Question

Calculate the compound interest on $ 60,000 for 1 year, at 8% per annum, compounded half-yearly.

Answer 1

Answer :

›»› The compound interest are Rs.4800.

Given :

• Compound interest on $ 60,000 for 1 year, at 8% per annum, compounded half-yearly.

To Find :

• Compound interest = ?

Solution :

Here in this question we have to find the compound interest. So, firstly we need to find the amount, after that we will find the compound interest on the basis of conditions given above.

To find the amount, we use the formula:-

$\star\boxed{\bf{AMOUNT = P {\bigg(\dfrac{1 + r}{100}}}\bigg)^{n}} \star$

• Principal = $60,000.
• Rate = 8% per annum.
• Time = 1 year.

According to the given question,

On putting the given values in the formula, we get

$\tt{:\implies \mathscr{A}mount = 6000 \bigg( 1 + \dfrac {8}{100} \bigg)^{1} }$

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$\tt{:\implies \mathscr{A}mount = 60000\bigg(\dfrac{100 + 8}{100} \bigg)^{1} }$

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$\tt{:\implies \mathscr{A}mount = 60000\bigg(\dfrac{108}{100} \bigg)^{1} }$

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$\tt{:\implies \mathscr{A}mount = 600\not0 \not0 \times \dfrac{108}{1 \not0 \not0}}$

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$\tt{:\implies \mathscr{A}mount = 600 \times 108}$

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$\bf{:\implies \mathscr{A}mount = 64800}$

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Now, we have two elements that used in formula.

To find the Compound interest, we use the formula:-

$\star\boxed{\bf{C.I = AMOUNT - PRINCIPAL}} \star$

• Amount = 64800.
• Principal = 60000.

On putting the given values in the formula, we get

⠀

$\tt{: \implies C.I = 64800 - 60000}$

⠀

$: \implies \red{\boxed {\blue{\textsf{\textbf{C.I = Rs. 4800}}}}}$

⠀

Hence, the compound interest are Rs.4800.

Answer 2

• GIVEN:-

Principal = Rs. 60,000

Time(n) = 1 year

Rate = 8%

• To Find:-

Compound interest.

• SOLUTION:-

We know that,

$\large\boxed{\tt{Compound \: Interest \: = \: Amount \: - Principal}}$

So,

$\large\boxed{\tt{Amount \: = P \: \times (1 + \frac{R}{100} )^{n}}}$

As it is said compounded half-yearly and 1 year is given so the time(n) = 2

So rate will be 8/2 = 4%

According to the question,

$\large\Longrightarrow{\tt{Amount \: = 60000 \times (1 + \frac{4}{100} )^{2}}}$

$\large\Longrightarrow{\tt{Amount \: = \: 60000 \times (1 + \frac{1}{25} )^{2} }}$

$\large\Longrightarrow{\tt{Amount \: = \: 60000 \times (\frac{25+1}{25} )^{2} }}$

$\large\Longrightarrow{\tt{Amount \: = 60000 \times ( \frac{26}{25} )^{2} }}$

$\large\Longrightarrow{\tt{Amount \: = 60000\times \frac{26}{25} \times \frac{26}{25} }}$

$\large\purple\therefore\boxed{\tt{\purple{Amount \: = Rs. \:64896}}}$

Now,

$\large\Longrightarrow{\tt{Compound \: Interest \: = \: Amount \: - \: Pincipal}}$

$\large\Longrightarrow{\tt{Compound \: Interest \: = \: Rs.(64896- 60000)}}$

$\large\pink\therefore\boxed{\tt{\pink{Compound \: Interest \: = Rs. \: 4896}}}$