Question

find the difference in C.I and S.I for p=r.5000, r= 4% p.a,n= 2 years
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Answer 1

❏ Using ForMuLaS

If amount of money=p

interest rate(per annum)=r%

time=t .

Number of cycles in a year=n

then ,The simple interest is given by,

$\longrightarrow\boxefld{S.I.= \frac{p\times r\times t}{100}}$

AND

Compound interest Interest is given by,

$\sf \longrightarrow\boxed{C.I.= p[(1+\frac{r}{100}){}^{nt}-1]}$

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❚ Let's Solve The Problem ❚

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❏ Solution

$Given \begin{cases}</p><p></p><p>principal(p)=5000\:Rs\\</p><p>Interest\:rate(r)=4\:\%</p><p> \\ </p><p>time(t)=2 \:Years\\</p><p>No. of cycle (n)=1 (\because compounded\: yearly)</p><p></p><p>\end{cases}$

$\therefore S.I.= \frac{50\cancel{00}\times 4\times 2}{1\cancel{00}}$

$\longrightarrow S.I.=( 50\times 4\times 2)$

$\longrightarrow\boxed{ S.I.=400\:Rs}$

And

$\sf \therefore C.I.= 5000\times[(1+\frac{4}{100}){}^{1\times2}-1]$

$\sf \therefore C.I.= 5000\times[(\frac{104}{100}){}^{1\times2}-1]$

$\sf \therefore C.I.= 5000\times[(\frac{104}{100}+1)(\frac{104}{100}-1)]$

$\sf \therefore C.I.= 5000\times(\frac{104+100}{100})\times(\frac{104-100}{100})]$

$\sf \therefore C.I.= \cancel5\cancel{000}\times(\frac{\cancel4\times204}{\cancel{10}\cancel{000}})$

$\sf \therefore C.I.= 2\times204$

$\sf \therefore\boxed{ C.I.= 416\:Rs}$

$\sf \therefore Difference\: between \:S.I.\: And \:C.I\:is=C.I.-S.I.$

$\sf \longrightarrow C.I.-S.I.=(416-400)\:Rs$

$\sf \longrightarrow \boxed{C.I.-S.I.=16\:Rs}$

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

#answerwithquality & #BAL

Answer 2

The answer is zero.

GIVEN

Principal amount = Rs 5000

Rate of interest = 4%

Period = 2 years

TO FIND

Difference in compound interest and simple interest.

SOLUTION

We can simply solve the above problem as follows;

The formula to calculate Simple Interest (S.I) is as follows;

SI = (PRT)/100

Putting the values in the above formula we get,

SI = (5000 × 4 × 2)/100

SI = Rs 400

The formula to calculate compound interest is as follows;

C.I = P(1+r/100)ᵗ - P

= 5000 ( 1 + 4/100)² - 5000

= 5000(1.04)² - 5000

= 5000 × 1.08 - 5000

= 5400 - 5000

= Rs 400

Difference between SI and CI = 400 - 400 = 0

Hence, The answer is zero.

#SPJ2