Question

What is the difference between compound interest and simple interest for Rs. 73,450 at 11% p.a for 1 year

Answer 1

Given:

• Principal (P) = Rs 73450

• Rate (R) = 11% p.a

• Time (n years) = 1 year

To calculate:

• The difference between compound interest and simple interest for Rs. 73,450 at 11% p.a for 1 year.

Calculation:

~ Calculating Compound Interest :

In order to calculate CI, we have to calculate amount first.

$\sf {\longrightarrow Amount = {P \Bigg ( 1 + \dfrac{R}{100} \Bigg )}^{n} }$

Inserting values, we get :

$\sf {\longrightarrow Amount = {73450 \Bigg ( 1 + \dfrac{11}{100} \Bigg )}^{1} }$

$\sf {\longrightarrow Amount = {73450 \Bigg ( \dfrac{100 + 11}{100} \Bigg )}^{1} }$

$\sf {\longrightarrow Amount = {73450 \Bigg ( \dfrac{111}{100} \Bigg )}^{1} }$

$\sf {\longrightarrow Amount = 73450 \times \dfrac{111}{100} }$

$\sf {\longrightarrow Amount = 7345 \times \dfrac{111}{10} }$

$\sf {\longrightarrow Amount =Rs \: \dfrac{815295}{10} }$

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

$\sf { \longrightarrow CI = Rs \Bigg ( \dfrac{815295}{10} - 73450 \Bigg ) }$

$\sf { \longrightarrow CI = Rs \Bigg ( \dfrac{815295- 73450}{10} \Bigg ) }$

$\longrightarrow\underline{\boxed{\sf{ CI = Rs \: \dfrac{741845}{10} }}} \: \red{\bigstar}$

Calculating Simple Interest :

$\sf { \longrightarrow SI = \dfrac{P RT}{100} }$

$\sf { \longrightarrow SI = \dfrac{ 11 \times 73450 \times 1}{100} }$

$\sf { \longrightarrow SI = \dfrac{ 807950}{100} }$

$\longrightarrow \underline{\boxed{\sf{ SI = \dfrac{ 80795}{10} }}} \: \red{\bigstar}$

Calculating difference :

$\sf { \longrightarrow Difference = CI - SI }$

$\sf { \longrightarrow Difference = Rs \Bigg ( \dfrac{741845}{10} - \dfrac{80795}{10} \Bigg )}$

$\sf { \longrightarrow Difference = Rs \Bigg (\cancel{ \dfrac{660870}{10}} \Bigg )}$

$\longrightarrow\underline{\boxed{\sf{ Difference = Rs \: 66087}}} \: \red{\bigstar}$

Henceforth, the difference between compound interest and simple interest for Rs. 73,450 at 11% p.a for 1 year is Rs 66087.