000 x (115/100)^2 A = 8000 x 1.3225 A = Rs 10580
CI = A - P = 10580 - 8000 = Rs 2580 Using Shortcut (Effective Rate): 2x15 + 225/100 = 30 + 2.25 = 32.25% CI = 32.25% of 8000 = Rs 2580. Same answer, much faster! ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ WORKED EXAMPLE 2 — CI vs SI Difference ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Question: The difference between CI and SI on Rs 5000 for 2 years is Rs 20. Find the rate of interest.
Use CI - SI = P x (R/100)^2 20 = 5000 x (R/100)^2 (R/100)^2 = 20/5000 = 1/250 Wait — let us recheck: 20/5000 = 0.004 (R/100)^2 = 0.004 R/100 = 0.0632... Let us try R = 20%: 5000 x (20/100)^2 = 5000 x 0.04 = 200. Too high. Try R = 2%: 5000 x (2/100)^2 = 5000 x 0.0004 = 2. Too low. Try R = 10%: 5000 x (10/100)^2 = 5000 x 0.01 = 50. No. Actual answer: Let us set 5000 x (R/100)^2 = 20 (R/100)^2 = 20/5000 = 1/250 R^2 = 10000/250 = 40 R = root of 40 = approximately 6.32% Note: SSC sets clean numbers. A cleaner version: If difference = Rs 50, P = Rs 5000: R = 10% (because 5000 x 0.01 = 50). This is how SSC frames it. Always work backwards using the shortcut formula in such questions. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
— THE NUMBER ONE TRAP ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Students apply annual compounding formula when the question says HALF-YEARLY compounding. If a question says 'compounded half-yearly at 10% per annum for 2 years,' many students use (1 + 10/100)^2. You must use (1 + 10/200)^(2x2) = (1 + 5/100)^4.
This single mistake can cost 2 marks. Always check the compounding frequency before writing the formula.
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