Question

Find the difference between compound interest and simple interest on Rs 25000 for 2 years at 8% p.a. compound annually.​

Answer 1

Given:-

• P = Rs. 25000
• R = 8% p.a.
• T = 2years.

To find:-

• Difference between CI and and SI.

Solution:-

1st case,

To find SI

We know,

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

=$\sf{SI = \dfrac{25000\times8\times2}{100}}$

=$\sf{SI = Rs. 4000}$

Now,

To find CI,

=$\sf{A = P{\bigg(1 + \dfrac{r}{100}\bigg)}^{t}}$

=$\sf{A = 25000{\bigg(1 + \dfrac{8}{100}\bigg)}^{2}}$

=$\sf{A = 25000{\bigg(\dfrac {100+8}{100}\bigg)}^{2}}$

=$\sf{A = 25000{\bigg(\dfrac {108}{100}\bigg)}^{2}}$

=$\sf{A = 25000 \times \dfrac {108}{100} \times \dfrac {108}{100}}$

=$\sf{A = Rs. 29160}$

=$\sf{CI = A - P}$

=$\sf{CI = 29160 - 25000}$

=$\sf{CI = Rs. 4160}$

Now,

Difference between CI and SI

=Rs.(4160 - 4000)

= Rs. 160.

From the Solution:-

P = Principal

R = Rate

T = Time

SI = Simple Interest

CI = Compound Interest

A = Amount

Answer 2

$\Huge\boxed {r.s=160}$

$\Large{\textsf{\textbf{\underline{\underline{Given\::}}}}}$

$p = rs.25000$

$r = 8\%p.a.$

$t = 2 \: years.$

$\Large{\textsf{\textbf{\underline{\underline{To.find\::}}}}}$

$●diffrence \: between \\ \: ci \: and \: si$

$\Large{\textsf{\textbf{\underline{\underline{formulas.used\::}}}}}$

$si = \frac{prt}{100}$

$A = p \: (1 + \frac{r}{100} )t$

$c.i = a-p$

$\Large{\textsf{\textbf{\underline{\underline{solusion\::}}}}}$

${\bf{1.case\::}}$

$➣to \: find \: s.i.$

$➣we \: know, \:$

$➣s.i. = \frac{p \times r \times t}{100}$

$➣s.i. = \frac{25000 \times 8 \times 2}{100}$

$\small{\textsf{\textbf{\underline{\underline{ ➣s.i = 4000\::}}}}}$

${\bf{2.case\::}}$

$➣to \: find \: ci,$

$➣we \: know, \:$

$➣A = p(1 + \frac{r}{100} )t$

$➣a = 25000(1 + \frac{8}{100} ) {}^{2}$

$➣a = 25000(100 + \frac{8}{100} ) {}^{2}$

$➣a = 25000( \frac{108}{100} ) {}^{2}$

$➣a = 25000 \times \frac{108}{100} \times \frac{108}{100}$

$\small{\textsf{\textbf{\underline{\underline{➣A = 29160\::}}}}}$

${\bf{3.case\::}}$

$➣to.find.c.i$

$➣we.know. c.i = A - p$

$➣c.i = Rs. 29160 - 25000$

$\small{\textsf{\textbf{\underline{\underline{➣c.i = 4160\::}}}}}$

$\small{\textsf{\textbf{\underline{\underline{now.finding.the.diffrence.between.ci.and.si\::}}}}}$

$➣c.i = 4160$

$➣s.i = 4000$

$➣difference = Rs. (4160 - 4000)$

$\Large{\textsf{\textbf{\underline{\underline{➣Rs. 160\::}}}}}$

$\Large{\textsf{\textbf{\underline{\underline{form.the.soluaion\::}}}}}$

$●p = principal \\ ●r = rate \: of \: interest \\ ●t = time \\ ●si = simple \: interest \\ ●ci = compound \: interest \\ ●a = amount$