Example 4.18 Find the difference in C.I and S.I for (i) P= 5000, r = 4% p.a, n = 2 years. (ii) P = 48000, r = 5% p.a, n = 3 years.
Answers
S.I -400,C.I -416
Step-by-step explanation:
SORRY,I CANT PROVIDE THE SOLUTION STEP,BUT THIS IS RHE ANSWER
Answer:
❏ 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}}⟶\boxefldS.I.=
100
p×r×t
AND
Compound interest Interest is given by,
\sf \longrightarrow\boxed{C.I.= p[(1+\frac{r}{100}){}^{nt}-1]}⟶
C.I.=p[(1+
100
r
)
nt
−1]
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❚ Let's Solve The Problem ❚
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❏ Solution
\begin{gathered}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} \end{gathered}
Given
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</p><p></p><p>principal(p)=5000Rs
</p><p>Interestrate(r)=4%</p><p>
</p><p>time(t)=2Years
</p><p>No.ofcycle(n)=1(∵compoundedyearly)</p><p></p><p>
\therefore S.I.= \frac{50\cancel{00}\times 4\times 2}{1\cancel{00}}∴S.I.=
1
00
50
00
×4×2
\longrightarrow S.I.=( 50\times 4\times 2)⟶S.I.=(50×4×2)
\longrightarrow\boxed{ S.I.=400\:Rs}⟶
S.I.=400Rs
And
\sf \therefore C.I.= 5000\times[(1+\frac{4}{100}){}^{1\times2}-1]∴C.I.=5000×[(1+
100
4
)
1×2
−1]
\sf \therefore C.I.= 5000\times[(\frac{104}{100}){}^{1\times2}-1]∴C.I.=5000×[(
100
104
)
1×2
−1]
\sf \therefore C.I.= 5000\times[(\frac{104}{100}+1)(\frac{104}{100}-1)]∴C.I.=5000×[(
100
104
+1)(
100
104
−1)]
\sf \therefore C.I.= 5000\times(\frac{104+100}{100})\times(\frac{104-100}{100})]∴C.I.=5000×(
100
104+100
)×(
100
104−100
)]
\sf \therefore C.I.= \cancel5\cancel{000}\times(\frac{\cancel4\times204}{\cancel{10}\cancel{000}})∴C.I.=
5
000
×(
10
000
4
×204
)
\sf \therefore C.I.= 2\times204∴C.I.=2×204
\sf \therefore\boxed{ C.I.= 416\:Rs}∴
C.I.=416Rs
\sf \therefore Difference\: between \:S.I.\: And \:C.I\:is=C.I.-S.I.∴DifferencebetweenS.I.AndC.Iis=C.I.−S.I.
\sf \longrightarrow C.I.-S.I.=(416-400)\:Rs⟶C.I.−S.I.=(416−400)Rs
\sf \longrightarrow \boxed{C.I.-S.I.=16\:Rs}⟶
C.I.−S.I.=16Rs
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\underline{ \huge\mathfrak{hope \: this \: helps \: you}}
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