a. The function that models the situation is F(t) = 48(1.08)ˣ
b. The price of the stock 6 years from now is $76.17
c. Find the graph in the attachment
d. I receive a dividend of $0.026.
<h3>a. Write a function f(t) that models the situation.</h3>Since the stock price increases at a rate of 8% every year, and is initially $48, it follows exponential growth.
So, the current price where
- A = price at current moment = $48,
- r = rate of growth = 8% = 0.08 and
- t = number of years
So,
So, the function that models the situation is F(t) = 48(1.08)ˣ
<h3>b. Determine the price of the stock 6 years from now?</h3>The price of the stock 6 years from now is gotten when t = 6.
So,
So, the price of the stock 6 years from now is $76.17
<h3>c. Sketch a graph of the price of the function vs time in years</h3>Find the graph in the attachment
<h3>d. Bonus</h3>Since every quarter, the company pays a dividend of 1.5 %, the rate per year would be r = 1.5 % ÷ 1/4 year = 1.5 % × 4 = 6 % per year.
Since they pay at a rate, r = 6 % = 0.06 of the stock price, F(t) as dividend.
After n years, the dividend is D = (r)ⁿF(t)
= (0.06)ⁿF(t)
So,
So, after 3 years when t = 3,
Since there are 3 shares, the total dividend would be D' = 3D
= 3 × 0.013
= 0.026
So, i receive a dividend of $0.026
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