Question

5. On what sum of money will the compound
interest for 2 years at 5 per cent per annum
amount to rupees
768.75 ? In book answer is rupees 7,500​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Principal=7,500\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given:}} \\ \tt: \implies Compound \: Interest(C.I) = 768.75 \: rupees \\ \\ \tt: \implies Time(t) = 2 \: years \\ \\ \tt: \implies Rate\% = 5\% \\ \\ \red{ \underline \bold{To \: Find:}} \\ \tt: \implies Principal(p) =?$

• According to given question :

$\bold{As \: we \: know\: that} \\ \tt: \implies C.I= A- p \\ \\ \tt: \implies 768.75 = A - p \\ \\ \tt : \implies A = 768.75 + p \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies A= p(1 + \frac{r}{100} )^{t} \\ \\ \tt: \implies 768.75 + p = (1 + \frac{5}{100} ) ^{2} \\ \\ \tt: \implies \frac{768.75 +p }{p} = (1 + 0.05)^{2} \\ \\ \tt: \implies 768.75 + p= p \times (1.05)^{2} \\ \\ \tt: \implies 768.75 = 1.1025p - p \\ \\ \tt: \implies 768.75 =0.1025p\\ \\ \tt: \implies p = \frac{768.75}{0.1025} \\ \\ \green{\tt: \implies p = 7,500 \: rupees}$

Answer 2

[

$\huge{\mathtt{Solution}}$

$\bold{\mathtt{Given}}$⟹

• Rate = 5%
• Time = 2 years
• Interest = 768.75

$\bold{\mathtt{Formula}}$

$\mathtt{ \boxed{p( {1 + \frac{r}{100}) }^{time} - p} }$

$768.75 = x(( {1 + \frac{5}{100}) }^{2} - 1)$

⟹ Here we have taken principal as x .

$768.75 = x( \frac{105}{100} . \frac{105}{100} - 1)$

$768.75 = x (\frac{21}{20} \times \frac{21}{20} - 1)$

$768.75 = x( \frac{441}{400} - 1)$

$768.75 = x( \frac{441 - 400}{400} )$

$768.75 = x( \frac{41}{400} )$

$768.75 \times 400 = 41x$

$\frac{307500}{41} = x$

$\boxed{x = 7500}$

So the principal amount will be Rs 7500