Question

Mr. X has two investment options: A (8% p.a. compounded semi-annually) or B (7.6% p.a. compounded quarterly). 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 an investment.

• A. (A), (B) and (D) only
• B. (A) and (C) only
• C. (B) and (D) only
• D. (A) and (D) only

Hint:

EAR allows you to compare interest rates across different compounding frequencies directly.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Effective Annual Rate (EAR) is calculated as \( (1 + r/n)^n - 1 \).

Step 2: Detailed Explanation:
Option A: \( r=0.08, n=2 \). \( EAR_A = (1 + 0.08/2)^2 - 1 = (1.04)^2 - 1 = 1.0816 - 1 = 8.16% \). (Statement A is True)
Option B: \( r=0.076, n=4 \). \( EAR_B = (1 + 0.076/4)^4 - 1 = (1.019)^4 - 1 \approx 1.0782 - 1 = 7.82% \). (Statement B is True)
Since \( 8.16% > 7.82% \), Option A is better. (Statement D is True)

Step 3: Final Answer:
Statements (A), (B), and (D) are true. Given the options, (A) is the most accurate.