On how much principal will the compound interest amount to Rs. $160$ in $2$ years at $4 %$ per annum?

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Solution

$C . I . = A - P = R s .160$
$A = P + 160$
$T = 2$ years
$R = 4 %$
$A = P {(1 + \frac{R}{100})}^{n}$
$\Rightarrow P + 160 = P {(1 + \frac{4}{100})}^{2}$
$P + 160 = P (1 + \frac{1}{25}) = P {(\frac{26}{25})}^{2}$
$\Rightarrow P + 160 = P (\frac{26}{25} \times \frac{26}{25})$
$\Rightarrow P + 160 = P (\frac{676}{625})$
$\Rightarrow \frac{P \times 676}{625} - P = 160$
$\Rightarrow \frac{676 P - 625 P}{625} = 160$
$\Rightarrow \frac{51 P}{625} = 160$
$51 P = 160 \times 625$
$\Rightarrow P = \frac{160 \times 625}{51}$
$\Rightarrow P = R s .1960 .78$

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On how much principal will the compound interest amount to Rs.160 in 2 years at 4% per annum?

C.I.=A−P=Rs.160A=P+160T=2 yearsR=4%A=P(1+R100)n⇒P+160=P(1+4100)2P+160=P(1+125)=P(2625)2⇒P+160=P(2625×2625)⇒P+160=P(676625)⇒P×676625−P=160⇒676P−625P625=160⇒51P625=16051P=160×625⇒P=160×62551⇒P=Rs.1960.78

On how much principal will the compound interest amount to Rs. $160$ in $2$ years at $4 %$ per annum?