Question

Ravi borrowed ₹25000 at 15% per annum simple interest for 2 yrs. On the same day, Rakesh borrowed the same amount at the same rate for the same time period but compounded annually. Who pays more interest and by how much? ​ plz give step by step answer

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

$\begin{gathered}\tt Given \: that - \begin{cases} & \tt{ Principal\: = \bf{25000 \: Rupees}} \\ & \tt{Rate \: of \: interest \: = \bf{15 \: percent}} \\ & \tt{Time \: = \bf{2 \: year's}} \end{cases}\\ \\\end{gathered}$

${\large{\bold{\rm{\underline{Using \; concepts}}}}}$

$\tt \:  Formula \: to \: find \: Simple \: Interest \: and \: Compound \: interest$

${\large{\bold{\rm{\underline{Using \; formulas}}}}}$

${\tt{\star Simple \: interest \: = \: \dfrac{P \times R \times T}{100}}}⋆$

${\tt{\star \: Compound \: interest \: = P \bigg((1+ \dfrac{R}{100})^{n} - 1 \bigg)}}$

$\; \; \; \; \; \; \; \; \; \; \;{\tt{Where,}}$

⚪P denotes Principal

⚪R denotes Rate

⚪T denotes Time

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Let's use the formula to find Simple Interest and implied the values and let us evaluate Simple Interest !!.

${\tt{:\implies Simple \: interest \: = \: \dfrac{P \times R \times T}{100}}}$

${\tt{:\implies Simple \: interest \: = \: \dfrac{25000 \times 15 \times 2}{100}}}$

${\tt{:\implies Simple \: interest \: = \:Rs \: 7500}} - - (1)$

~ Now let's find the compound interest on the same amount at the same rate of interest for the same period by using formula to find Compound interest.

${\tt{ \: Compound \: interest \: = P \bigg((1+ \dfrac{R}{100})^{n} - 1 \bigg)}}$

${\tt{\: Compound \: interest \: = 25000 \bigg((1+ \dfrac{15}{100})^{2} - 1 \bigg)}}$

${\tt{\: Compound \: interest \: = 25000 \bigg((\dfrac{115}{100})^{2} - 1 \bigg)}}$

${\tt{\: Compound \: interest \: = 25000 \bigg( (\dfrac{23}{20})^{2} - 1 \bigg)}}$

${\tt{\: Compound \: interest \: = 25000 \bigg(\dfrac{529}{400} - 1 \bigg)}}$

${\tt{\: Compound \: interest \: = 25000 \bigg(\dfrac{529 - 400}{400} \bigg)}}$

${\tt{\: Compound \: interest \: = 25000 \bigg(\dfrac{129}{400} \bigg)}}$

${\tt{\: Compound \: interest \: = \: Rs \: 8062.50}} - - (2)$

$\tt \:  From \: (1) \: and \: (2), \: we \: conclude \: that$

$\tt \:  ⟼Compound \: interest \: > \: Simple \: interest$

$\bf\implies \:Rakesh \: paid \: more \: interest.$

$\tt \:Difference \: = Compound \: interest \: - \: Simple \: interest$

$\tt \:  ⟼ \: Difference = 8062.50 - 7500$

$\tt \:  ⟼ \: Difference \: = \: Rs \: 562.50$