Question

ᴀɴsᴡᴇʀ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ ᴡɪᴛʜ ғᴜʟʟ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ
sᴘᴀᴍ ᴡɪʟʟ ʙᴇ ʀᴇᴘᴏʀᴛᴇᴅ ​

Answer 1

Answer:

For Compound Interest,

Amount=Principal(1+

100

Rate

)

Time

Compound Interest = Amount- Principal

Therefore, in this case, since the interest is compounded annually the time =2.5 years

and rate =4.5% per half year

Amount=8000(1+

200

9 ) 2

Amount =8736.20

Compound Interest = Amount - Principal =8736.20−8000=Rs.736.20

Answer 2

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

Here we need to find out the C.I. This can be done by using the formula of C.I. for half yearly calculation to find the Amount. After finding the amount, we can find out the Compound Interest. We know that while finding compound interest, if the rate is compound half yearly, then the rate becomes half and the time becomes twice as two show two parts in one year.

Let's do it !!

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★ Formula Used :-

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

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

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★ Solution :-

Given,

» Principal = P = Rs. 80,000

» Rate = 9%

Since, this principal is compounded half yearly, then rate will be halved.

» Rate = R = ½ × 9 % per half year

» Time = T = 1 year = 2 (half years, since 6 months + 6 months = 1 year)

Now using the formula of Compound Interest, we get,

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

By applying values in this formula, we get,

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{80000\;\times\;\bigg(1\;+\;\dfrac{\bigg(\dfrac{9}{2}\bigg)}{100}\bigg)^{2}}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{80000\;\times\;\bigg(1\;+\;\dfrac{9}{2\;\times\;100}\bigg)^{2}}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{80000\;\times\;\bigg(1\;+\;\dfrac{9}{200}\bigg)^{2}}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{80000\;\times\;\bigg(\dfrac{200\;+\;9}{200}\bigg)^{2}}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{80000\;\times\;\bigg(\dfrac{209}{200}\bigg)^{2}}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{80000\;\times\;\dfrac{209\;\times\;209}{200\;\times\;200}}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{80000\;\times\;\dfrac{209\;\times\;209}{2\;\times\;2\;\times\;10000}}}}$

Cancelling the numerator and denominator by 10000, we get,

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{8\;\times\;\dfrac{209\;\times\;209}{2\;\times\;2}}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{4\;\times\;\dfrac{209\;\times\;209}{2}}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{2\;\times\;209\;\times\;209}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{2\;\times\;43681}}}$

$\\\;\;\displaystyle{\bf{:\rightarrow\;\;Amount\;=\;\bf{\red{Rs.\;\;87362}}}}$

$\\\;\underline{\boxed{\tt{\odot\;\;Hence,\;\;Amount\;=\;\bf{\blue{Rs\;\;87362}}}}}$

• Now using the formula to calculate C.I., we get,

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

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;Amount\;=\;\bf{Principal\;+\;C.I.}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;C.I.\;=\;\bf{Amount\;-\;Principal}}}$

$\\\;\;\displaystyle{\sf{:\rightarrow\;\;C.I.\;=\;\bf{87362\;-\;80000}}}$

$\\\;\;\displaystyle{\bf{:\rightarrow\;\;C.I.\;=\;\bf{Rs.\;\;7362}}}$

$\\\;\underline{\boxed{\tt{\odot\;\;Hence,\;\;Compound\;\;Interest\;=\;\bf{\blue{Rs\;\;7362}}}}}$

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★ More to know :-

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