A person has set up a sinking fund in order to have Rs. 10,00,000 after 10 years for his child education. The amount should put bi-annually into account paying 5% per annum compounded semi-annually is: [Given $(1.025)^{20}= 1.6386$]

Rs. 39148.14

The correct answer is Option (2) → Rs. 39148.14

Future value required: $S = 10,00,000$

Rate per half-year: $i = \frac{5\%}{2} = 0.025$

Number of half-yearly deposits: $n = 10 \times 2 = 20$

Future value of an ordinary annuity formula:

$S = R \frac{(1+i)^n - 1}{i}$

Substitute values:

$10,00,000 = R \frac{(1.025)^{20} - 1}{0.025}$

Compute $(1.025)^{20} \approx 1.638616$

$(1.025)^{20} - 1 \approx 0.638616$

Divide by 0.025: $\frac{0.638616}{0.025} \approx 25.54464$

$R = \frac{10,00,000}{25.54464} \approx 39136$

Bi-annual deposit ≈ Rs. 39,136