Question

ᴀɴsᴡᴇʀ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ ᴡɪᴛʜ ғᴜʟʟ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ
sᴘᴀᴍ ᴡɪʟʟ ʙᴇ ʀᴇᴘᴏʀᴛᴇᴅ ​

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the concept of Simple Interest and Compound Interest has been used. For first case we will find the Simple Interest of the given Principal and then we will find the Amount. Then we will find the Amount using the Formula of Compound Interest and then we will find the Compound Interest. For final answer we will subtract Amount with S.I. from Amount of C.I.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{S.I.\;=\;\bf{\dfrac{P\;\times\;R\;\times\;T}{100}}}}$

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

$\\\;\boxed{\sf{Amount\;=\;\bf{Principal\;+\;Interest}}}$

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★ Solution :-

Given,

» Principal = P = Rs. 12000

» Rate = R = 6%

» Time = 2 years

» Amount with Simple Interest = A₁

» Amount with Compound Interest = A₂

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~ For Amount using S.I. that is A₁ ::

We know that,

$\\\;\displaystyle{\sf{:\rightarrow\;\;S.I.\;=\;\bf{\dfrac{P\;\times\;R\;\times\;T}{100}}}}$

By applying values in this formula, we get,

$\\\;\displaystyle{\sf{:\Longrightarrow\;\;S.I.\;=\;\bf{\dfrac{12000\;\times\;6\;\times\;2}{100}}}}$

$\\\;\displaystyle{\sf{:\Longrightarrow\;\;S.I.\;=\;\bf{120\;\times\;6\;\times\;2}}}$

$\\\;\displaystyle{\bf{:\Longrightarrow\;\;S.I.\;=\;\bf{Rs.\;\;1440}}}$

Now let's find amount using this Simple Interest.

$\\\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{Principal\;+\;Interest}}}$

$\\\;\displaystyle{\sf{:\Longrightarrow\;\;Amount_{1}\;=\;\bf{Principal\;+\;Simple\;Interest}}}$

$\\\;\displaystyle{\sf{:\Longrightarrow\;\;Amount_{1}\;=\;\bf{12000\;+\;1440}}}$

$\\\;\displaystyle{\bf{:\Longrightarrow\;\;Amount_{1}\;=\;\bf{\green{Rs.\;\;13440}}}}$

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~ For Amount using C.I. that is A₂ ::

We know that,

$\\\;\displaystyle{\sf{:\rightarrow\;\;A\;=\;\bf{P\;\times\;\bigg(1\;+\;\dfrac{R}{100}\bigg)^{T}}}}$

This formula gives the amount compounded annually using C.I. so we no need to find C.I. differently, because we just need the Amount.

$\\\;\displaystyle{\sf{:\rightarrow\;\;A_{2}\;=\;\bf{12000\;\times\;\bigg(1\;+\;\dfrac{6}{100}\bigg)^{2}}}}$

$\\\;\displaystyle{\sf{:\rightarrow\;\;A_{2}\;=\;\bf{12000\;\times\;\bigg(\dfrac{100\;+\;6}{100}\bigg)^{2}}}}$

$\\\;\displaystyle{\sf{:\rightarrow\;\;A_{2}\;=\;\bf{12000\;\times\;\bigg(\dfrac{106}{100}\bigg)^{2}}}}$

$\\\;\displaystyle{\sf{:\rightarrow\;\;A_{2}\;=\;\bf{12000\;\times\;\bigg(\dfrac{11236}{10000}\bigg)}}}$

$\\\;\displaystyle{\sf{:\rightarrow\;\;A_{2}\;=\;\bf{12000\;\times\;1.1236}}}$

$\\\;\displaystyle{\bf{:\rightarrow\;\;A_{2}\;=\;\bf{\green{Rs.\;\;13483.2}}}}$

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~ For extra amount that is to be paid ::

We have the Amount that is using C.I. means A₂ and the Amount that is using S.I. means A₁.

Now their difference will be the extra amount that will be paid.

$\\\;\displaystyle{\sf{:\mapsto\;Extra\;amount\;=\;\bf{Amount_{(C.I.)}\;-\;Amount_{(S.I.)}}}}$

$\\\;\displaystyle{\sf{:\mapsto\;Extra\;amount\;=\;\bf{Amount_{2}\;-\;Amount_{1}}}}$

$\\\;\displaystyle{\sf{:\mapsto\;Extra\;amount\;=\;\bf{13483.2\;-\;13440}}}$

$\\\;\displaystyle{\bf{:\mapsto\;Extra\;amount\;=\;\bf{\red{Rs.\;\;43.2}}}}$

$\\\;\underline{\boxed{\tt{Extra\;\;Amount\;\;to\;\;be\;\;paid\;=\;\bf{\purple{Rs.\;\;43.2}}}}}$

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★ More to know :-

• Principal : The initial amount of money that is taken.

• Rate : It is the percentage of interest that is taken with the principal after completion of the due date of borrowed money.

• Time : It is the time period for which the interest is liable on the initial sum.

Answer 2

Answer:

Rs.43.20

Step-by-step explanation:

Given P=Rs.12000N=2R=6%

S.I.=

100

PPN

SI =

100

12000×6×2

=1440

A=SI+P=1440+12000= Rs. 13440

Compound interest:

A=P(1+ 100r ) n

=12000(1+ 100) 6

(2)

=12000(1.1236)

=Rs.13483.2

Amount =Rs.13483.20

CI=A−P=13483.20−12000

=Rs.1483.20

Extra interest =13483.20−13440=Rs.43.20

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