Question

select the correct answer.
an investment firm offers three types of equity investments, a, b, and c. of the firms clients, 30% invest in a, 50% invest in b, and 20% invest in c. the rates of return are 10%, 6%, and 7% for a, b, and c, respectively. what is the expected value of the total return rate for the firms clients?
a. 6.2%
b. 7.1%
c. 7.4%
d. 8.2%

Explanation:

Step1: Define weighted return formula

The expected total return is the weighted average of individual returns, calculated as:
$$E(R) = w_A \times R_A + w_B \times R_B + w_C \times R_C$$
where $w_A, w_B, w_C$ are the client percentages, and $R_A, R_B, R_C$ are the return rates.

Step2: Substitute given values

Substitute $w_A=0.3, R_A=0.10$; $w_B=0.5, R_B=0.06$; $w_C=0.2, R_C=0.07$:
$$E(R) = (0.3 \times 0.10) + (0.5 \times 0.06) + (0.2 \times 0.07)$$

Step3: Calculate each term

Compute each weighted component:
$$0.3 \times 0.10 = 0.03, \quad 0.5 \times 0.06 = 0.03, \quad 0.2 \times 0.07 = 0.014$$

Step4: Sum the components

Add the calculated values together:
$$E(R) = 0.03 + 0.03 + 0.014 = 0.074$$

Answer:

C. 7.4%