Natalia Sandino was given 750 shares of stock in the fitness center where she is employed as a salary bonus. The shares were valued at $8.05 when they were placed in her stock portfolio. The shares paid quarterly dividends of $.60 per share. After 7 years, Natalia sold the shares for $10.67. What was her annual rate of return? Round to the nearest hundredth of a percent.
Please help me homework due in half an hour (this is 25 pnts question)
the stock appreciated $2.62 over 7 yrs ... $0.36 per year
quarterly dividends of $2.40 per yr
annual return ... $2.76
annual rate ... (2.76 / 8.05) * 100% ... pretty good return
To calculate Natalia's annual rate of return, we need to determine the total return she received from the stock investment over the 7-year period, and then divide it by the initial investment.
Step 1: Calculate the initial investment:
Natalia was given 750 shares of stock valued at $8.05 per share, so the initial investment is:
Initial investment = 750 shares * $8.05/share = $6037.50
Step 2: Calculate the total return:
The total return includes both the dividends received and the capital gain from selling the shares.
Dividends received:
Natalia received quarterly dividends of $0.60 per share, so the annual dividends can be calculated as:
Annual dividends = (0.60/share * 750 shares)/7 years = $514.29
Capital gain from selling the shares:
The shares were sold for $10.67 each, so the total proceeds from selling the shares can be calculated as:
Total proceeds = 750 shares * $10.67/share = $8002.50
The capital gain is the difference between the total proceeds and the initial investment:
Capital gain = Total proceeds - Initial investment = $8002.50 - $6037.50 = $1965.00
The total return is the sum of the dividends received and the capital gain:
Total return = Dividends received + Capital gain = $514.29 + $1965.00 = $2479.29
Step 3: Calculate the annual rate of return:
To find the annual rate of return, we divide the total return by the initial investment, and then multiply by 100 to express it as a percentage:
Rate of return = (Total return / Initial investment) * 100 = ($2479.29 / $6037.50) * 100
Now, let's calculate it:
Rate of return = (0.410998) * 100 ≈ 41.10%
Therefore, Natalia's annual rate of return on the stock investment is approximately 41.10%.