Question

Find the difference between compound interest and simple interest on rs12000 in 1×1/2 years at 10% compounded half yearly​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Difference=91.5\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies Principal(p) = 12000\:rupees \\ \\ \tt: \implies Time(t) = \frac{3}{2} \: year \\ \\ \tt: \implies Rate\%(r) = 10\% \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies C.I- S.I=?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies S.I= \frac{p \times r \times t}{100} \\ \\ \tt: \implies S.I= \frac{12000 \times 10 \times 3}{2 \times 100} \\ \\ \tt: \implies S.I = 120 \times 15\\ \\ \green{\tt: \implies S.I = 1800 \: rupees} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies A= p(1 + \frac{ \frac{r}{2} }{100} ) ^{2t} \\ \\ \tt: \implies A = 12000 \times (1 + \frac{10}{2 \times 100} )^{3} \\ \\ \tt: \implies A= 125000 \times (1 + 0.05)^{3} \\ \\ \tt: \implies A = 12000 \times (1.05)^{3} \\ \\ \tt: \implies A= 12000 \times 1.157625 \\ \\ \green{\tt: \implies A= 13891.5\: rupees} \\ \\ \bold{For \: compound \: interest : }\\ \tt: \implies C.I= A - p \\ \\ \tt: \implies C.I= 13891.5 - 12000\\ \\ \green{\tt: \implies C.I= 1891.5 \: rupees} \\ \\ \bold{For \: Difference : } \\ \tt: \implies Difference= C.I - S.I\\ \\ \tt: \implies Difference = 1891.5 - 1800 \\ \\ \green{\tt: \implies Difference= 91.5 \: rupees}$

Answer 2

Aɴꜱᴡᴇʀ

➜ $\large \tt{} \purple{C.I-S.I = 91.5 \: rupees}$

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Gɪᴠᴇɴ

✭ Principal (p) = 12000

✭ Time (t) = $\tt1\frac{3}{2}$ years

✭ Rate (r) = 4%

__________________

ᴛᴏ ꜰɪɴᴅ

☞ The difference between the simple interest and the compound interest.

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Sᴛᴇᴘꜱ

❍ First let's find the value of simple interest. And it is given by,

$\large \tt{}S.I = \frac{p \times r \times t}{100}$

Substituting our given values,

$\large \tt \leadsto{}S.I = \frac{12000 \times 10\times 3}{100 \times 2} \\ \\ \large \tt \leadsto{}S.I = \cancel\frac{360000}{200} \\ \\ \large\tt \leadsto{ \pink{1800\: rupees}}$

➤ So next let's find the value of A. And its given by,

$\large \tt{}A = p(1 + \frac{ \frac{r}{2} }{100} {)}^{2t}$

➤ Substituting the given values,

$\dashrightarrow \large \tt{}A = 12000(1 + \frac{ \frac{10}{2} }{100} {)}^{2( \frac{3}{2} )} \\ \\ \tt \large \dashrightarrow12000(1 + 0.05 {)}^{3} \\ \\ \tt \large \dashrightarrow12000 \times 1.157625 \\ \\ \tt \large \dashrightarrow{ \red{A = 13891 .5\: rupees}}$

➤ So now we can find the compound interest with the use of A-p

$\large \tt{} \longrightarrow{}C.I = 13891.5 - 12000\\ \\ \tt \large \longrightarrow{} \pink{C.I =1891.5 \: rupees}$

➤ Now we can find their difference by,

$\large \tt \hookrightarrow C.I-S.I = 1891.5- 1800 \\ \\ \large \tt \orange{\hookrightarrow{}C.I-S.I =91.5 \: rupees}$

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