Question

How much will Rs 25000 invested at compound interest amount to in 1 year at 4% annum compounded half yearly ?​

Answer 1

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

$\green{\tt{\therefore{Compound\:Interest=1,010\:rupees}}}$

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

$\green{ \underline \bold{Given :}} \\ \tt: {\implies Principal(p) = 25,000\: rupees} \\ \\ \tt: \implies Rate\%(r) = 4\% \\ \\ \tt: \implies Time(t) = 1 \: years \\ \\ \red{ \underline \bold{To \: Find:}} \\ \tt: \implies Compound \: Interest \: half \: yearly(C.I) = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies A = p(1 + \frac{ \frac{r}{2} }{100} )^{2t} \\ \\ \tt: \implies A = 25000(1 + \frac{4}{2 \times 100} )^{2 \times 1} \\ \\ \tt: \implies A= 25000 \times (1 + 0.02)^{2} \\ \\ \tt: \implies A = 25000 \times (1.02)^{2} \\ \\ \green{\tt: \implies A = 26,010 \: rupees} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies C.I = A - p \\ \\ \tt: \implies C.I= 26010 - 25000 \\ \\ \green{\tt: \implies C.I =1,010 \: rupees}$

Answer 2

Given :

• Principal (P) = 25000 Rs
• Rate (r) = 4%
• Time = 1 year

To Find :

• Half yearly compound interest

______________________________

We know that :

$\qquad \sf{A = P \bigg(1 + \dfrac{ \frac{r}{2} }{100} \bigg)^{2t} } \\ \\ \longrightarrow \: \sf{A = 25000 \bigg(1 + \dfrac{ \cancel{\frac{4}{2}} }{100} \bigg)^{2 \times 1} } \\ \\ \longrightarrow \: \sf{A = 25000 \bigg(1 + \dfrac{ 2}{100} \bigg)^{2} } \\ \\ \longrightarrow \: \sf{A = 25000 \times \big(1 + 0.02 \big)^{2} } \\ \\ \longrightarrow \: \sf{A = 25000 \times \big(1.02 \big)^{2} } \\ \\ \longrightarrow \: \sf{A = 25000 \times1.04} \\ \\ \longrightarrow \: \boxed{\sf{A = 26010 \: Rs}}$

______________________________

Now,

$\qquad \sf{C.I = A - P} \\ \\ \longrightarrow \: \sf{C.I = 26010 - 2500} \\ \\ \longrightarrow \: \sf{C.I = 1010 \: Rs}$

$\underline{ \boxed{ \textbf{So, the half yearly compound interest is 1010 Rs}}}$