The buying and selling commission schedule shown below is from a well-known online discount brokerage firm.?

Taking into consideration the buying and selling commissions in the schedule find annual rate of interest earned by each investment?

Transaction Size Commission Rate
$0-$2,500 $19+ 1.6% of principal
$2,501-$6,000 $44 + 0.6% of principal
$6,001-$22,000 $62 + 0.3% of principal
$22,001-$50,000 $84 + 0.2% of principal
$50,001-$500,000 $134 + 0.1% of principal
$500,001+ $234+ 0.08% of principal

An investor purchases 500 shares at $14.20 a share, holds the stock for 39 weeks, and then sells the stock for $16.84 a share.

What you have listed are investment commissions.

The total charge was in this case $7200 plus $62 + 21.30. That is 7283.39. The stock was sold for $16.84 a share, or $8420.00 There would be selling commission of %62 + 25.26 = 87.26

The net return on the buying and selling of the stock would be
8420. - 7283.39 - 83.30 - 87.26 = 966.05

966.05 profit in 39 weeks on a purchase of 7283.39 is an annual percentage rate gain of 17.7%

To find the annual rate of interest earned by the investment, we need to calculate the total buying and selling commissions paid and compare them to the profit made from the investment.

1. Calculate the buying commission:
Since the investor purchased 500 shares at $14.20 per share, the total purchase price is 500 * $14.20 = $7100.

Looking at the commission schedule, the transaction size falls under the $6,001-$22,000 range. Therefore, the buying commission is $62 + 0.3% of $7100.
$62 + (0.3% * $7100) = $62 + $21.30 = $83.30

2. Calculate the selling commission:
The investor sells the 500 shares at $16.84 per share, resulting in a sales price of 500 * $16.84 = $8420.

Again, referring to the commission schedule, the transaction size falls under the $6,001-$22,000 range. Thus, the selling commission is $62 + 0.3% of $8420.
$62 + (0.3% * $8420) = $62 + $25.26 = $87.26

3. Calculate the profit from the investment:
The profit is the difference between the sales price and the purchase price:
$8420 - $7100 = $1320

4. Calculate the annual rate of interest:
To find the annual rate of interest, we need to know the holding period in years. Assuming a year consists of 52 weeks, the holding period is 39 / 52 = 0.75 years.

The annual rate of interest can be calculated using the following formula:
Annual Rate of Interest = (Profit / Total Commissions) / Holding Period

Total Commissions = Buying Commission + Selling Commission
Total Commissions = $83.30 + $87.26 = $170.56

Annual Rate of Interest = ($1320 / $170.56) / 0.75
Annual Rate of Interest = 7.7

Therefore, the annual rate of interest earned by the investment is approximately 7.7%.