Question

A certain sum of money amounts to ₹5832 in 2 years and ₹6298.56 in 3 years when interest is compounded yearly. Find the rate percent and the sum of money.

Answer 1

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Answer 2

$Let \: the \: sum \: of \: money = Rs \: P$

$Amount (A_{1}) = Rs \: 5832$

$Time (T_{1}) = 2 \: years$

$Amount \: in \: 3 \: years \: A_{2} = Rs \: 6298.56$

$Time (T_{2}) = 3 \: years$

$Principal \: in \: end \: of \: second \: year (P_{2} )$

$= A_{1}$

$= Rs \: 5832$

$Interest \:paid \: third \: year (I)$

$= A_{2} - A_{1}$

$= Rs \: 6298.56 - Rs \: 5832$

$= Rs \: 466.56$

$Time ( T_{2} ) = 1 \: year$

$Let \: rate \:of \: Interest = R$

$R = \frac{ 100 \times I }{P_{2} \times T_{2}}$

$= \frac{ 100 \times 466.56 }{5832 \times 1}$

$= \frac{ 46656}{5832}$

$\green {\therefore R = 8\% }$

$Now, The \: sum \: of \:money = \frac{ A_{2} \times 100}{ 100 + T_{2}R }$

$= \frac{ 5832 \times 100 }{ 100 + 2 \times 8 }$

$= \frac{ 583200 }{ 116}$

$= Rs \: 5027.586$

$= Rs \: 5027.59$

Therefore.,

$\red{ The \: sum \: of \:money} \green { = Rs \: 5027.59}$

$\red{ Rate \:of \: Interest } \green { = 8 \% }$

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