Question

in what time will rs 2500 amount to rs2809 at 12% p. a compounded semi anually? ​

Answer 1

Answer:

$principal(p) = \: rs \: 2500 \\ amount(a) = \: rs \: 2809 \\ rate(r) = 12\% \: per \: annum \\ convert \: rate \: in \: semi \: annually \\ rate = \frac{12}{2} \% = 6\% \: per \: semi \: annually \\ let \: the \: time \: in \: annually \: be \: t \\ then \\ convert \: time \: in \: semi \: annually \\ time = 2t$

$a = p \times (1 + \frac{r}{100} ) {}^{2t} \\ 2809 = 2500 \times (1 + \frac{6}{100} ) {}^{2t } \\ (1 + \frac{3}{50} ) {}^{2t} = \frac{2809}{2500} \\ ( \frac{50 + 3}{50} ) {}^{2t} = ( \frac{53}{50} ) {}^{2} \\ (\frac{53}{50}) {}^{2t} = (\frac{53}{50} ) {}^{2} \\ base \: are \: same \: so \\ 2t = 2 \\ t = 1 \: year = 2 \: semi \: year$