Question

the simple interest on a sum of money from 2 years at 4%per annum is rs 340. find. i) sum of money. ii) the compound interest on this sum for one year payable half yearly at the same rate

please please help me it is urgent​

Answer 1

Given:-

• Simple interest = Rs. 340

• Time = 2 years

• Rate = 4% per annum

To find:-

• sum of money

• the compound interest on this sum for one year payable half yearly at the same rate.

SoluTion:-

☯ Lets the sum of money be Rs x.

As we know that,

$\maltese\;{\underline{\boxed{\bf{SI = \dfrac{P \times R \times T}{100}}}}}$

⠀⠀⠀

$\small\sf\;\;\dag\; \underline{Put\;the\;givEn\;values\;:-}$

⠀⠀⠀

$\dashrightarrow\sf 340 = \dfrac{x \times 4 \times 2}{100}$

⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow\sf x = \dfrac{340 \times 100}{4 \times 2}$

⠀⠀⠀

$\dashrightarrow{\underline{\boxed{\purple{\bf{x = Rs. \;4250 }}}}}$

━━━━━━━━━━━━━━━

☯ C.I for Rs. 4250 for one year payable half - yearly.

Therefore

• Time = 1 year i.e. 2 half year

• Rate = $\dfrac{4}{2}$ = 2%

As we know that,

$\maltese\;{\underline{\boxed{\bf{A = P \bigg( 1 + \dfrac{R}{100} \bigg)^T}}}}$

⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow\sf A = 4250 \bigg( 1 + \dfrac{2}{100} \bigg)^2$

⠀⠀⠀

$\dashrightarrow\sf A = 4250 \bigg( \dfrac{100 + 2}{100} \bigg)^2$

⠀⠀⠀

$\dashrightarrow\sf A = 4250 \bigg( \dfrac{102}{100} \bigg)^2$

⠀⠀⠀

$\dashrightarrow\sf A = 4250 \times \dfrac{51}{50} \times \dfrac{51}{50}$

⠀⠀⠀

$\dashrightarrow{\underline{\boxed{\purple{\bf{A = Rs.\; 4421.70 }}}}}$

━━━━━━━━━━━━━━━

⠀⠀⠀

Now,

We have to find compound Interest,

Therefore,

$\maltese\;{\underline{\boxed{\bf{C.I = A - P}}}}$

⠀⠀⠀

$\dashrightarrow\sf C.I = 4421.70 - 4250$

⠀⠀⠀

$\dashrightarrow{\underline{\boxed{\pink{\bf{C.I = Rs.\;171.70 }}}}}$ ★

⠀⠀⠀

$\dag\;\sf \underline{Hence,\;the\;sum\;of\;money\;is\;Rs.\;4250\;and\;Compound\; Interest\;is\;Rs.\;171.70}$

━━━━━━━━━━━━━━━

Answer 2

Answer:

Given:-

Simple interest = Rs. 340

Time = 2 years

Rate = 4% per annum

To find:-

sum of money

the compound interest on this sum for one year

payable half yearly at the same rate.

SoluTion:-

☯ Lets the sum of money be Rs x.

As we know that,

$\maltese\;{\underline{\boxed{\bf{SI = \dfrac{P \times R \times T}{100}}}}}$✠

SI=

100

P×R×T

⠀⠀⠀

$\small\sf\;\;\dag\; \underline{Put\;the\;givEn\;values\;:-}†$

PutthegivEnvalues:−

⠀⠀⠀

$\dashrightarrow\sf 340 = \dfrac{x \times 4 \times 2}{100}$⇢340=

100

x×4×2

⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow\sf x = \dfrac{340 \times 100}{4 \times 2}$⇢x=

4×2

340×100

⠀⠀⠀

$\dashrightarrow{\underline{\boxed{\purple{\bf{x = Rs. \;4250 }}}}}$⇢

x=Rs.4250

━━━━━━━━━━━━━━━

☯ C.I for Rs. 4250 for one year payable half - yearly.

Therefore

Time = 1 year i.e. 2 half year

Rate = \dfrac{4}{2}

2

4

= 2%

As we know that,

$\maltese\;{\underline{\boxed{\bf{A = P \bigg( 1 + \dfrac{R}{100} \bigg)^T}}}}$✠

A=P(1+

100

R

)

T

⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow\sf A = 4250 \bigg( 1 + \dfrac{2}{100} \bigg)^2$⇢A=4250(1+

100

2

)

2

⠀⠀⠀

$\dashrightarrow\sf A = 4250 \bigg( \dfrac{100 + 2}{100} \bigg)^2$⇢A=4250(

100

100+2

)

2

⠀⠀⠀

$\dashrightarrow\sf A = 4250 \bigg( \dfrac{102}{100} \bigg)^2$⇢A=4250(

100

102

)

2

⠀⠀⠀

$\dashrightarrow\sf A = 4250 \times \dfrac{51}{50} \times \dfrac{51}{50}$⇢A=4250×

50

51

×

50

51

⠀⠀⠀

$\dashrightarrow{\underline{\boxed{\purple{\bf{A = Rs.\; 4421.70 }}}}}$⇢

A=Rs.4421.70

━━━━━━━━━━━━━━━

⠀⠀⠀

Now,

We have to find compound Interest,

Therefore,

$\maltese\;{\underline{\boxed{\bf{C.I = A - P}}}}$✠

C.I=A−P

⠀⠀⠀

$\dashrightarrow\sf C.I = 4421.70 - 4250$⇢C.I=4421.70−4250

⠀⠀⠀

$\dashrightarrow{\underline{\boxed{\pink{\bf{C.I = Rs.\;171.70 }}}}}$⇢

C.I=Rs.171.70

★

⠀⠀⠀

$\dag\;\sf \underline{Hence,\;the\;sum\;of\;money\;is\;Rs.\;4250\;and\;Compound\; Interest\;is\;Rs.\;171.70}†$

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