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Ex 8.2

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Chapter 8 Class 11 Sequences and Series

Serial order wise

Last updated at May 29, 2023 by Teachoo

Ex 8.2 31 (Method 1) What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually? We use the formula A = P ("1 + " 𝑟/100)^t Here, P = principal r = rate of interest t = time A be the amount Putting values Amount = 500("1 +" 10/100)^10 = 500 ("1 +" 1/10)^10 = 500 ((10 + 1)/10)^10 = 500 (11/10)^10 = 500 (1.1)10 Hence, amount is Rs 500 × (1.1)10 Ex 8.2 31 (Method 2) What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually? The series is 550, 605, 665.5 … This is a G.P. as 605/550 = 1.1 & 665.5/605 = 1.1 So, common ratio = 1.1 & first term = a = 550 We need to calculate amount of 10th year i.e. a10 We know that nth term of GP is an = arn – 1 Putting a = 550, r = 1.1, n = 10 a10 = 550(1.1)10 – 1 = 550 (1.1)9 = (500 × 1.1)(1.1)9 = 500(1.1)(1.1)9 = 500(1.1)9 + 1 = 500(1.1)10 Hence amount in 10 years = Rs 500(1.1)10