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यह Compound Interest प्रश्न “4500 रुपये पर 5 प्रतिशत वार्षिक दर से 2 वर्षों का चक्रवृद्धि ब्याज कितना होगा” के लिए सही सूत्र चुनने की क्षमता विकसित करता है। अभ्यर्थी को मूलधन, वार्षिक दर, कुल compounding periods तथा पूछा गया मान—राशि, ब्याज, दर, समय या मूलधन—पहचानना होता है।
इस प्रश्न में दिए मूलधन, ब्याज-दर, समय और compounding frequency को एक ही इकाई में बदलकर ही मान रखने चाहिए। उपलब्ध गणना है: CI = P((1+R/100)^T - 1) = 461.25। चक्रवृद्धि ब्याज साधारण ब्याज से इसलिए अलग है कि प्रत्येक अवधि का ब्याज शेष राशि में जुड़ जाता है और अगली अवधि में उसी बढ़ी हुई राशि पर ब्याज लगता है। इसलिए घात में कुल compounding periods आते हैं, केवल वर्षों की लिखी संख्या नहीं। अन्य विकल्प 161.25, 61.25, 461.25 साधारण ब्याज लगा देने, मूलधन घटाना भूलने, बीच में जल्दी rounding करने या अवधि के अनुसार दर न बदलने से मिल सकते हैं।
FAQ
Common questions and clear answers for this topic.
Compound Interest (CI) is interest calculated on both the principal amount and the accumulated interest from previous periods. Simple Interest (SI) is calculated only on the principal. CI formula: A = P(1 + r/n)^(nt). CI gives more interest than SI for the same principal and rate. Both are important topics for SSC CGL, Bank PO, and CAT exams.
Compound Interest Formula: A = P(1 + R/100)^n where A = Final Amount, P = Principal, R = Annual Rate of Interest, n = Number of years. CI = A - P = P[(1 + R/100)^n - 1]. For half-yearly compounding: A = P(1 + R/200)^(2n). For quarterly: A = P(1 + R/400)^(4n). This formula is essential for SSC CGL and banking aptitude tests.
Annual Compounding: Interest added once a year. Half-yearly Compounding: Rate halved (R/2), time doubled (2n). Quarterly Compounding: Rate quartered (R/4), time quadrupled (4n). Monthly Compounding: Rate divided by 12, time multiplied by 12. More frequent compounding means more interest earned. Understanding this helps solve CI questions in SSC and Bank PO exams.
For half-yearly CI: A = P(1 + R/200)^(2n). Example: P = 10000, R = 10% per annum, n = 2 years. A = 10000(1.05)^4 = 12155. CI = 12155 - 10000 = Rs. 2155. This type of calculation is common in SSC CGL Tier-2 and Bank PO quantitative aptitude sections.
Shortcuts for CI problems: For 2 years CI = SI + SI(R/100), Difference between CI and SI for 2 years = P(R/100)^2, Use net percentage concept for multi-year problems, Remember if rate is 10% CI for 2 years is 21% not 20%, Successive percentage approach helps. Memorize these tricks for quick solving in SSC CGL and IBPS PO exams.
