Question

Difference of C. I. & S. I. on Rs.1000 at 10% p. a. for 2 years is Rs​

Answer 1

• Difference of C.I and S.I is Rs 10 .

Step-by-step explanation:

Given:-

• Principal is Rs 1000 .
• Rate of interest is 10% .
• Time period is 2 years.

To find:-

• Difference of C.I and S.I .[Compound interest and simple interest]

Solution:-

• For difference first we need to find C.I and S.I.

So,

$\boxed{\sf \bold{\star \: S.I = \dfrac{Principal \times Rate \times time} {100} }}$

Put the values in formula :

$\sf \longrightarrow S.I = \dfrac{10 \cancel{00} \times 10 \times 2}{1 \cancel{00}}$

$\sf \longrightarrow S.I = 100 \times 2$

$\longrightarrow \pink{ \boxed{ \sf \bold{S.I = 200}} \star}$

S.I is Rs 200

• Here, Work is going annually. We will use Compounded annually formula for Amount.

Now,

C.I = Amount - Principal

Or,

$\boxed{\sf \bold{\star \: C.I = \bigg[P \bigg( 1 + \dfrac{r}{100} \bigg) ^{n} \bigg] - P}}$

Where,

• n is time period, P is principal and r is rate of interest.

Put values in formula :

$\sf \longrightarrow C.I = \bigg[1000 \times \bigg(1 + \dfrac{10}{100} \bigg)^{2} \bigg ] - 1000$

$\sf \longrightarrow C.I = \bigg[ 1000 \times \bigg( \dfrac{100 + 10}{100} \bigg)^{2} \bigg ] - 1000$

$\sf \longrightarrow C.I = \bigg[ 1000 \times \bigg( \dfrac{110}{100} \bigg) ^{2} \bigg ] - 1000$

$\sf \longrightarrow C.I = \bigg[10 \cancel{00 }\times \dfrac{110}{1 \cancel{00}} \times \dfrac{110}{100} \bigg] - 1000$

$\sf \longrightarrow C.I = \bigg[ \cancel{ \dfrac{12100}{100} } \bigg] - 1000$

$\sf \longrightarrow C.I = 1210 - 1000$

$\longrightarrow \purple{ \boxed{ \sf \bold{C.I =210}} \star}$

C.I is Rs 210 .

★ Difference = C.I - S.I

$\sf \longrightarrow 210 - 200$

$\longrightarrow \red{\boxed{\sf \bold{10}}\bigstar}$

Therefore,

Difference of C.I and S.I is Rs 10.

Answer 2

Answer:

Given :-

• Principal is Rs 1000 .
• Rate of interest is 10% .
• Time period is 2 years.

To Find :-

Difference between CI and SI

Solution :-

As we know that

$\boxed { \bf \: simple \: intrest \: = \frac{p \times \: r \: \times t }{100} }$

$\sf \: simple \: intrest \: = \dfrac{1000 \times 10 \times 2}{100}$

$\sf \: simple \: intrest \: = \dfrac{20000}{100}$

$\sf \: simple \: intrest \: = \cancel \dfrac{20000}{100}$

$\sf \: simple \: intrest \: = 200$

$\huge \sf \: C.I=[P(1+ \frac{r}{100} ) {}^{2} ]−P$

$\sf \: CI = [1000(1 + \dfrac{10}{100}) {}^{2}] - 1000$

$\sf \: CI \: = [1000( \frac{100 + 10}{100}) {}^{2} -] 1000$

$\sf \: CI \: = [ 1000 \times ( \frac{110}{100} ) {}^{2} ] - 1000$

$\sf \: CI \: = [1000 \times \dfrac{110}{100} \times \dfrac{110}{100} ] - 1000$

$\sf \: CI \: = \cancel\dfrac{12100}{100} - 1000$

$\sf \: CI = 1210 - 1000$

$\sf \: CI = 210$

Now,

Finding Difference

$\sf \: Difference \: = 210 - 200$

$\sf \: Difference = 10$