A father has setup a sinking fund in order to have Rs. 2,40,000 after 10 years for his daughter's marriage. How much amount should he set aside bi-annually into an account paying 5% per annum compounded half-yearly?
[given : \( (1.025)^{20}\approx1.6 \)]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 10,000
The deposits are made every half-year, so \( n=10\times2=20 \) and the rate per period is \( i=\frac{5}{2}\%=0.025 \). By the sinking fund formula,
\( \displaystyle A=P\,\frac{(1+i)^{n}-1}{i} \)
With A = 2,40,000 and \( (1.025)^{20}\approx1.6 \),
\( \displaystyle 2{,}40{,}000=P\cdot\frac{1.6-1}{0.025} \)
\( \displaystyle 2{,}40{,}000=24P \)
\( \displaystyle P=\text{Rs. }10{,}000 \)