Question

You are looking at an investment that has an effective annual rate of 14.3 percent. a. What is the effective semiannual return? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the effective quarterly return? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c. What is the effective monthly return? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a. The effective semiannual return is approximately 6.92%. b. The effective quarterly return is approximately 3.31%. c. The effective monthly return is approximately 1.18%.

Step-by-step explanation:

a. To find the effective semiannual return, we use the formula:

(1 + r)^n = (1 + R)^m

Where:

• r is the semiannual return
• R is the effective annual rate
• n is the number of periods in a year (2 for semiannual)
• m is the number of periods in a year (1 for annual)

Plugging in the values, we have:

(1 + r)^2 = (1 + 0.143)^1

Solving for r, we get:

r ≈ 0.0692

So, the effective semiannual return is approximately 6.92%.

b. To find the effective quarterly return, we use the same formula:

(1 + r)^n = (1 + R)^m

Where now n is the number of periods in a year (4 for quarterly)

Plugging in the values, we have:

(1 + r)^4 = (1 + 0.143)^1

Solving for r, we get:

r ≈ 0.0331

So, the effective quarterly return is approximately 3.31%.

c. To find the effective monthly return, we use the same formula again:

(1 + r)^n = (1 + R)^m

Where now n is the number of periods in a year (12 for monthly)

Plugging in the values, we have:

(1 + r)^12 = (1 + 0.143)^1

Solving for r, we get:

r ≈ 0.0118

So, the effective monthly return is approximately 1.18%.

Answer 2

Answer: The effective semiannual return is = 6,91 percent.

The effective quarterly return is= 3,40 percent.

The effective monthly return is = 1,12 percent.

Step-by-step explanation:

The effective semiannual return is:
`( 1 + 0,143 ) ^{(6)/(12) } - 1 = 6,91` percent.

The effective quarterly return is:
`( 1 + 0,143 ) ^{(3)/(12) } - 1 = 3,40` percent.

The effective monthly return is:
`( 1 + 0,143 ) ^{(1)/(12) } - 1 = 1,12` percent.