Question

Find the compound interest on 3,000 at the rate of 6% per annum for 1*1/2
years compounded half-yearly​

Answer 1

Solution :

$\underline{\bf{Given\::}}}$

• Principal, (P) = Rs.3000
• Rate, (R) = 6% p.a
• Time, (n) = 1 1/2 years = 3/2 years

$\underline{\bf{Explanation\::}}}$

Using formula of the compounded half - yearly;

$\boxed{\bf{Amount = Principal \bigg(1+\frac{R}{2\times 100} \bigg)^{2n}}}$

A/q

$\mapsto\sf{A=3000\bigg(1+\dfrac{6}{2\times 100} \bigg)^{\cancel{2}\times 3/\cancel{2}} }\\\\\\\mapsto\sf{A=3000\bigg(1+\cancel{\dfrac{6}{200}} \bigg)^{3}}\\\\\\\mapsto\sf{A=3000 \bigg(1+\dfrac{3}{100} \bigg)^{3}}\\\\\\\mapsto\sf{A=3000\bigg(\dfrac{100 + 3}{100} \bigg)^{3}}\\\\\\\mapsto\sf{A=3000 \bigg(\dfrac{103}{100} \bigg)^{3}}\\\\\\\mapsto\sf{A=30\cancel{00} \times \dfrac{103}{\cancel{100}} \times \dfrac{103}{100} \times \dfrac{103}{100} }$

$\mapsto\sf{A=\dfrac{30\times 103 \times 103 \times 103 }{10000} }\\\\\\\mapsto\sf{A=\cancel{\dfrac{32781810}{10000} }}\\\\\\\mapsto\bf{A=Rs.3278.18}$

Now;

As we know that compound Interest;

$\longrightarrow\sf{C.I.=Amount - Principal}\\\\\longrightarrow\sf{C.I.=Rs.3278.18 - Rs.3000}\\\\\longrightarrow\bf{C.I.=Rs.278.18}$

Thus;

The compound Interest will be Rs.278.18 .