Question

Find the difference between simple interest and compound interest on rupees 125000 for 3/2 year at 4% per annum compound interest revoked semi yearly

Answer 1

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

$\green{\tt{\therefore{Difference=151\:rupees}}}$

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

$\green{\underline \bold{Given: }} \\ \tt: \implies Principal(p) = 125000\:rupees \\ \\ \tt: \implies Time(t) = \frac{3}{2} \: year \\ \\ \tt: \implies Rate\%(r) = 4\% \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies C.I- S.I=?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies S.I= \frac{p \times r \times t}{100} \\ \\ \tt: \implies S.I= \frac{125000 \times 4 \times 3}{2 \times 100} \\ \\ \tt: \implies S.I = 1250 \times 6 \\ \\ \green{\tt: \implies S.I = 7500 \: rupees} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies A= p(1 + \frac{ \frac{r}{2} }{100} ) ^{2t} \\ \\ \tt: \implies A = 125000 \times (1 + \frac{4}{2 \times 100} )^{3} \\ \\ \tt: \implies A= 125000 \times (1 + 0.02)^{3} \\ \\ \tt: \implies A = 125000 \times (1.02)^{3} \\ \\ \tt: \implies A= 125000 \times 1.061208 \\ \\ \green{\tt: \implies A= 132651 \: rupees} \\ \\ \bold{For \: compound \: interest : }\\ \tt: \implies C.I= A - p \\ \\ \tt: \implies C.I= 132651 - 125000 \\ \\ \green{\tt: \implies C.I= 7651 \: rupees} \\ \\ \bold{For \: Difference : } \\ \tt: \implies Difference= C.I - S.I\\ \\ \tt: \implies Difference = 7651 - 7500 \\ \\ \green{\tt: \implies Difference= 151 \: rupees}$

Answer 2

Aɴꜱᴡᴇʀ

➜ $\large \tt{} \purple{C.I-S.I = 151 \: rupees}$

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Gɪᴠᴇɴ

✭ Principal (p) = 125000

✭ Time (t) = $\tt\frac{3}{2}$ years

✭ Rate (r) = 4%

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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,

$\large \tt \leadsto{}S.I = \frac{125000 \times 4 \times 3}{100 \times 2} \\ \\ \large \tt \leadsto{}S.I = \cancel\frac{1500000}{200} \\ \\ \large\tt \leadsto{ \pink{7500 \: rupees}}$

➤ 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,

$\dashrightarrow \large \tt{}A = 125000(1 + \frac{ \frac{4}{2} }{100} {)}^{2( \frac{3}{2} )} \\ \\ \tt \large \dashrightarrow125000(1 + 0.02 {)}^{3} \\ \\ \tt \large \dashrightarrow125000(1.02 {)}^{3} \\ \\ \tt \large \dashrightarrow125000 \times 1.061208 \\ \\ \tt \large \dashrightarrow{ \red{A = 132651 \: rupees}}$

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

$\large \tt{} \longrightarrow{}C.I = 132651 - 125000 \\ \\ \tt \large \longrightarrow{} \pink{C.I =7651 \: rupees}$

➤ Now we can find their difference by,

$\large \tt \hookrightarrow C.I-S.I = 7651 - 7500 \\ \\ \large \tt \orange{\hookrightarrow{}C.I-S.I = 151 \: rupees}$

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