Ajesh has set up a sinking fund in order to have ₹10,00,000 after 10 years for his son's education. The amount should be set aside at the end of every 6 months into an account paying 5% per annum compounded half yearly is: [given $(1.025)^{20} = 1.6386$]

₹39,148.1

The correct answer is Option (3) → ₹39,148.1

$\text{Required amount}=1000000.$

$\text{Interest rate}=5\%\text{ p.a. compounded half-yearly}.$

$i=\frac{5}{2}\%=2.5\%=0.025.$

$n=10\times2=20.$

$\text{For sinking fund: }A=R\frac{(1+i)^n-1}{i}.$

$1000000=R\frac{(1.025)^{20}-1}{0.025}.$

$\text{Given }(1.025)^{20}\approx1.64.$

$1000000=R\frac{1.64-1}{0.025}.$

$1000000=R\frac{0.64}{0.025}.$

$1000000=25.6R.$

$R=\frac{1000000}{25.6}.$

$R=39062.5.$

$\text{Amount to be deposited every 6 months}=₹39,062.50.$