Ex 8.3, 1 (d) Calculate the amount and compound interest on (d) Rs 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify).
Given,
Principal (P) = 8,000
Rate (R) = 9% per Annum Compounded half Yearly
= 9/2 % Per half year.
Time (N) = 1 Year
= 2 half years.
Now,
Amount (A) = P (1+𝑅/100)^𝑛
= 8000 (1+(9/2)/100)^2
= 8000 × (1+9/(2 × 100))^2
= 8000 × (1+9/200)^2
= 8000 × ((200 + 9)/200)^2
= 8000 × (209/200)^2
= 8000 × (209 × 209)/(200 × 200)
= 8 × (209 × 209)/(2 × 20)
= 8 × (209 × 209)/40
= 8/4 × (209 × 209)/10
= 2 × (209 × 209)/10
= (418 × 209)/10
= 87362/10
= 8736.2
∴ Amount = 8736.2
Now,
Amount = Principal + Interest
8736.2 = 8000 + Interest
8736.2 − 8000 = Interest
736.2 = Interest
∴ Interest = 736.2
∴ Amount = Rs 8736.20
& Compound interest = Rs 736.20

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.