Rs. 16000 invested at 10% per annum compounded semi-annually amounts to Rs. 18522. Find the time period of the investment.
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Solution :-
Principal (P) = Rs. 16000
Rate of interest = 10 %
⇒ 10/2 = 5 % compounded semi annually
Amount (A) = Rs. 18522
Let the number of six monthly period be 'n'
A = P(1 + R/100)ⁿ
⇒ 18522 = 16000(1 + 10/100)ⁿ
⇒ 18522/16000 = [(20 + 1)/20]ⁿ
⇒ 9261/8000 = (21/20)ⁿ
⇒ (21*21*21)/(20*20*20) = (21/20)ⁿ
⇒ (21/20)³ = (21/20)ⁿ
⇒ n = 3
Three periods of 6 months = 1 1/2 years.
Answer.
Principal (P) = Rs. 16000
Rate of interest = 10 %
⇒ 10/2 = 5 % compounded semi annually
Amount (A) = Rs. 18522
Let the number of six monthly period be 'n'
A = P(1 + R/100)ⁿ
⇒ 18522 = 16000(1 + 10/100)ⁿ
⇒ 18522/16000 = [(20 + 1)/20]ⁿ
⇒ 9261/8000 = (21/20)ⁿ
⇒ (21*21*21)/(20*20*20) = (21/20)ⁿ
⇒ (21/20)³ = (21/20)ⁿ
⇒ n = 3
Three periods of 6 months = 1 1/2 years.
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