Compound Interest Questions for CDS

Core Concept: What is Compound Interest?

In Simple Interest, interest is always calculated on the original principal. In Compound Interest, interest earned each period is added back to the principal, and the next period's interest is calculated on this new (larger) amount. This is called 'interest on interest'. The period after which interest is compounded can be annual, half-yearly, quarterly, or monthly.

• CI grows faster than SI for the same rate and time.
• For 1 year, CI and SI are equal (when compounded annually).
• For 2 years, CI minus SI = P times (R/100) squared.
• Compounding frequency matters: more frequent compounding means more interest.
• CI is always calculated on Amount (Principal + accumulated interest), not just on P.

Essential Formulas

These are the core formulas you must memorise cold. The Amount formula is the backbone — CI is simply Amount minus Principal. Adjust the rate and time based on compounding frequency.

• Amount = P(1 + R/100)^n for annual compounding.
• For half-yearly: replace R with R/2 and n with 2n.
• For quarterly: replace R with R/4 and n with 4n.
• CI = Amount minus P.
• Difference between CI and SI for 2 years = P(R/100)^2.
• Difference between CI and SI for 3 years = P(R/100)^2 times (R/100 + 3).

Finding Rate or Time (Reverse Problems)

CDS sometimes gives you the Amount or CI and asks you to find Rate or Time. For time-based questions, use the logic of matching powers. For rate-based questions, set up the equation and solve. These are slightly harder but follow a fixed pattern.

• If Amount doubles at rate R compounded annually, use 2P = P(1+R/100)^n to find n.
• Common trap: if money doubles in n years at SI, it does NOT double in same n years at CI — it doubles faster in CI.
• Ratio method: if A1/P = (1+R/100)^n, take the n-th root to find (1+R/100).
• For questions like 'a sum becomes Rs X in 2 years and Rs Y in 3 years', Rate = (Y-X)/X × 100.

Population Growth and Depreciation

These are word-problem disguises of the CI formula. Population increasing at r% per year uses the same formula as compound interest. Depreciation (machines, cars losing value) uses minus instead of plus. CDS GK-Maths crossover questions sometimes appear here.

• Population after n years = P0 × (1 + r/100)^n.
• Depreciated value after n years = P0 × (1 - r/100)^n.
• If different rates apply in different years, multiply each year's factor separately.
• Example pattern: 'A machine costs Rs 50,000. It depreciates 10% yearly. Find value after 2 years.'

• Forgetting to adjust rate and time when compounding is half-yearly or quarterly. Students apply annual rate directly — this is the most common error.
• Confusing CI with Amount. CI = Amount minus Principal. Many students write the Amount as the final answer when CI is asked.
• Using the SI formula for CI problems when the word 'interest' appears without reading if it says 'compound'. Always check the compounding keyword.
• In depreciation problems, adding rate instead of subtracting. Population grows (use +), assets depreciate (use -).
• When rate or time is asked and Amount is given for two different years, students try to solve using the full CI formula instead of using the simple ratio shortcut: Rate = (A3 - A2)/A2 × 100.

• HART mnemonic for adjusting compounding: H = Half-yearly (divide R by 2, multiply n by 2), A = Annual (no change), R = Remember to subtract P for CI, T = Time adjustment is always paired with Rate adjustment.
• The 2-year shortcut rhyme: CI beats SI, by P times R-squared over 100-squared. Lock this formula — it appears in almost every CDS paper.
• Think of CI like a snowball rolling downhill — it picks up more snow (interest) as it grows bigger. SI is like carrying a fixed bag of snow every year.
• For Population vs Depreciation: Population PLUS (growing), Depreciation MINUS (shrinking). Plus for birth, Minus for rust.

• CDS typically asks 2-3 CI questions per paper. At least one is a straightforward Amount/CI calculation for 2-3 years at a clean rate like 10%, 5%, or 20% — do not waste time on these, solve in under 60 seconds using the formula.
• The CI minus SI difference formula for 2 years is tested almost every year in some form. Memorise P(R/100)^2 cold and use it to verify answers or solve directly.
• Half-yearly compounding questions appear regularly. The trick is mechanical — halve the rate, double the time — then apply the standard formula. Practice 2-3 such problems before the exam.
• Depreciation word problems are increasing in frequency in recent CDS papers. They look like GK/applied questions but are pure formula substitution — do not be intimidated.
• When stuck on a reverse problem (find Rate or Time), use the answer options. Plug back each option into A = P(1+R/100)^n and check which satisfies the condition. This back-substitution saves time in MCQ format.