Rs. 10,000 is deposited at the end of every year for 3 years in a sinking fund earning 10% per annum compounded annually. Which of the following statements are correct?
(A) The amount in the fund at the end of 3 years is Rs. 33,100.
(B) The total interest earned by the fund is Rs. 3,310.
(C) If the deposits were made at the beginning of every year instead, the amount at the end of 3 years would be Rs. 33,100.
(D) The first deposit grows to Rs. 12,100 by the end of 3 years.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) and (D) only
The deposits are made at the end of years 1, 2 and 3, so they earn interest for 2, 1 and 0 years. Each grows by compound interest:
\(10000 \times (1.1)^2 = 12100\)
\(10000 \times 1.1 = 11000\)
\(10000 \times 1 = 10000\)
\(A = 12100 + 11000 + 10000 = 33100\)
The interest earned is the amount minus the deposits:
\(33100 - 30000 = 3100\)
If the deposits are made at the beginning of each year (an annuity due), each earns one more year of interest:
\(33100 \times 1.1 = 36410\)
So the fund holds Rs. 33,100, the interest is Rs. 3,100, beginning-of-year deposits would give Rs. 36,410, and the first deposit grows to Rs. 12,100.
Checking the statements
(A) The amount in the fund at the end of 3 years is Rs. 33,100. — Correct. 12100 + 11000 + 10000 = 33100.
(B) The total interest earned by the fund is Rs. 3,310. — Incorrect. The interest is 33100 − 30000 = Rs. 3,100.
(C) If the deposits were made at the beginning of every year instead, the amount at the end of 3 years would be Rs. 33,100. — Incorrect. Each deposit earns one more year, giving 33100 × 1.1 = Rs. 36,410.
(D) The first deposit grows to Rs. 12,100 by the end of 3 years. — Correct. It earns interest for 2 years: 10000 × 1.21 = 12100.