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Compound Interest
Last updated at Nov. 12, 2018 by Teachoo
Ex 8.3, 7 Maria invested Rs 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find (i) The amount credited against her name at the end of the second year. Given, Principal (P) = Rs 8000 Rate (R) = 5% per annum Time = 2 Years We need to find the amount after 2 years So, we use the formula A = P ("1 + " π/100)^π Putting values A = 8000 ("1 + " 5/100)^2 = 8000 ("1 + " 1/20)^2 = 8000 ((20 + 1)/20)^2 = 8000 (21/20)^2 = 8000 Γ ((21 Γ 21)/(20 Γ 20)) = 80 Γ ((21 Γ 21)/(2 Γ 2)) = 20 Γ 21 Γ 21 = 20 Γ 441 = 8820 β΄ Amount after 2 years = Rs 8,820 Ex 8.3, 7 (Method 1) Maria invested Rs 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find (ii) The interest for the 3rd year. Interest in 3rd year = Amount after 2 years Γ Rate = 8820 Γ 5/100 % = 8820 Γ 5/100 = 8820 Γ 1/20 = 882/2 = 441 β΄ Interest for the 3rd year = Rs 441 Ex 8.3, 7 (Method 2) Maria invested Rs 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find (ii) The interest for the 3rd year. Now, Interest for the 3rd year = Amount after 3 years β Amount after 2 years Finding Amount after 3 years Amount after 3 years = P (1+π /100)^π Putting values Amount = 8000 (1+5/100)^3 = 8000 (1+1/20)^3 = 8000 ((20 + 1)/20)^3 = 8000 (21/20)^3 = 8000 Γ (21 Γ 21 Γ21)/(20 Γ 20 Γ20) = 8000 Γ (441 Γ 21)/(400 Γ 20) = 8000 Γ 9261/8000 = 9261 Therefore, Interest for the 3rd year = Amount after 3 years β Amount after 2 years = 9261 β 8820 = 441 β΄ Interest for the 3rd year = Rs 441