Question

The difference between the simple interest and the compound interest compounded annually at the rate of 12% per annum on Rs. 5,000 for two years will be ​

Answer 1

Answer:

The Difference between the CI and SI is Rs. 72

Step-by-step explanation:

Given :

Rate = 12%

Principal = Rs. 5,000

Time = 2 years

To find :

The Difference between the SI and CI

Solution :

✯ $\textsf{\underline{\underline{Simple Interest -}}}$

• P = 5,000
• R = 12 %
• T = 2 years

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

$\sf{\longrightarrow} \: SI = \dfrac{5000 \times 12 \times 2}{100} \\ \\ \sf{\longrightarrow} \: SI = \dfrac{50 \times 12 \times 2}{1} \\ \\ \sf{\longrightarrow} \: SI =600 \times 2 \\ \\ \sf{\longrightarrow} \: SI =1200$

Simple Interest = Rs. 1,200

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Compound Interest - }}}$

$\boxed{\sf{CI= \left[P\left( 1 + \frac{R}{100}\right)^{N}}\right]- P}}$

$\sf{\longrightarrow} \: CI = 5000 \: \left( 1 + \dfrac{12}{100} \right)^{2} - 5000 \\ \\ \sf{\longrightarrow} \: CI = 5000 \times \dfrac{112}{100} \times \dfrac{112}{100} - 5000 \\ \\ \sf{\longrightarrow} \: CI = 5 \times 112 \times \dfrac{112}{10} - 5000 \\ \\ \sf{\longrightarrow} \: CI = 112 \times 56 - 5000 \\ \\ \sf{\longrightarrow} \: CI = 6272 - 5000 \\ \\ \sf{\longrightarrow} \: CI = 1272$

Compound Interest = Rs. 1272

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Difference between SI and CI -}}}$

• SI = 1200
• CI = 1272

$\sf{\longrightarrow} \: 1272 - 1200 \\ \\ \sf{\longrightarrow} \: 72$

Difference = Rs. 72

$\therefore$ The Difference between the CI and SI is Rs. 72.

Answer 2

AnswEr :

Difference = Rs.72

$\bf{\large{\underline{\underline{\bf{Given\::}}}}}}}$

Simple Interest and the compound Interest compounded annually at the rate of 12% per annum on Rs.5000 for 2 years.

$\bf{\large{\underline{\underline{\bf{To\:find\::}}}}}}}$

The difference.

$\bf{\Large{\underline{\underline{\tt{\red{Explanation\::}}}}}}$

$\bf{\Large{\underline{\bigstar{\sf{SIMPLE\:INTEREST\:(S.I)\::}}}}}}}$

We have;

• Principal = Rs.5000
• Rate = 12%
• Time = 2 years

Formula use :

$\bf{\large{\boxed{\rm{S.I.=\frac{P*R*T}{100}}}}}}$

$\dashrightarrow\tt{S.I.\:=\:\dfrac{50\cancel{00}*12*2}{\cancel{100}} }\\\\\\\\\dashrightarrow\tt{S.I.\:=\:Rs.(50*12*2)}\\\\\\\\\dashrightarrow\tt{\orange{S.I.\:=\:Rs.1200}}$

$\bf{\Large{\underline{\bigstar{\sf{COMPOUND\:INTEREST\:(C.I)\::}}}}}}}$

We have;

• Principal = Rs.5000
• Rate = 12%
• Time = 2 years

Formula use :

$\bf{\large{\boxed{\sf{C.I.\:=\:P\bigg(1+\frac{R}{100}\bigg )^{n} -P}}}}}$

$\dashrightarrow\tt{C.I.=5000\bigg(1+\dfrac{\cancel{12}}{\cancel{100}} \bigg)^{2} -5000}\\\\\\\\\dashrightarrow\tt{C.I.=5000\bigg(1+\dfrac{3}{25} \bigg)^{2}-5000} \\\\\\\\\dashrightarrow\tt{C.I.=5000\bigg(\dfrac{25+3}{25} \bigg)^{2} -5000}\\\\\\\\\dashrightarrow\tt{C.I.=5000\bigg(\frac{28}{25} \bigg)^{2} -5000}\\\\\\\\\dashrightarrow\tt{C.I.=\cancel{5000}*\dfrac{28}{\cancel{25}} *\dfrac{28}{\cancel{25}} -5000}\\\\\\\\\dashrightarrow\tt{C.I.=Rs.(8*28*28)-5000}$

$\dashrightarrow\tt{C.I.=Rs.(6272-5000)}\\\\\\\\\dashrightarrow\tt{\orange{C.I.=Rs.1272}}$

Now,

$\bigstar$Difference Between S.I. & C.I.

$\longrightarrow\sf{C.I.\:-\:S.I.}\\\\\\\longrightarrow\sf{Rs.(1272-1200)}\\\\\\\longrightarrow\sf{\red{Rs.72}}$

_________________________________________

$\bigstar$Tricks for difference S.I. and C.I.

$\dashrightarrow\tt{Difference=P\bigg(\dfrac{R}{100} \bigg)^{2} }\\\\\\\dashrightarrow\tt{Difference=5000\bigg(\dfrac{12}{100} \bigg)^{2} }\\\\\\\dashrightarrow\tt{Diffference=5\cancel{000}*\dfrac{12}{\cancel{100}} *\dfrac{12}{10\cancel{0}} }\\\\\\\dashrightarrow\tt{Difference=\dfrac{5*12*12}{10} }\\\\\\\dashrightarrow\tt{Difference=Rs.(5*1.2*12)}\\\\\\\dashrightarrow\tt{\red{Difference=Rs.72}}$

∴ The difference between S.I. and C.I. is Rs.72.