A person has set up a sinking fund so that he can accumulate Rs 100000 in 10 years for his children's higher education. How much amount should he deposit every six months if interest is 5% per annum compounded semi-annually ?

₹3924.64

The correct answer is option (1) : ₹3924.64

Given $A= ₹10000$

$r=\frac{5}{2}$% per half year

$i=\frac{2.5}{100}=0.025$

$n= 29$ half years

Using formula

$A=R\left[\frac{(1+i)^n-1}{i}\right]$

$100000= R\left[\frac{(1.025)^{20}-1}{0.025}\right]$

$R=\frac{100000×0.025}{(1.025)^{20}-1}$

Let $x= (1.025)^{20}$

Taking log on both sides, we get

$log\, x = 20\, log 1.025$

$log\, x = 20×0.0107$

$log\, x = 0.2140$

$x= antilog\, 0.2140$

$x= 1.637$

$R=\frac{2500}{1.637-1}=\frac{2500}{0.637}$

$R= ₹3924.64$