Question

Compare compound interest (C.I.) and simple interest(S.I.), if Bhavesh borrows a sum of Rs.3000 from a bank at 4%p.a. for 1 year. ​

Answer 1

$\bf \pink {Answer}$

★GIVEN★

• Principal = Rs. 3000
• Rate = 4% per annum
• Time = 1 years

★TO FIND★

The difference between the simple interest

(S.I.) and compound interest (C.I.).

★SOLUTION ★

$\large{\blue{\underline{\underline{\sf{1)\:Simple\:Interest\:(S.I.)\::-}}}}}$

Formula,

$\large{\blue{\underline{\boxed{\bf{SI=\dfrac{P\times\:R\times\:T}{100}}}}}}$

where,

• P is principal = Rs. 3000
• R is rate per annum = 4%
• T is no of years or time = 1 year.

Putting the values,

$\implies{\sf{SI=\dfrac{P\times\:R\times\:T}{100}}}$

$\implies{\sf{SI=\dfrac{3000\times4\times1}{100}}}$

$\implies{\sf{SI=\dfrac{30\:\cancel{00}\times4\times1}{1\:\cancel{00}}}}$

$\large\implies{\sf{SI=30\times4\times1}}$

$\large\therefore\boxed{\sf{\blue{Simple\:Interest=Rs.\:120}}}$

$\large{\blue{\underline{\underline{\sf{2)\:Compound\:Interest\:(C.I.)\::-}}}}}$

Formula,

$\large{\blue{\underline{\boxed{\bf{CI=\huge[\large\:P\huge(\large1+{\dfrac{R}{100}}\huge)\large^{n}\huge]-P}}}}}$

where,

P is Principal = Rs. 3000

n = 1

R = 4%

A is amount

Putting the values,

$\large\implies{\sf{A=P(1+{\dfrac{R}{100}})^{n}}}$

$\large\implies{\sf{A=3000(1+{\dfrac{1}{100}})^{3}}}$

$\large\implies{\sf{A=3000(1+{\dfrac{{1}}{{100}}})^{3}}}$

$\large\implies{\sf{A=3000(1+{\dfrac{1}{100}})^{3}}}$

$\large\implies{\sf{A=3000({\dfrac{100+1}{100}})^{3}}}$

$\large\implies{\sf{A=3000({\dfrac{101}{100}})^{3}}}$

$\large{\sf{A=3000(\dfrac{101}{100}\times\dfrac{101}{100}\times\dfrac{101}{100})}}$

$\large\implies{\sf{A=3000\times\dfrac{1030301}{1000000}}}$

$\large\implies{\sf{A = 3000 \times 1.030301}}$

$\large\implies{\sf{A = Rs.3090.903 }}$

$\large\therefore\boxed{\sf{A=Rs.\:3,090.903}}$

$\large\boxed{\bf{CI=Amount-Principal}}$

$\large{\sf{cp - sp=Rs.\:(3,090.903 - 120)}}$

Difference between them,

CI - SI = ₹(3090.903-120)

= ₹ 2,970.903

$\large{\blue{\underline{\boxed{\sf{Differnce\:etween\:SI\:and\:CI=Rs.\:2,970.903}}}}}$

$\bf \orange{hope \: it's \: helps \: you }$