Find the compound interest for Rs.\6000\ at \9%\ per annum for \18\ months if interest is compounded semi-annually?

Hint:To find the compound interest for the question, we first find the amount generated for the time period of three years by using the formula of:
\[A=P{{\left[ 1+\dfrac{R}{100} \right]}^{nt}}\]
where \[A\] is the amount generated by the compound interest, \[P\] is the principal, \[R\] is the rate of interest, \[n\] is the value of compounding, \[t\] is the value of the time period. After this we find the compound interest by subtracting the amount and principal.

Complete step by step solution:
According to the question given, the principal amount of the investment is given as Rs.\[6000\].
The rate of interest for the investment is given as \[9%\] per annum.
The time period for the investment is given as \[18\] months.
Now to find the time period for the investment when invested semi-annually is given as the product of \[nt\] where the value of \[n\] is given as \[2\] and the time period is given as \[3\text{ }years\].
Hence, The total time period for compounding semi-annually is \[2\times 3=6\].
Now placing the values in the formula for the compound interest is given as:
\[\Rightarrow A=6000{{\left[ 1+\dfrac{9}{100} \right]}^{6}}\]
\[\Rightarrow A=6000{{\left[ \dfrac{109}{100} \right]}^{6}}\]
\[\Rightarrow A=6000{{\left[ 1.09 \right]}^{6}}\]
Applying the power form the value as:
\[\Rightarrow A=Rs.10062\]
Applying the formula of the compound interest as the subtraction between the amount and the principal as:
Compound Interest \[=\] Amount \[-\] Principal
Compound Interest \[=Rs.10062-Rs.6000\]
Compound Interest \[=Rs.4062\]
Therefore, the value of the compound interest as \[Rs.4062\].

Note: Semi-annually means twice a year, annually means yearly, quarterly means four times in a year. Compound interest is different from simple interest as in compound interest the interest every year is applied on the interest before and time period changes according to the period of compounding of the investment.