Question

find the difference between the simple interest and the compound interest on rupees 5000 for 2 years at 9% per annum​

Answer 1

Step-by-step explanation:

Prncipal = Rs5000

Rate = 9%

Time = 2 years

Simple Interest =

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

$\implies \: \dfrac{5000 \times 9 \times 2}{100}$

$\huge{\boxed{\tt{Rs\: 900}}}$

Compound Interest =

$\sf \: Amount = P \: ( 1 + \dfrac{ r}{100})^{n}$

$\implies \sf \: 5000(1 + \dfrac{9}{100} ) ^{2}$

$\implies \sf \: \: 5000 \times (\dfrac{109}{100} ) ^{2}$

$\implies \: \sf \: 5940.5$

Compound Interest = Amount - Principal

Compound Interest = Rs5940.5 - Rs 5000

$\huge{\boxed{\tt{Rs\:940.5}}}$

Difference Between Them =

$\sf \: 940.5 - 900$

$\huge{\boxed{\tt{Rs\:40.5}}}$

Answer 2

$\bf \huge \underline { Answer:-}$

$\bf \LARGE \underline {Given:-}$

Principal(P) = 5000 Rs.

Time(T) = 2 years

Rate(R) = 9%

______________________________

$\bf \LARGE \underline {To \; Find:-}$

Difference between simple interest and compound interest.

______________________________

$\bf \LARGE \underline {Solution:-}$

We Know that,

$\mathbf{\boxed{\boxed{\LARGE{\sf{Simple \: interest = \frac{P{\times}R{\times}T}{100}}}}}}$

___________[Put Values]

» (5000 × 9 × 2)/100

» (10000 × 9)/100

» (90000)/100

» 900 Rupees

${\mathbf{\underline{\boxed{\LARGE{\sf{Simple\: interest = 900 \: Rupees }}}}}}$

_____________________

We know that,

$\boxed{ \blue{ \bf{amount = p {(1 + \frac{r}{100} )}^{n} }}}$

___________[Put Values]

${amount \: = 5000({1 + \frac{9}{100} )}^{2} } \\ \\ {amount = 5000 \times { (\frac{109}{100}) }}^{2} \\ \\ {amount = 5940.5 \: Rupees}$

Now, Compound interest = Amount - principal

» Compound interest = 5940.5 - 5000

» Compound interest = 940.5

______________________

${\mathbf{\boxed{\boxed{\red{Compound \:interest = 940.5 \: Rupees }}}}}$

Now, Difference = Compound interest - Simple interest

» 940.5 - 940

» 40.5 Rupees

${\mathbf{\boxed{\boxed{\red{Differnce = 40.5 \: Rupees}}}}}$