Question

₹16000 invested at 10 percent p.a. compunded semiannually amounts to rupees 18522 find the time period of the investment

Answer 1

HEY DEAR ...

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.

HOPE , IT HELPS ...

Answer 2

Question : ₹16000 invested at 10 percent p.a. compounded semiannually amounts to rupees 18522 find the time period of the investment

Solution :

     Invested amount = Rs 16000

      Received amount at the end of period is = Rs 18522

      Let the time is = t year

      So,                 n = 2 t

       Rate = 10% per annum = 5 % half yearly

       $\therefore 18522 = 16000 \bigg ( 1+ \frac{5}{100} \bigg)^n$

        $\bigg ( \frac{18522}{16000} \bigg) = \bigg ( \frac{21}{20} \bigg )^n$

       $\bigg ( \frac{21}{20} \bigg )^3 = \bigg ( \frac {21}{20} \bigg )^n$

$On\ comparing\, we\ get\\n = 3\\2t = 3 \implies t = \frac {3}{2} yr \implies t = 1 \frac {1}{2} yr$