Question

Please solve this with explanation it is very important. step by step ​

Answer 1

Question:-

Find the compound interest on Rs.5000 at 12% p.a. for 1 year, compounded half-yearly.

Required Answer:-

Given:-

$\sf{\rightarrow{Principle \: amount \: \bold{P} = Rs.5000}}$

$\sf{\rightarrow{Rate \: of \: interest \: \bold{R} = 12\% }}$

$\sf{\rightarrow{Time \:\bold{T} = 1\:year}}$

To Find:-

$\sf{\rightarrow{Compound \: interest \: \bold{C} \: compounded \: half \: yearly}}$

Solution:-

As we know that:-

$\boxed{\sf{\blue{A = P(1 + \frac{R}{n} ) {}^{nt} }}}$

Substituting the values,

$\\ \sf{\bold{A} = 5000(1 + \frac{12\%)}{2} ) {}^{2 \times 1}}$

$\\ \sf{\implies{\bold{A} = 5000(1 + 6\% ) {}^{2} }}$

$\\ \sf{\implies{\bold{A} = 5000 \times ( \frac{106}{100} ) {}^{2} }}$

$\\ \sf{\implies{\bold{A} = 5000 \times \frac{106}{100} \times \frac{106}{100}}}$

$\\ \sf{\implies{\bold{A} = \orange{5618}}}$

Therefore,

Compound interest = Amount - Principal amount

Compound interest = Rs.(5618 - 5000)

Compound interest =Rs. 618

Hence, the compound interest is Rs.618