Compound Interest Questions for SSC CGL

Core Concept and Basic Formula

In Compound Interest, interest is calculated on the principal PLUS the previously accumulated interest. Think of it as interest earning interest. The compounding can happen annually, half-yearly, or quarterly, which changes the effective rate and time period. SSC CGL almost always uses annual compounding unless stated otherwise.

• CI formula gives the final Amount (A), not directly the interest.
• CI = A - P, where A is the maturity amount.
• Half-yearly: rate becomes R/2, time becomes 2T.
• Quarterly: rate becomes R/4, time becomes 4T.
• If compounded annually but rate differs each year, multiply factors: A = P x (1 + R1/100) x (1 + R2/100).

CI vs SI Difference — The Most Tested Pattern

SSC CGL loves asking the difference between CI and SI for 2 or 3 years. For 2 years, there is a clean formula. For 3 years, there is a slightly longer formula. Memorise both. The key insight: for 2 years, the difference is simply the interest on the first year's interest.

• For 2 years: Difference = P x (R/100)^2
• For 3 years: Difference = P x (R/100)^2 x (3 + R/100)
• SI for 2 years = 2PR/100; CI for 2 years is always more than SI.
• If difference is given and you need P or R, reverse the formula.
• This shortcut avoids full calculation and saves 40-50 seconds.

Ratio and Multiplier Shortcut

Instead of calculating with large numbers, convert rates to multipliers. For R = 10%, the multiplier is 1.1. For R = 20%, it is 1.2. For R = 25%, it is 1.25 = 5/4. Use fractions when the rate gives a clean fraction — this is faster than decimals on paper. SSC setters often choose rates like 10%, 20%, 25%, 331/3% specifically so you can use fractions.

• 10% per annum: multiplier = 11/10. For 2 years: (11/10)^2 = 121/100.
• 20%: multiplier = 6/5. For 2 years: 36/25.
• 25%: multiplier = 5/4. For 2 years: 25/16.
• 50%: multiplier = 3/2. For 2 years: 9/4.
• Population growth and depreciation use the same CI formula — just replace P with population or value.

Effective Rate and Instalments (Tier 2 Focus)

Effective annual rate means what annual rate would give the same result as a given compounding frequency. For half-yearly compounding at R%, the effective rate is more than R%. Instalment questions ask: what equal yearly payment clears a loan in n years at r% CI? These appear in Tier 2 and require the present value concept.

• Effective rate for half-yearly at R%: Reff = 2R/100 + (R/100)^2 x 100 approximately.
• For instalments: sum of present values of all instalments equals principal.
• Each instalment PV = Instalment / (1 + R/100)^n for the nth payment.
• SSC Tier 2 sometimes gives 2-instalment problems — set up two PV terms and solve.
• Do not confuse instalment-based SI with instalment-based CI — check compound vs simple.

• Forgetting to adjust rate and time for half-yearly or quarterly compounding — always halve the rate AND double the time for half-yearly.
• Calculating CI directly instead of finding Amount first and then subtracting Principal — leads to sign errors.
• Using the SI formula for depreciation — depreciation uses (1 - R/100)^T not subtraction of simple interest.
• In CI-SI difference formula, squaring R/100 correctly — students often write R^2/100 instead of R^2/10000.
• Assuming compounding is annual when the question says compounded half-yearly — read the question fully before applying the formula.

• PART mnemonic: P = Principal, A = Amount, R = Rate, T = Time. CI = A minus P, always find A first.
• For CI-SI diff in 2 years, remember: the difference is the interest on first year's SI. So SI for year 1 = PR/100, then interest on that = (PR/100) x R/100 = P(R/100)^2. Visualise it as a small extra triangle of interest.
• Multiplier trick mantra: 10% means every 100 becomes 110. Write it as 11/10. Raise to the power of years. No calculator needed if rate is 10%, 20%, or 25%.
• Depreciation vs Growth: Growth is plus, depreciation is minus inside the bracket. Think: (1 + R/100) = the thing GROWS older, (1 - R/100) = the machine RUSTS away.

• SSC CGL Tier 1 typically has 1-2 CI questions at easy-to-moderate level — usually direct CI for 2 years or CI-SI difference. These should be solved in under 60 seconds using multiplier shortcuts.
• Tier 2 Paper 1 (Math) pushes harder: expect depreciation, population growth, instalments, and different annual rates. Budget 90 seconds per CI question.
• Rates chosen in SSC papers are almost always clean: 5%, 10%, 12.5%, 20%, 25%. Prepare fraction multipliers for all five and you will rarely need long multiplication.
• If a question mentions compounded annually but gives three different rates for three years, use the chain multiplier: A = P x (1+R1/100)(1+R2/100)(1+R3/100). This appears as a surprise question in Tier 1.
• Avoid over-calculating: if the answer choices are far apart, approximate using SI + a small extra amount (CI is always more than SI for same P, R, T). This helps eliminate options and save time.