Question

find the compound interest using the formula if principal = 3000; rate =10% per annum compounded half yearly; time= 2 years

Answer 1

Amount = P[1+r/200]²ⁿ

As compounded half yearly,

So

A = 3000 [ 1 + 10/200]⁴

 = 3000 × (21/20)⁴

 = 583443000/160000 = 3646.5

CI = A - P = 3646.5 - 3000 = 646.5

Thank u.

Answer 2

$\\rate \: = 10 \div 2 = 5\%p.a \\ time \: = 2 \times 2 = 4 \: halfyears \\ compound \: amount \: = 3000(1 + \frac{5}{100} ) {}^{4} \: \: \: = 3000(1 + \frac{1}{20} ) {}^{4} \: \ \: = 3000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} \\ = \frac{3 \times 21 \times 21 \times 21 \times 21}{16} \\ = \frac{583443}{160} \: = 3646.51 \: \\ compound \: interest \: = 3646.51 - 3000 \: \\ compound \: interest= 646.51$