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 $(1.025)^{20}= 1.6386$]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 39148.14
GivenFuture 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: $\frac{0.638616}{0.025} \approx 25.54464$
$R = \frac{10,00,000}{25.54464} \approx 39136$
AnswerBi-annual deposit ≈ Rs. 39,136