Question

6. Find the difference between the simple interest
(S.I.) and compound interest (C.I.) on 5,000 at
4% p.a. for 3 years​

Answer 1

★GIVEN★

• Principal = Rs. 5,000
• Rate = 4% per annum
• Time = 3 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. 5,000
• R is rate per annum = 4%
• T is no of years or time = 3 years

Putting the values,

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

$\large\implies{\sf{SI=\dfrac{5000\times4\times3}{100}}}$

$\large\implies{\sf{SI=\dfrac{50\:\cancel{00}\times4\times3}{1\:\cancel{00}}}}$

$\large\implies{\sf{SI=50\times4\times3}}$

$\large\therefore\boxed{\sf{\blue{Simple\:Interest=Rs.\:600}}}$

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

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. 5,000
• n = 3
• R = 4%
• A is amount

Putting the values,

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

$\large\implies{\sf{A=5000(1+{\dfrac{4}{100}})^{3}}}$

$\large\implies{\sf{A=5000(1+{\dfrac{\cancel{4}}{\cancel{100}}})^{3}}}$

$\large\implies{\sf{A=5000(1+{\dfrac{1}{25}})^{3}}}$

$\large\implies{\sf{A=5000({\dfrac{25+1}{25}})^{3}}}$

$\large\implies{\sf{A=5000({\dfrac{26}{25}})^{3}}}$

$\large\implies{\sf{A=5000(\dfrac{26}{25}\times\dfrac{26}{25}\times\dfrac{26}{25})}}$

$\large\implies{\sf{A=5000\times\dfrac{17576}{15625}}}$

$\large\implies{\sf{A=Rs.5624.32}}$

$\large\therefore\boxed{\sf{A=Rs.\:5624.32}}$

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

$\large\implies{\sf{CI=Rs.\:(5624.32-5000)}}$

$\large\therefore\boxed{\sf{\blue{Compound\:Interest=Rs.\:624.32}}}$

Difference between them,

CI - SI = ₹(624.32-600)

= ₹ 24.32

$\large{\blue{\underline{\boxed{\sf{Differnce\:between\:SI\:and\:CI=Rs.\:24.32.}}}}}$