Question

9. At what rate per cent per annum will * 6,000
amount to * 6,615 in 2 years when interest
is compounded annually ?
und interest does​

Answer 1

GivEn:-

• Principal = Rs. 6,000

• Amount = Rs. 6,615

• Time = 2 years

To find:-

• Rate of interest.

SoluTion:-

✩ As we know that,

$\dag\;{\underline{\boxed{\bf{\blue{Simple\; Interest\;(S.I.) = Amount - Principal}}}}}$

$:\implies$ S.I. = (6,615 - 6,000) Rs.

$:\implies{\underline{\boxed{\bf{\pink{S.I. = Rs.\;615}}}}}$ ★

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☯ Now, We have to find Rate % :-

✩ As we know that,

$\dag{\underline{\boxed{\bf{\purple{Simple\; Interest = \dfrac{P \times R \times T}{100}}}}}}$

$\small\sf\;\;\star\; {\underline{\green{Putting\;values\;in\;above\;formula:-}}}$

$:\implies\sf 615 = \dfrac{60 \cancel{00} \times 2 \times R}{1 \cancel{00}}$

$:\implies$ 615 = 120 × R

$:\implies\sf R = \dfrac{615}{120}$

$:\implies{\underline{\boxed{\bf{\pink{R = 5.125 \% \;per\;annum}}}}}$ ★

$\dag$ Hence, The Rate of interest is 5.125% per annum.

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$\begin{lgathered}\begin{lgathered}\boxed{\begin{minipage}{7 cm}\boxed{\underline{\underline{\bigstar\:\bf\:Extra\:Brainly\:knowlegde\:\bigstar}}}\\\\1) Profit = SP - CP\\\\2) Loss = CP - SP\\\\3) Profit\% = (Profit in Rs.)*100/CP\\\\4) Loss\% = (Loss in Rs.)*100/CP\\\\5) SP = CP*(100+P\%)/100\\\\6) SP = CP*(100-L\%)/100\\\\7) CP = SP*100/(100+P\%)\\\\8) CP = SP*100/(100-L\%)\\\\9) Discount =MP - SP\\\\10) Discount\%=(Discount in Rs.)*100/MP\\\\11) SP = MP*(100-D\%)/100\\\\12) MP = SP*100/(100-D\%)\\\\\end{minipage}}\end{lgathered}\end{lgathered}$

Answer 2

Solution :

$\underline{\bf{Given\::}}}}$

• Principal, (P) = Rs.6000
• Amount, (A) = Rs.6615
• Time, (n) = 2 years

$\underline{\bf{To\:find\::}}}}$

The rate & Interest of the compounded annually.

$\underline{\bf{Explanation\::}}}}$

Using formula of the compounded annually :

$\boxed{\bf{Amount=Principal\bigg(1+\frac{R}{100} \bigg)^{n} }}}$

$\longrightarrow\sf{6615=6000\bigg(1+\dfrac{R}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{\cancel{\dfrac{6615}{6000} }=\bigg(1+\dfrac{R}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{\dfrac{441}{400}=\bigg(1+\dfrac{R}{100} \bigg)^{2}}\\\\\\\longrightarrow\sf{2\sqrt{\dfrac{441}{400} } =1+\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{21}{20} =1+\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{21}{20} -1=\dfrac{R}{100}}\\\\\\\longrightarrow\sf{\dfrac{21-20}{20} =\dfrac{R}{100} }$

$\longrightarrow\sf{\dfrac{1}{20} =\dfrac{R}{100} }\\\\\longrightarrow\sf{20R=100}}\\\\\longrightarrow\sf{R=\cancel{100/20}}\\\\\longrightarrow\bf{R=5\%}$

We know that compound Interest, we get;

⇒ C.I = Amount - Principal

⇒ C.I = Rs.6615 - Rs.6000

⇒ C.I = Rs.615

Thus;

The rate of the Interest will be 5% & Interest Rs.615 .