Question

in what time will rupees 4400 become Rupees 4576 at 8% per annum interest compounded half yearly​

Answer 1

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

${\bold{\therefore Time=\frac{1}{2}\:years}}$

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

$\underline \bold{Given : } \\ \implies Amount( A) = 4576 \: rupees \\ \\ \implies Principal(p) = 4400 \: rupees \\ \\ \implies Rate = 8\%\\ \\ \underline \bold{To \: Find : } \\ \implies Time = ?$

• According to given question :

$\bold{Using \: formula \: of \: Compounded \: half \: yearly : } \\ \implies A= p(1 + \frac{ \frac{r}{2} }{100} )^{2t} \\ \\ \implies 4576 = 4400 \times (1 + \frac{ \frac{8}{2} }{100} )^{2t} \\ \\ \implies \frac{4576}{4400} = (1 + \frac{1}{25} ) ^{2t} \\ \\ \implies 1.04 = (\frac{25 + 1}{25}) ^{2t} \\ \\ \implies 1.04 = (1.04)^{2t} \\ \\ \bold{Both \: side \: bases \: are \: equal }\\ \bold{So ,\: powers \: are \: also \: equal} \\ \implies 1 = 2t \\ \\ \bold{\implies t = \frac{1}{2} \: years}$

Answer 2

$\bold{using \: formula \: of \: compounded \: half \: yearly : } \\ \implies a = p(1 + \frac{ \frac{r}{2} }{100} )^{2t} \\ \\ \implies 4576 = 4400 \times (1 + \frac{ \frac{8}{2} }{100} )^{2t} \\ \\ \implies \frac{4576}{4400} = (1 + \frac{1}{25} ) ^{2t} \\ \\ \implies 1.04 = (\frac{25 + 1}{25}) ^{2t} \\ \\ \implies 1.04 = (1.04)^{2t} \\ \\ \bold{both \: side \: bases \: are \: equal }\\ \bold{so \: powers \: are \: also \: equal} \\ \implies 1 = 2t \\ \\ \bold{\implies t = \frac{1}{2} \: years}$