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 $(1.025)^{20} = 1.6386$]
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹39,148.1
$\text{Required amount}=1000000.$
$\text{Interest rate}=5\%\text{ p.a. compounded half-yearly}.$
$i=\frac{5}{2}\%=2.5\%=0.025.$
$n=10\times2=20.$
$\text{For sinking fund: }A=R\frac{(1+i)^n-1}{i}.$
$1000000=R\frac{(1.025)^{20}-1}{0.025}.$
$\text{Given }(1.025)^{20}\approx1.64.$
$1000000=R\frac{1.64-1}{0.025}.$
$1000000=R\frac{0.64}{0.025}.$
$1000000=25.6R.$
$R=\frac{1000000}{25.6}.$
$R=39062.5.$
$\text{Amount to be deposited every 6 months}=₹39,062.50.$