Question

In how many years will a sum of $\text{Rs.}6400$ compounded semi-annually at $5\%p.a.$ amount to $\text{Rs.}6569$?

Answer 1

Amount$=6569$,

Principal$=P=6400$

Rate$R==5\%$,

Time$=T=?$

Since, we know (for half yearly)

Amount$=P{(1+\frac{R}{200})}^{2T}$

$6569=6400(1+5/200{)}^{2T}$

$\frac{6569}{6400}={\left(\frac{41}{40}\right)}^{2T}$

$(1.02{)}^1=(1.02{)}^{2T}$

Comparing the powers when base are same:

$1=2T$

$T=\frac{1}{2}\text{years}$.