Answer

Verified

454.2k+ views

**Hint**: To calculate compound interest, we have given formula:

$ A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}} $

Where, A = final amount

P = initial amount

r = interest rate

t = number of time periods

Hence, compound interest is the difference of final amount and initial amount.

$ \Rightarrow CI=A-P $

Substitute the values in the formula to calculate compound interest.

**:**

__Complete step-by-step answer__As given in the question, the interest is compounded half-yearly, therefore the rate of interest is reduced half times.

That means, interest rate = 10% per annum, so, for compounding half-yearly, the interest rate = 5%.

So, r = 5 %

In the given question, the time period is $ 1\dfrac{1}{2} $ , i.e. three times a six-months interval.

So, t = 3

We have principal = Rs 12000

Using values of P, r and t, we get amount (A) as:

$ \begin{align}

& {{\left( SI \right)}_{3}}=\dfrac{{{A}_{2}}\times r\times t}{100} \\

& =\dfrac{13230\times 5\times 1}{100\times 2} \\

& =Rs.661.50

\end{align} $

Hence, Amount = Rs 13891.50

So, compound interest is:

$ \begin{align}

& CI=A-P \\

& =13891.50-12000 \\

& =1891.50

\end{align} $

Hence, compound interest = Rs 1891.50

**Note**: The other way to find compound interest compounded half-yearly is applying simple interest for every 6 months for the same interest rate and adding the interest in the initial value to calculate for another 6 months until for the total time period:

As it is given:

P = Rs 12000

r = 5%

t = $ 1\dfrac{1}{2} $ years = 3 $ \times $ 6 months

So, Simple interest for first 6 months is:

$ \begin{align}

& {{\left( SI \right)}_{1}}=\dfrac{P\times r\times t}{100} \\

& =\dfrac{12000\times 5\times 1}{100\times 2} \\

& =Rs.600

\end{align} $

Amount after first 6 months is:

\[\begin{align}

& CI={{\left( SI \right)}_{1}}+{{\left( SI \right)}_{2}}+{{\left( SI \right)}_{3}} \\

& =600+630+661.50 \\

& =Rs.1891.50

\end{align}\]

Now, consider $ {{A}_{1}} $ as principal for another 6 months. So simple interest for another 6 months is:

$ \begin{align}

& {{\left( SI \right)}_{2}}=\dfrac{{{A}_{1}}\times r\times t}{100} \\

& =\dfrac{12600\times 5\times 1}{100\times 2} \\

& =Rs.630

\end{align} $

Amount after another 6 months is:

$ \begin{align}

& {{A}_{2}}={{A}_{1}}+{{\left( SI \right)}_{2}} \\

& =12600+630 \\

& =Rs.13230

\end{align} $

Now, consider $ {{A}_{2}} $ as principal for another 6 months. So simple interest for another 6 months is:

$ \begin{align}

& {{\left( SI \right)}_{3}}=\dfrac{{{A}_{2}}\times r\times t}{100} \\

& =\dfrac{13230\times 5\times 1}{100\times 2} \\

& =Rs.661.50

\end{align} $

Final amount after another 6 months is:

$ \begin{align}

& {{A}_{3}}={{A}_{2}}+{{\left( SI \right)}_{3}} \\

& =13230+661.50 \\

& =Rs.13891.50

\end{align} $

Hence, total interest is

\[\begin{align}

& CI={{\left( SI \right)}_{1}}+{{\left( SI \right)}_{2}}+{{\left( SI \right)}_{3}} \\

& =600+630+661.50 \\

& =Rs.1891.50

\end{align}\]

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Who was the Governor general of India at the time of class 11 social science CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference Between Plant Cell and Animal Cell