Mr. Dileep Rao has set up a sinking fund so that he can accumulate Rs. 10,00,000 in 10 years for his children’s higher education. How much amount should Dileep Rao deposit at the beginning of each year to accumulate this amount at the end of 10 years. If the interest rate is 12% compounded annually ? Given that \((1.12)^{11}=3.477\) (Rounded off to the nearest paise)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 50912.18
Deposits at the beginning of each year form an annuity due. Its amount after n years, for a deposit R at rate i, is
\( \displaystyle A = R\,\frac{(1+i)^{n} - 1}{i}\,(1+i) = R\,\frac{(1+i)^{n+1} - (1+i)}{i} \)
Here A = 1000000, i = 0.12 and n = 10:
\( \displaystyle 1000000 = R\,\frac{(1.12)^{11} - 1.12}{0.12} \)
\( \displaystyle = R\,\frac{3.477 - 1.12}{0.12} = R\,\frac{2.357}{0.12} \)
So
\( \displaystyle R = \frac{1000000 \times 0.12}{2.357} = \frac{120000}{2.357} \)
\(R \approx 50912.18\)
So the yearly deposit is Rs. 50912.18.