Question

9. Find the difference between compound
interest and simple interest on * 12,000 and
1
in 1 years at 10% p.a. compounded yearly
.
2​

Answer 1

Answer:

this is The Solution For The sum

Answer 2

Answer :-

• The difference between the compound interest and simple interest on Rs 12000 in 1 year at 10% p.a. compounded annually is Rs 0, which means that there is no difference between them.

To find :-

• The difference between compound interest and simple interest on Rs 12000 in 1 year at 10% p.a. compounded yearly.

Step-by-step explanation :-

• Here the principal, rate and time have been given to us. We have to find the difference between simple and compound interest.

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

Let's find the simple interest first!

We know that :-

$\underline{\boxed{\sf SI = \dfrac{Principal \times Rate \times Time}{100}}}$

Here,

• Principal = Rs 12000.
• Rate = 10% p.a. compounded annually.
• Time = 1 year.

$\underline{\underline{\mathfrak{Substituting\: the \:given \:values,}}}$

$\tt SI = \dfrac{12000 \times 10 \times 1}{100}$

Cutting off the zeroes,

$\tt SI = \dfrac{120 \times 10 \times 1}{1}$

Now let's multiply the remaining numbers.

$\tt SI = 120 \times 10 \times 1$

Multiplying the numbers,

$\overline{\boxed{\tt SI = Rs \: 1200}}$

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

Now 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 12000.
• Rate = 10% p.a. compounded annually.
• Time = 1 year.

$\underline{\underline{\mathfrak{Substituting\: the \:given \:values,}}}$

$\rm Amount = 12000 \Bigg(1 + \dfrac{10}{100} \Bigg)^{1}$

Reducing 10/100 to it's simplest form,

$\rm Amount = 12000 \Bigg(1 + \dfrac{1}{10} \Bigg)^{1}$

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

$\rm Amount = 12000 \Bigg(\dfrac{1 \times 10 + 1 \times 1}{10} \Bigg)^{1}$

On simplifying,

$\rm Amount = 12000 \Bigg(\dfrac{10 + 1}{10} \Bigg)^1$

Adding 1 to 10,

$\rm Amount = 12000 \Bigg(\dfrac{11}{10} \Bigg)^1$

The power here is 1, so it won't have any effect on our calculations, therefore removing the brackets,

$\rm Amount = 12000 \times \dfrac{11}{10}$

Cutting off the zeroes,

$\rm Amount = 1200 \times \dfrac{11}{1}$

Now let's multiply the remaining numbers.

$\rm Amount = 1200 \times 11$

Multiplying the numbers,

$\overline{\boxed{\rm Amount = Rs \: 13200}}$

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

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

We know that :-

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

Here,

• Amount = Rs 13200.
• Principal = Rs 12000.

Hence,

$\bf CI = 13200 - 12000$

$\bf CI = Rs \: 1200$

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

Finally let's find the difference between the simple interest and compound interest.

Here,

• Simple interest = Rs 1200.
• Compound interest = Rs 1200.

Hence,

$\bf Difference=1200-1200$

$\bf Difference = Rs \: 0$

__________________________

• Therefore, there is no difference between the simple interest and compound interest here.