Rs. 20,000 is deposited at the end of every six months for 1½ years in a sinking fund that earns 8% per annum compounded half-yearly. Which of the following statements are correct?
(A) The amount in the fund at the end of 1½ years is Rs. 62,432.
(B) The total interest earned by the fund is Rs. 2,400.
(C) The interest earned in the last six months is Rs. 1,632.
(D) The fund grows at an effective rate of 8% per annum.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (C) only
The rate per half-year is 4%, and there are 3 deposits. Following the fund half-year by half-year:
End of 1st half-year: \( 20000 \)
End of 2nd half-year: \( 20000 + 800 + 20000 = 40800 \)
End of 3rd half-year: \( 40800 + 1632 + 20000 = 62432 \)
The deposits total Rs. 60,000, so the interest earned is
\( 62432 - 60000 = 2432 \)
The effective rate of 8% compounded half-yearly is
\( (1.04)^2 - 1 = 0.0816 \)
So the fund amounts to Rs. 62,432, the total interest is Rs. 2,432, the last half-year’s interest is Rs. 1,632 and the effective rate is 8.16%.
Checking the statements
(A) The amount in the fund at the end of 1½ years is Rs. 62,432. — Correct. 20,000 × 3.1216 = 62,432.
(B) The total interest earned by the fund is Rs. 2,400. — Incorrect. It is 62,432 − 60,000 = Rs. 2,432.
(C) The interest earned in the last six months is Rs. 1,632. — Correct. 4% of 40,800 = 1,632.
(D) The fund grows at an effective rate of 8% per annum. — Incorrect. (1.04)2 − 1 = 8.16%.