What is the compound interest on a sum Rs. 10,000 at 12% per annum for 1 year and 4 months, when the interest is compounded at every 8 months?
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Answer (Detailed Solution Below)Option 2 : Rs. 1,664
Free SSC GD Previous Paper 2 (Held On: 13 Feb 2019 Shift 1)_Hindi 100 Questions 100 Marks 90 Mins Given: Principal = Rs. 10,000 Rate of interest = 12% Time = 1 year and 4 months = 16 months Formula used: A = P (1 + r/100)n C.I = A - P Where, A = Amount, P = Principal, n = Time, C.I = Compound interest Calculation: Interest is compounded on 8 months, So, Time = 16/8 = 2 years Rate of interest = 12% × (8/12) = 8% A = P (1 + r/100)n ⇒ Amount = 10,000 × (1 + 8/100)2 ⇒ Amount = 10,000 × (108/100)2 ⇒ Amount = (108)2 ⇒ Amount = Rs. 11,664 C.I = A - P ⇒ C.I = 11,664 – 10,000 ⇒ C.I = 1,664 ∴ The compound interest is Rs. 1,664. Alternate Method Interest is compounded on every 8 months So, Time = 16/8 = 2 years Rate of interest = 12% × (8/12) = 8% Effective rate formula for two years = (A + B + AB/100) Here, A = B = 8% ⇒ Effective rate formula for two years = {8 + 8 + (64/100)} = 16.64% ⇒ Compound interest = 10,000 × 16.64% ⇒ Compound interest = Rs. 1664 ∴ The compound interest is Rs. 1,664. Latest SSC GD Constable Updates Last updated on Nov 29, 2022 SSC GD Constable Vacancies Increased from 24369 to 45284. Earlier, the SSC GD Constable Exam Dates were out for the 2022 cycle. The exam will be conducted from 10th January 2023 to 14th February 2023. The candidates who will be appearing in exam must attempt SSC GD Constable Previous Year Papers. The vacancies have been released for the recruitment of GD Constables in various departments like BSF, CRPF, CISF, etc. Candidates can apply for SSC GD Constable 2022 till 30th November 2022. Applicants must note that they can apply for this recruitment only through the official website. The SSC GD Constable Exam Patternhas also been changed. Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now! - AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan. ₹ 9999/- ₹ 8499/- - AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan. ₹ 13999/- ₹ 12499/- - AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan. ₹ 9999/- ₹ 8499/- - AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan. ₹ 13999/- ₹ 12499/- Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,. ₹ 7999/- ₹ 4999/- Solution: What is known: Principal, Time Period, and Rate of Interest What is unknown: Amount and Compound Interest (C.I.) Reasoning: A = P[1 + (r/100)]n P = ₹ 10,000 n = \(1{\Large\frac{1}{2}}\) years R = 10% p.a. compounded annually and half-yearly where , A = Amount, P = Principal, n = Time period and R = Rate percent For calculation of C.I. compounded half-yearly, we will take the Interest rate as 5% and n = 3 A = P[1 + (r/100)]n A = 10000[1 + (5/100)]3 A = 10000[1 + (1/20)]3 A = 10000 × (21/20)3 A = 10000 × (21/20) × (21/20) × (21/20) A = 10000 × (9261/8000) A = 5 × (9261/4) A = 11576.25 Interest earned at 10% p.a. compounded half-yearly = A - P = ₹ 11576.25 - ₹ 10000 = ₹ 1576.25 Now, let's find the interest when compounded annually at the same rate of interest. Hence, for 1 year R = 10% and n = 1 A = P[1 + (r/100)]n A = 10000[1 + (10/100)]1 A = 10000[1 + (1/10)] A = 10000 × (11/10) A = 11000 Now, for the remaining 1/2 year P = 11000, R = 5% A = P[1 + (r/100)]n A = 11000[1 + (5/100)] A = 11000[(105/100)] A = 11000 × 1.05 A = 11550 Thus, amount at the end of \(1{\Large\frac{1}{2}}\)when compounded annually = ₹ 11550 Thus, compound interest = ₹ 11550 - ₹ 10000 = ₹ 1550 Therefore, the interest will be less when compounded annually at the same rate. ☛ Check: NCERT Solutions for Class 8 Maths Chapter 8 Video Solution: Find the amount and the compound interest on ₹ 10,000 for \(1{\Large\frac{1}{2}}\) years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 8 Summary: The amount and the compound interest on ₹ 10,000 for \(1{\Large\frac{1}{2}}\) years at 10% per annum, compounded half-yearly is ₹ 11576.25 and ₹ 1576.25 respectively. The interest will be less when compounded annually at the same rate. ☛ Related Questions:
What is the compound interest of 10000 in 2 years?∴ C.I. = ₹(10824.32 - 10000) = ₹824.32.
What is the compound interest on Rs 10000 for 2 years at rate of interest 10% per annum?10000 after 2 years, compounded annually with rate of interest being 10% per annum during the first year and 12% per annum during the second year, would be: - (a) Rs. 11320.
How much will Rs 10000 amount to in 2 years at compound interest compounded annually the rates of interest for the successive years being 9% and 10% respectively?total amount = amount + previous year intrest. total amount = 10900. which amounts to = 1090. hence, total 10000 amounts to 11,990 (10,900+1090).
What is compound interest a sum of Rs 10000 for 2 years at 10% per annum compounded annually?∴ The compound interest is Rs. 4884.
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