Question

what is the deference between simple interest and compound interest for 2 years at the rate of 5% on Rs. 1000 ?​

Answer 1

Step-by-step explanation:

simple interest = pnr/100

= 1000x2x5/100

= 10x2x5

= 100/-

total amount = 1000+100

= 1100/-

compound interest = p(1+r/100)^n

= 1000( 1+ 5/100)^2

= 1000( 105/100)^2

= 1000 x 105/100 x 105/100

= 105 x 105/10

= 21 x 105 /2

= 2115/2

= 1057.5/-

total amount = 1000+1057.5

= 2057.5/-

difference between simple interest and compound interest,

2057.5 - 1000 = 1057.5/-

hope this answer will help you

Answer 2

Answer :-

• The difference is Rs 2.5

Given :-

• Principal = Rs 1000.
• Rate = 5%.
• Time = 2 years.

To find :-

• The difference between simple interest and compound interest for 2 years at the rate of 5% on Rs 1000.

Step-by-step explanation :-

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

Before finding their difference, we have to find the simple interest and compound interest!

$\underline{\boxed{\sf To\: find \:the \:simple \:interest :-}}$

Let's find the simple interest first!

We know that :-

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

Here,

• Principal = Rs 1000.
• Rate = 5%.
• Time = 2 years.

Hence,

$\tt SI = \dfrac{1000 \times 5\times2}{100}$

Cutting off the zeroes,

$\tt SI =\dfrac{10\times5\times2}{1}$

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

$\tt SI = 10 \times 5 \times 2$

Multiplying the numbers,

$\overline{\boxed{\tt SI = Rs \: 100.}}$

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

$\underline{\boxed{\sf To\: find \:the\: compound\: interest :-}}$

Let's find the compound interest now!

To find the compound interest, we first have to find the amount.

We know that :-

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

Here,

• Principal = Rs 1000.
• Rate = 5%
• Time = 2 years.

Hence,

$\rm Amount = 1000 \Bigg(1 + \dfrac{5}{100} \Bigg)^2$

Making 1 a fraction by taking 1 as the denominator,

$\rm Amount = 1000 \Bigg(\dfrac{1}{1} + \dfrac{5}{100} \Bigg)^2$

LCM of 1 and 100 is 100, so adding the fractions using their denominators,

$\rm Amount = 1000 \Bigg(\dfrac{1 \times 100 + 5 \times 1}{100} \Bigg)^2$

On simplifying,

$\rm Amount = 1000 \Bigg( \dfrac{100+5}{100} \Bigg)^2$

Adding 5 to 100,

$\rm Amount = 1000 \Bigg(\dfrac{105}{100} \Bigg)^2$

The power here is 2, so removing the brackets and multiplying 105/100 with itself 2 times,

$\rm Amount = 1000 \times \dfrac{105}{100} \times \dfrac{105}{100}$

Let's multiply 105/100 with 105/100 first.

$\rm Amount =1000\times \dfrac{105\times105}{100\times100}$

On multiplying,

$\rm Amount = 1000 \times \dfrac{11025}{10000}$

Cutting off the zeroes,

$\rm Amount = 1\times \dfrac{11025}{10}$

Multiplying 1 with 11025/10,

$\rm Amount = \dfrac{11025}{10}$

Reducing the numbers,

$\rm Amount = \dfrac{2205}{2}$

Dividing 2205 by 2,

$\overline{\boxed{\rm Amount = Rs \: 1102.5}}$

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

Now, we know that :-

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

Here,

• Amount = Rs 1102.5
• Principal = Rs 1000.

Hence,

$\tt CI = 1102.5 - 1000$

$\overline{\boxed{\tt CI = Rs \: 102.5}}$

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

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

Here,

• Simple Interest = Rs 100.
• Compound Interest = Rs 102.5

Hence,

$\bf Difference = 102.5 - 100$

$\overline{\boxed{\bf Difference = Rs \: 2.5}}$

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

• Hence, the difference is Rs 2.5

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Abbreviations used :-

SI = Simple Interest.

CI = Compound Interest.