Compound Interest for fraction years

Chapter 7 Class 8 Comparing Quantities
Concept wise

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### Transcript

Question 6 Find CI paid when a sum of Rs 10,000 is invested for 1 year and 3 months at 8 1/2 % per annum compounded annually Given Principal = P = Rs 10,000 Rate = 8 1/2 % R = 17/2 % Time = 1 year 3 months = 1 3/12 years = 1 1/4 years Since time is in fraction, We use the formula Compound interest for 1 1/4 years = Compound interest for 1 year + Simple interest for next 1/4 years Compound interest for 1 year P = Rs 10,000 R = 17/2 % Time = 1 year β΄ n = 1 Now A = P (1+π/100)^π = 10000 (1+(17/2)/100) = 10000 (1+17/(2 Γ 100)) = 10000 Γ (1+17/200) = 10000 Γ ((200 + 17)/200) = 10000 Γ 217/200 = 100 Γ 217/2 = 10850 Since, Amount = Principal + Interest 10850 = 10000 + Interest 10850 β 10000 = Interest 850 = Interest Interest = 850 Simple interest for π/π next year Principal will be the amount after 1 year P = 10850 R = 17/2 % T = 1/4 year β΄ SI = (π Γ π Γ π)/100 = (10850 Γ 17/2 Γ 1/4)/100 = (10850 Γ17)/(2 Γ 4 Γ 100) = (1085 Γ 17)/(2 Γ 4 Γ10) = (1085 Γ 17)/80 = 18445/80 = 230.56 Interest for 1/4 years = Rs 230.56 Now, Compound interest for 1 1/4 years = Compound interest for 1 year + Simple interest for 1/4 years = 850 + 230.56 = 1080.56 β΄ Compound interest after 1 1/4 years = Rs 1080.56