An investor purchases 75 shares at 37.90 a share, holds the stock for 150 days, and then sells the stock for 41.20 a share. Find the annual interest rate earned.
principal
under 3000
3000-10,000
over 10,000
commission
32+1.8% of principal
56+1% of principal
106+0.5% of principal
What's the answer
3.2%
To find the annual interest rate earned, we need to calculate the total gain from the investment and then convert it into an annual rate.
First, let's calculate the principal invested in the stock:
Principal = Number of shares * Price per share
Principal = 75 shares * $37.90/share
Principal = $2,842.50
Next, let's determine the commission paid for purchasing the stock:
Commission = $32 + 1.8% of Principal
Commission = $32 + 1.8/100 * $2,842.50
Commission = $32 + $51.16
Commission = $83.16
The total cost of purchasing the stock is the principal + the commission:
Total Cost = Principal + Commission
Total Cost = $2,842.50 + $83.16
Total Cost = $2,925.66
Now, let's calculate the total earnings from selling the stock:
Earnings = Number of shares * Selling price per share
Earnings = 75 shares * $41.20/share
Earnings = $3,090.00
Next, let's determine the commission paid for selling the stock:
Commission = $106 + 0.5% of Principal
Commission = $106 + 0.5/100 * $2,842.50
Commission = $106 + $14.21
Commission = $120.21
The total amount received from selling the stock is the earnings - the commission:
Total Amount Received = Earnings - Commission
Total Amount Received = $3,090.00 - $120.21
Total Amount Received = $2,969.79
The gain from the investment is the total amount received - the total cost:
Gain = Total Amount Received - Total Cost
Gain = $2,969.79 - $2,925.66
Gain = $44.13
The holding period is given as 150 days. To calculate the annual interest rate, we need to convert this holding period into a year.
Number of days in a year = 365
Annual Interest Rate = (Gain / Total Cost) * (365 / Holding Period)
Annual Interest Rate = ($44.13 / $2,925.66) * (365 / 150)
Annual Interest Rate = 0.015083 * 2.4333333
Annual Interest Rate = 0.0366685
Finally, let's convert the annual interest rate into a percentage:
Annual Interest Rate = 0.0366685 * 100
Annual Interest Rate = 3.67%
Therefore, the annual interest rate earned from this investment is approximately 3.67%.
To calculate the annual interest rate earned, we need to calculate the total interest earned and then convert it to an annual rate.
First, let's calculate the total cost of purchasing the shares:
Total Cost = Number of shares * Purchase price per share
= 75 shares * $37.90/share
= $2,842.50
Next, let's calculate the total revenue from selling the shares:
Total Revenue = Number of shares * Selling price per share
= 75 shares * $41.20/share
= $3,090.00
Now, let's calculate the total profit:
Total Profit = Total Revenue - Total Cost
= $3,090.00 - $2,842.50
= $247.50
Since the investor held the stock for 150 days, let's calculate the daily profit:
Daily Profit = Total Profit / Number of days held
= $247.50 / 150
= $1.65 per day
To calculate the annual interest rate, we need to determine the principal amount. Based on the given commission rates, we can calculate the principal as follows:
If the principal is under $3,000, the commission is $32 + 1.8% of the principal.
If the principal is between $3,000 and $10,000, the commission is $56 + 1% of the principal.
If the principal is over $10,000, the commission is $106 + 0.5% of the principal.
Let's determine the principal based on the commission:
Since the total commission is not provided, we can't directly determine the principal. However, we can try different principal amounts and calculate the corresponding commission to find the actual principal.
For example, let's assume the principal is $5,000 and calculate the commission:
Commission = $56 + 1% of $5,000
= $56 + $50
= $106
The calculated commission matches with the commission mentioned for the principal in the range of $3,000 to $10,000. Therefore, we can assume the principal as $5,000 for this calculation.
Now, let's calculate the annual interest rate:
Annual Interest Rate = (Daily Profit / Principal) * 365 * 100
= ($1.65 / $5,000) * 365 * 100
= 0.033 * 365 * 100
= 12.045%
Therefore, the annual interest rate earned is approximately 12.045%.