Mr. X has two investment options, option A, either 8% annum compounded semi annually or option B 7.6% per annum compounded quarterly. Then which of the following are TRUE?
(A) Effective rate for option A is 8.16%
(B) Effective rate for option B is 7.82%
(C) Effective rate for option B is 8.82%
(D) Option A is better than option B as investment.
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 effective rate is \( \left(1+\frac{r}{m}\right)^m-1 \), where m is the number of compounding periods per year.
Option A: 8% compounded half-yearly, so r/m = 0.04 and m = 2:
\( \displaystyle (1.04)^2-1=0.0816 \)
Option B: 7.6% compounded quarterly, so r/m = 0.019 and m = 4:
\( \displaystyle (1.019)^4-1\approx 0.0782 \)
So the effective rate is 8.16% for option A and 7.82% for option B.
Checking the statements
(A) Effective rate for option A is 8.16% — Correct. \( (1.04)^2-1=0.0816 \).
(B) Effective rate for option B is 7.82% — Correct. \( (1.019)^4-1\approx 0.0782 \).
(C) Effective rate for option B is 8.82% — Incorrect. The effective rate for B is 7.82%.
(D) Option A is better than option B as investment. — Correct. 8.16% > 7.82%.