Question

rachel bought 1,500 shares of cawh consolidated bank at a price of $24.85 each. as the price climbed, she sold off parts of her holdings. she sold off 250 shares at $28.32 apiece, she sold 800 of her shares at $33.60 apiece, and she sold off the remainder of her shares at $39.94 apiece. if rachels broker charges a commission of $65 per $1,000 of stock bought or sold, how much profit did rachel make, to the nearest dollar?
a. $20,459
b. $51,933
c. $14,661
d. $8,859

Explanation:

Step1: Calculate total cost of buying

Total shares bought = 1500, price per share = $24.85.
Total cost (before commission) = \( 1500 \times 24.85 = 37275 \) dollars.

Commission on buying: Total value is $37275. Commission rate is $65 per $1000.
Number of $1000 units: \( \frac{37275}{1000} = 37.275 \), so commission = \( 37.275 \times 65 = 2422.875 \) dollars.
Total cost (including commission) = \( 37275 + 2422.875 = 39697.875 \) dollars.

Step2: Calculate total revenue from selling

First sale: 250 shares at $28.32. Revenue = \( 250 \times 28.32 = 7080 \) dollars.
Second sale: 800 shares at $33.60. Revenue = \( 800 \times 33.60 = 26880 \) dollars.
Remaining shares: \( 1500 - 250 - 800 = 450 \) shares.
Third sale: 450 shares at $39.94. Revenue = \( 450 \times 39.94 = 17973 \) dollars.
Total revenue (before commission) = \( 7080 + 26880 + 17973 = 51933 \) dollars.

Commission on selling: Total value is $51933.
Number of $1000 units: \( \frac{51933}{1000} = 51.933 \), so commission = \( 51.933 \times 65 = 3375.645 \) dollars.
Total revenue (after commission) = \( 51933 - 3375.645 = 48557.355 \) dollars.

Step3: Calculate profit

Profit = Total revenue (after commission) - Total cost (including commission)
Profit = \( 48557.355 - 39697.875 = 8859.48 \) dollars, which rounds to $8859.

Answer:

d. $8,859