The amount should be deposited at the end of every 6 months to accumulate Rs.50,000 in 8 years if money is worth 6% p.a. compounded semiannually, is: (Given \((1.03)^{16} = 1.6047\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 2480.57
Equal deposits at the end of each period form an ordinary annuity. Its amount (future value) after n periods is
\( \displaystyle A = R\left[\frac{(1 + i)^n - 1}{i}\right] \)
Half-yearly compounding for 8 years:
\( \displaystyle i = \frac{6\%}{2} = 0.03, \quad n = 8 \times 2 = 16 \)
Substituting A = 50000 and \((1.03)^{16} = 1.6047\):
\( \displaystyle 50000 = R\left[\frac{1.6047 - 1}{0.03}\right] \)
\( \displaystyle R = \frac{50000 \times 0.03}{0.6047} \)
\( \displaystyle R = \frac{1500}{0.6047} \approx 2480.57 \)
So Rs. 2480.57 must be deposited every 6 months.