A sum of Rs. 41000 amounts to Rs. 53300 in 3 years at a certain rate percent per annum simple interest. The same sum will amount to what in 1 year at the same rate if the interest is compounded half yearly? (in nearest 1 Rs)

45203

           Sum          Amount

           21000     :     27300

                 10    :      13

SI = 3 unit

  3 =\(\frac{10×R×3}{100}\)

 ⇒ R = 10%

CI rate half yearly = \(\frac{10}{2}\)= 5%

                    5% → \(\frac{1}{20}\)

               principal      amount

1st year        20          21

2nd year      (20)²¹       (21)2

2nd year       400          441

                 400 unit = 41000

                441 unit =\(\frac{41000}{400}\)×441

= 45202.5 = ∼ 45203