Ex 8.3, 8 Class 8 - NCERT Solutions of Chapter 8 Maths - Teachoo

Ex 8.3, 8 - Chapter 8 Class 8 Comparing Quantities - Part 2
Ex 8.3, 8 - Chapter 8 Class 8 Comparing Quantities - Part 3 Ex 8.3, 8 - Chapter 8 Class 8 Comparing Quantities - Part 4 Ex 8.3, 8 - Chapter 8 Class 8 Comparing Quantities - Part 5 Ex 8.3, 8 - Chapter 8 Class 8 Comparing Quantities - Part 6 Ex 8.3, 8 - Chapter 8 Class 8 Comparing Quantities - Part 7 Ex 8.3, 8 - Chapter 8 Class 8 Comparing Quantities - Part 8

 

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Transcript

Question 8 Find the amount and the compound interest on Rs 10,000 for 1 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? Given, Principal (P) = 10000 Rate (R) = 10 % P.A Compounded half Yearly = 10/2 % Per Half year = 5 % per half year Time = 1 1/2 Years = 3/2 years = 3/2 × 2 half years = 3 Half Years Amount(A) = P (1+𝑅/100)^𝑛 = 10000 × (1+5/100)^3 = 10000 × (1+1/20)^3 = 10000 × ((20 + 1)/20)^3 = 10000 × (21/20)^3 = 10,000 × (21 × 21 × 21)/(20 × 20 × 20) = 10 × (441 × 21)/(2 × 2 × 2) = 10 × 9261/8 = 92610/8 = 11576.25 Now, Amount = Principal + Interest 11576.25 = 10,000 + Interest 11576.25 − 10000 = Interest 1576.25 = Interest ∴ Interest = 1576.25 Interest when Compounded Annually P = 10000 R = 10% P.A. N = 1 1/2 years Since n is in fraction, We use the formula Compound Interest for 1 1/2 years = Compound Interest for 1 Year + Simple Interest for next 1/2 year Compound Interest for 1 year: P = 10000 R = 10% N = 1 Amount = P (1+𝑅/100)^𝑛 = 10000 (1+10/100)^1 = 10000 (1+1/10) = 10000 ((10 + 1)/10) = 10000 (11/10) = 11000 Now, Amount = Principal + Interest 11000 = 10000 + Interest 11000 − 10000 = interest 1000 = Interest ∴ Interest = 1000 Simple Interest for next 𝟏/𝟐 year P = Amount of Previous Year = 11000 R = 10% T = 1/2 year Interest (I) = (𝑃 × 𝑅 × 𝑇)/100 = (11000 × 10 × 1/2)/100 = (11000 × 10)/(2 × 100) = 1100/2 = 550 Interest = 550. Now, Interest for 1 1/2 years = Compound interest for 1 year + Simple Interest for 1/2 year = 1000 + 550 = 1550 Therefore, Interest when compounded half yearly = Rs 1576.25 & Interest when compounded annually = Rs 1550 ∴ Interest when Compounded half yearly is more than the Interest when compounded Annually.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.