Ritu invested Rs. 1,60,000 in a fund. At the end of one year, the value of her investment was Rs. 1,84,000. During the year she paid Rs. 3,200 as fund charges. Which of the following are correct?
(A) The gain in the value of the investment is Rs. 24,000.
(B) The nominal rate of return is 15%.
(C) The actual rate of return, after the fund charges, is 17%.
(D) The actual rate of return is less than the nominal rate of return.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
The gain in value is
\(184000 - 160000 = 24000\)
The nominal rate of return uses this gain with no expenses taken out:
\( \displaystyle \frac{24000}{160000} \times 100 = 15\% \)
The actual rate of return takes the expenses away from the money earned:
\(24000 - 3200 = 20800\)
\( \displaystyle \frac{20800}{160000} \times 100 = 13\% \)
So the gain is Rs. 24,000, the nominal rate of return is 15% and the actual rate of return is 13%.
Checking the statements
(A) The gain in the value of the investment is Rs. 24,000. — Correct. 1,84,000 − 1,60,000 = 24,000.
(B) The nominal rate of return is 15%. — Correct. 24000 ÷ 160000 = 0.15.
(C) The actual rate of return, after the fund charges, is 17%. — Incorrect. 17% comes from adding the charges (27200 ÷ 160000); they must be subtracted, giving 13%.
(D) The actual rate of return is less than the nominal rate of return. — Correct. 13% is less than 15%, because the charges reduce the money earned.