Question

Find the amount and the compound interest on 5000 for 2 years at 6% per annum,
interest payable yearly.

(Please give the full explanation for doing this sum)
​

Answer 1

Given :-

• Principal (P) = Rs.5000
• Time (t) = 2years
• Rate of interest (R) = 6%

To Find :-

• Amount and Compound interest.

Solution :-

As we know that,

${ \boxed{ \tt{ \red{A = P(1+\frac{R}{100}) {}^{t} }}}}$

[ Putting values ]

$\mapsto\tt \:A = 5000(1 + \frac{6}{100} ) {}^{2}$

$\mapsto \tt \:A = 5000( \frac{106}{100} ) {}^{2}$

$\mapsto \tt \:A = 5000 \times \frac{106}{100} \times \frac{106}{100}$

$\mapsto \tt \:A = 5 \cancel{000} \times \frac{106}{1 \cancel{00}} \times \frac{106}{10 \cancel{0}}$

$\mapsto\tt \:A = 5 \times 106 \times \frac{106}{10}$

$\mapsto\tt \:A = 53 \cancel0 \times \frac{106}{1 \cancel0}$

$\mapsto \tt \: \blue {A =5618 }$

.°. Amount is Rs. 5618 .

Now, We know that,

${ \boxed{ \tt{ \pink{Interest = Amount - Principal}}}}$

[ Putting values ]

$\mapsto \: \tt \: Interest = 5618 - 5000$

$\mapsto \: \tt \: \green{Interest =618}$

.°. Compound interest is Rs.618 .

Answer 2

$Given \: Principal (P) = Rs \:5000$

$Rate \: of \: Interest (R) = 6\%\: per \:annum$

$Time = 2 \: years$

$Conversation \: period (n) = 2$

$Let \: the \: Amount = A$

$\boxed{ \pink{ A = P\Big( 1 + \frac{R}{100}\Big)^{n} }}$

$\implies A = 5000 \Big( 1 + \frac{6}{100}\Big)^{2}$

$= 5000 \Big( \frac{100+6}{100}\Big)^{2}$

$= 5000 \Big( \frac{106}{100}\Big)^{2}$

$= 5000 \Big( \frac{53}{50}\Big)^{2}$

$= Rs \: 5618$

Therefore.,

$\red{ Amount} \green { = Rs \: 5618}$

$\red{ Compound \: Interest } = A - P$

$= Rs \: 5618 - Rs \: 5000$

$\green { = Rs \: 618 }$

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