Compound Interest in Hindi: चक्रवृद्धि ब्याज (Compound Interest), क्वांटिटेटिव एप्टीट्यूड सेक्शन में सबसे अधिक स्कोरिंग और महत्वपूर्ण टॉपिक में से एक है। आमतौर पर चक्रवृद्धि ब्याज से 1 से 2 प्रश्नों के सेट पूछे जाते हैं, इसलिए इन विषयों में उत्कृष्टता प्राप्त करने के लिए उम्मीदवारों को यह जानना होगा कि इसे कैसे हल किया जाए। पज़ल वाले प्रश्नों को हल करने में उम्मीदवारों की मदद करने के लिए, इस लेख में हमने चक्रवृद्धि ब्याज से संबंधित सभी आवश्यक विवरण प्रदान किए हैं, जैसे चक्रवृद्धि ब्याज की परिभाषा, टिप्स, ट्रिक्स, अवधारणाएं, प्रश्न, उत्तर, स्पष्टीकरण, आदि।
चक्रवृद्धि ब्याज की परिभाषा (Definition Of Compound Interest)
जब एक निश्चित समय के बाद दिया जाने वाला ब्याज जमाकर्ता को न देकर मूलधन में जोड़ दिया जाता हैं और प्राप्त मिश्रधन पर ब्याज लगाया जाता हैं तो इस प्रकार प्राप्त ब्याज चक्रवृद्धि ब्याज कहलाता हैं। चक्रवृद्धि ब्याज को “ब्याज पर ब्याज (interest on Interest)” के रूप में माना जा सकता है। यह साधारण ब्याज की तुलना में एक मूलधन को तेज दर से बढ़ाता है, जिसकी गणना मूलधन पर की जाती है। यह प्रारंभिक मूलधन और पिछली अवधियों से संचित ब्याज दोनों के आधार पर गणना किए गए ऋण या जमा पर ब्याज है।
चक्रवृद्धि ब्याज की गणना कैसे करें (How to Calculate Compound Interest)
उम्मीदवार एक साधारण फॉर्मूले से चक्रवृद्धि ब्याज की गणना कर सकते हैं।
चक्रवृद्धि ब्याज सूत्र है:
A = P (1+r/n)nt
C.I. = चक्रवृद्धि ब्याज
A = मिश्रधन,
P = मूलधन,
r = ब्याज की वार्षिक दर,
n = एक वर्ष में कुल ब्याज की संख्या
t = कुल समय (वर्ष में)
- वह बैंक या व्यक्ति जिससे हम रुपया उधार लेते हैं, त्रणदाता या साहूकार (Iender) कहलाता हैं।
- उधार लिया गया धन मूलधन (Principal) कहलाता है।
- वह निद्रिष्ट अवधि जब तक के लिए रुपया उधार लिया गया हो समय (Time) कहलाता है।
- वापस की गई राशि अर्थात मूलधन और ब्याज के सम्मिलित रूप को मिश्रधन (Amount) कहते हैं।
- किसी धन पर ब्याज की राशि मूलधन, समय की अवधि तथा ब्याज की दर पर निर्भर करती हैं।
चक्रवृद्धि ब्याज टिप्स, ट्रिक्स और कॉन्सेप्ट (Compound Interest Tips, Tricks, & Concepts)
- ब्याज देय होने पर ब्याज की राशि का तुरंत भुगतान किया जाता हैं, इस ब्याज की रकम को पुनः उधार देकर या दूसरी जगह लगाकर ब्याज प्राप्त किया जा सकता हैं।
- इस प्रकार प्राप्त किये गए ब्याज को मूलधन में जोड़कर एक नया मूलधन प्राप्त होता हैं, जिसे पुनः उधार दिया जा सकता हैं या दूसरी जगह लगाया जा सकता हैं।
- इस प्रकार यह क्रिया कई काल-अवधियों के लिए दोहराई जा सकती हैं, अन्तिम अवधि के अंत में मिश्रधन तथा प्रारम्भिक मूलधन के बीच का अंतर चक्रवृद्धि ब्याज (Compound Interest) कहलाता हैं इसे सूद-दर-सूद भी कहा जाता हैं।
- ब्याज प्रायः एक वर्ष, छः माह या तीन माह के या तीन माह के अंत में दिया जाता हैं, तब हम इसे क्रमशः संयोजित प्रतिवर्ष, संयोजित प्रति छमाही या प्रति तिमाही कहते हैं।
Compound Interest Questions, Answers, & Explanation
Q1. A man invested a sum in a scheme ‘P’ which offer 10% C.I.P.A. for 3 years and earn Rs. 1655. Find the interest earned by a man, if he invested the total amount he gets from scheme ‘P’, in scheme Q which offers 8% S.I.P.A for 5 years.
(a) Rs.4317
(b) Rs.1655
(c) Rs.1331
(d) Rs.2662
(e) Rs.2000
Q2. A sum becomes Rs. 4840 in two years and Rs. 5856.4 in four years when compounded annually. What would be the amount if the same sum was invested at 15% S.I. for 3 years (in Rs.)?
(a) 5600
(b) 5000
(c) 6400
(d) 6200
(e) 5800
Q3. The difference of the interest received when a sum is invested at 15% p.a. at SI for two years and the interest received when that sum is invested at 20% p.a. for one year compounded half yearly is Rs 432, find the sum?
(a) Rs. 5400
(b) Rs. 5000
(c) Rs. 4500
(d) Rs. 4000
(e) Rs. 4800
Q4. If Sonu invests a sum at compound interest compounding annually and earns Rs. 372 in the second year. Find the amount he invested (in Rs.)?
(a) 3377
(b) 2211
(c) 3300
(d) 3784
(e) 3751
Q5. Veer, Sameer, and Neeraj invested their amount on simple interest in the ratio of 4: 5: 8 respectively. The rate of interest for Veer, Sameer, and Neeraj is 12.5%, 10%, and 20% respectively. After two years of investment Veer, Sameer and Neeraj joined a business with the amount obtained from interest only for 12 months, 18 months, and 15 months respectively. If the total profit from the business is Rs 8450, then find the difference between the profit shares of Neeraj and Sameer?
(a) 3625 Rs.
(b) 3650 Rs.
(c) 3850 Rs.
(d) 3750 Rs.
(e) 3250 Rs.
Q6. Aman divided his total saving between his son and daughter in the ratio of 5 :3. His son invested his share on CI for two years at the rate of 10% and received the interest Rs. 480 less than his sister, who invested her share on SI for three years at the rate of 15%. Find Share of Aman’s son and daughter respectively?
(a) 10800 Rs, 2000 Rs
(b) 9600 Rs, 4200 Rs
(c) 8000 Rs, 4800Rs.
(d) 9800 Rs, 3000 Rs
(e) 7000 Rs , 5800 Rs
Q7. An amount is invested at S.I. for three years at a rate of 5% and S.I. received on that amount is Rs. 180. If the same amount is invested for two years at 10% C.I. for the first year & R% C.I. for 2nd year & the total C.I. received in two years is Rs. 318 then find the value of R?
(a) 15%
(b) 12%
(c) 22%
(d) 18%
(e) 25%
Q8. A lent B Rs.12000 on C.I. at the rate of 20% per annum and at the end of the first year B borrowed Rs. ‘x’ more from A on C.I. at the same rate. If at the end of the second year, B paid a total amount of Rs.20400 to A, then find the value of x?
(a) Rs.2400
(b) Rs.2000
(c) Rs.3600
(d) Rs.2600
(e) Rs.4000
Q9. A sum becomes Rs 6888 in 8 years and becomes Rs 7380 in 10 years at the same rate on simple interest. Find compound interest earned in 3 years on Rs 4000 at same rate of interest.
(a) Rs 630.5
(b) Rs 1261
(c) Rs 784.5
(d) Rs 1008
(e) Rs 1080
Q10. Satish invested Rs. 14,000 partially in scheme A which offer 20% p.a. at C.I. and remaining in scheme B which offers 25% at S.I. Find the amount invested in scheme B if total interest earns after 2 years is Rs. 6640.
(a) 6000
(b) 7000
(c) 8000
(d) 9000
(e) 10,000
Q11. Deepak invested some amount on SI out of Rs.47000 and rest amount on C.I. for two years. If S.I. is offering 12% p.a. and C. I. is offering 15% p.a. compounding annually and C.I. is Rs.532.5 more than S.I., then find amount invested by Deepak on C.I?
(a) Rs.23000
(b) Rs.22000
(c) Rs.21000
(d) Rs.25000
(e) Rs.24000
Q12. Aman spends 18,000 partially in scheme ‘A’ which offers 15% pa at C.I. and remaining in scheme ‘B’ which offers 25% p.a. at C.I. After 2 year he earns Rs. 7725 as interest. Find amount invested on scheme ‘B’ is what percent less or more than the amount invested on scheme ‘A’.
(a) 25%
(b) 20%
(c) 15%
(d) 50%
(e) 30%
Q13. If the difference between S.I on Rs. 2000 and C.I on 1600 for two year at the same rate of interest is Rs. 64. Find the rate of interest. (S.I > C.I)
(a) 5%
(b) 10%
(c) 20%
(d) 8.5%
(e) 12.5%
Q14. Arun invested Rs. 10,000 for three years at CI at the rate of 20% per annum. If in 1st and 3rd-year interest is calculated annually and in 2nd year it was calculated half-yearly, then find the total interest received by Arun in three years?
(a) Rs 7554
(b) Rs 7424
(c) Rs 7868
(d) Rs 7262
(e) Rs 7343
Q15. The difference between CI received in the first 1.5 years (compounded annually) at 20% per annum and CI received in last 1.5 years when compounded half yearly at the same rate of interest on the same sum is Rs 715 then find the sum?
(a) Rs. 66,000
(b) Rs. 65,000
(c) Rs. 64,500
(d) Rs. 65,500
(e) Rs. 67,500
FAQs: Compound Interest
Q1. What is Compound Interest?
Ans. Compound Interest occurs when interest gets added to the principal amount invested or borrowed, and then the interest rate applies to the new principal. Compound Interest can be thought of as “interest on Interest”.
Q2. In which examination Compound Interest Questions are asked?
Ans. Compound Interest Questions are asked in various competitive exams like IBPS PO, SSC GCL, MTS, Railways, SBI PO, SO Clerk, RRB PO, Clerk, SO, LIC AAO, ADO, Assistant, etc.
Q2. How to calculate Compound Interest?
Ans. Candidates can check short tricks and tips to calculate Compound Interest in the given above article.
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