Question

find the difference between the compound interest and simple interest on rupees 5000 for two years at 5% per annum.​

Answer 1

Question :

Find the difference between the compound interest and simple interest on Rs 5000 for two years at 5% per annum.

Solution :

$\underline{\bold {Given :}}$

• Principal = Rs 5000
• Rate = 5% p.a.
• Time = 2 years.

$\underline{\bold {To\:Find :}}$

• The difference between the compound interest and simple interest.

$\rule {193}{1}$

☆Simple Interest :

$\boxed{\purple{SI= \frac{P \times R \times T }{100}}}$

$\implies SI= \frac{P \times R \times T }{100} \\\\ \implies SI= Rs \: (\frac{5000 \times 5 \times 2 }{100} ) \\\\ \implies SI= Rs \:(50 \times 5 \times 2) \\\\ \implies SI=Rs \:500$

$\rule {193}{1}$

☆Compound Interest :

$\boxed {\purple{CI=P( {1 + \frac{R}{100} })^{T} - P}}$

$\implies CI=P( {1 + \frac{R}{100} })^{T} - 1\\\\ \implies CI=Rs \: 5000( {1 + \frac{5}{100} })^{2} - 1 \\\\\implies CI= Rs \: 5000 (1 + \frac{1}{20}) ^{2} - 1\\\\ \implies CI= Rs \: 5000 ( \frac{20 + 1}{20} )^{2} - 1 \\\\ \implies CI= Rs \:5000 \times \frac{21}{20} \times \frac{21}{20} - 1 \\\\ \implies CI = Rs \: 5512.50 - 1 \\\\ \implies CI = Rs \: 5511.50$

$\rule {193}{1}$

☆The difference between the compound interest and simple interest :

$\implies Difference =CI - SI \\\implies Difference = Rs \:( 5511.50 - 500) \\\implies Difference = Rs \: 5011.50$

$\boxed{\green{\therefore{The\: difference\: between\: the \:compound\: interest\: and\:simple\: interest \:is\:Rs \: 5011.50.}}}$

Answer 2

$<marquee>$ REFER TO ATTACHEMNT

HOPE ITS HELP U