Question

Find the compound interest on Rs 25000 for 12 months at 8% per annum,

compounded half yearly.​

Answer 1

Given :-

• Principal = ₹25,000
• Rate = 8 % per annum
• Time = 12 months

To Find :-

• Compounded half yearly

Formulae Used :-

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

Solution :-

As we know that formula of the compounded half-yearly;

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

A/q

$\longrightarrow\tt{A = P\bigg(1+\dfrac{R}{2 \times 100} \bigg)^{2n}}$

$\longrightarrow\tt{A = 25000 \bigg(1+\dfrac{8}{2 \times 100} \bigg)^{2\times 1}}$

$\longrightarrow\tt{A = 25000 \bigg(1+\dfrac{8}{200} \bigg)^{2}}$

$\longrightarrow\tt{A = 25000 \bigg(1+\cancel{\dfrac{8}{200}} \bigg)^{2}}$

$\longrightarrow\tt{A = 25000 \bigg(1+\dfrac{1}{25} \bigg)^{2}}$

$</p><p>\longrightarrow\tt{A = 25000 \bigg(\dfrac{25+1}{25} \bigg)^{2}}$

$\longrightarrow\tt{A = 25000 \bigg(\dfrac{26}{25} \bigg)^{2}}$

$\longrightarrow\tt{A = \cancel{25000} \times \dfrac{26}{\cancel{25}} \times \dfrac{26}{\cancel{25}} }$

$\longrightarrow\tt{A = Rs.(40 \times 26 \times 26)}$

$\longrightarrow\bf{A = Rs.27040}$

Now, as we know that compound Interest;

→ C.I. = Amount - Principal

→ C.I. = Rs.27040 - Rs.25000

→ C.I. = Rs.2040

Thus,

The compound Interest will be Rs.2040 .