Compound Interest for fraction years

Chapter 7 Class 8 Comparing Quantities
Concept wise

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### Transcript

Question 1 1 (b) Calculate the amount and compound interest on (b) Rs 18,000 for 2 1/2 years at 10% per annum compounded annually. Given, Principal = 18,000 Time (n) = 2 1/2 years Rate (R) = 10 % per Annum. Since n is in fraction, we use the formula. Compound interest for 2 1/2 years = Compound interest for 2 years + Simple interest for 1/2 π¦πππ. Compound interest for 2 years P = 18,000 N = 2 R = 10% Amount = P (1+π/100)^π Putting values = 18,000 (1+10/100)^2 = 18000 (1+1/10)^2 = 18000 ((10 + 1)/10)^2 = 18000 (11/10)^2 = 18000 Γ 121/100 = 180 Γ 121 = 21,780 Since Amount = Principal + Interest 21,780 = 18000 + Interest 21,780 β 18,000 = Interest 3780 = Interest Interest = 3780 β΄ Interest for 2 years = Rs 3780 & Amount after 2 years = Rs 21780 Simple interest for the next π/π year Principal will be the amount after 1 year P = 21,780 R = 10% T = 1/2 year Interest = (π Γπ Γ π)/100 = (21780 Γ 10 Γ 1/2)/100 = (21780 Γ 10)/(2 Γ 100) = 21780/2 = 1089 β΄ Simple interest for next 1/2 year = Rs 1089 Now, Interest for 2 1/2 years = Compound interest for 2 years + Simple Interest for 1/2 year = 3780 + 1089 = 4869 Amount = Principal + interest = 18000 + 4869 = 22869 β΄ Amount = Rs 22,869 & Interest = Rs 4,869