Question

Rs 16000 lent at 10 % pa compounded half-yearly amounts to Rs 18522. Find the time period for which the sum was lent?

Answer 1

Step-by-step explanation:

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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