Question

Find the compound interest for 3 years on ₹4000 at 10% per annum, if the interest is compounded yearly.
​

Answer 1

Correct option is

C

Rs 961

Principal (P)=Rs.4000

Rate of Interest (r)=10%

Time =2 years and 3 months

Here first we take n=2 years.

⇒ Amount for first 2 years (A)=P(1+

100

r )

n

=4000(1+

100

10

)

2

=4000(

10

11

)

2

=4000×

100

121

=Rs.4840

⇒ The amount after two years =Rs.4840

⇒ Now, Principal =Rs.4840

Simple interest for last 3 months i.e.

4

1

years =

100

PRT

=

100×4

4840×10×1

=Rs.121

⇒ Amount after 2 years and 3 months =Rs.4840+Rs.121=Rs.4961

⇒ C.I.=A−P

=Rs.4961−Rs.4000

=Rs.961

∴ The compound interest is Rs.961

Answer 2

Answer :-

• The compound interest is Rs 1324.

Given :-

• Principal = Rs 4000.
• Rate = 10% per annum.
• Time = 3 years.

To find :-

• The compound interest.

Step-by-step explanation :-

• Before finding the compound interest, let's find the amount!

We know that :-

$\underline{ \boxed{\sf Amount = Principal\Bigg(1 + \dfrac{Rate}{100} \Bigg)^{Time}}}$

Here,

• Principal = Rs 4000.
• Rate = 10% per annum.
• Time = 3 years.

Hence,

$\rm Amount =4000 \bigg(1 + \dfrac{10}{100} \bigg)^{3}$

Converting 10/100 into it's simplest form,

$\rm Amount =4000 \bigg(1 + \dfrac{1}{10} \bigg)^{3}$

The LCM of 1 and 10 is 10, so adding the fractions using their denominators,

$\rm Amount =4000 \bigg( \dfrac{1 \times 10 +1 \times 1}{10} \bigg)^{3}$

On simplifying,

$\rm Amount =4000 \bigg( \dfrac{10 + 1}{10} \bigg) ^{3}$

Adding 1 to 10,

$\rm Amount =4000 \bigg( \dfrac{11}{10} \bigg)^{3}$

Here, the power is 3, so removing the brackets and multiplying 11/100 with itself 3 times,

$\rm Amount =4000 \times \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10}$

Let's multiply 11/10 with itself 3 times first.

$\rm Amount =4000 \times \dfrac{11 \times 11 \times 11}{10 \times 10 \times 10}$

On multiplying,

$\rm Amount =4000 \times \dfrac{1331}{1000}$

Cutting off the zeroes,

$\rm Amount =4 \times \dfrac{1331}{1}$

Now let's multiply the remaining numbers since we can't reduce them anymore.

$\rm Amount =4 \times 1331$

Multiplying the numbers,

$\overline{ \boxed{ \rm Amount= Rs \: 5324}}$

• Now as we know the amount, let's find the compound interest!

We know that :-

$\underline{ \boxed{ \sf CI = Amount - Principal}}$

Here,

• Amount = Rs 5324.
• Principal = Rs 4000.

Hence,

$\boxed{ \bf CI = 5324 - 4000}$

Subtracting 4000 from 5324

$\overline{\boxed{ \bf CI = Rs \: 1324}}$

----------------

• Hence, the compound interest is Rs 1324.