Apple issues dividend every quarter (see more information below). (a) The close prices on August 6, 2021 and May 6, 2022 is $ \$ 146.14 $ and $ \$ 157.28 $. What is Apple's stock return? And what is the growth rate of dividend implied by current stock price? Date dividends (\$) $ \begin{array}{cc}\text { 6-May-22 } & 0.23 \\ \text { 4-Feb-22 } & 0.22 \\ \text { 5-Nov-21 } & 0.22 \\ \text { 6-Aug-21 } & 0.22\end{array} $

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Stock Investments are based on the following chart, which shows monthly figures for Apple stock in $2010:^{17}$ Marked are the following points on the chart: $$\begin{array}{|c|c|c|c|c|c|}\hline \text { Jan. 10 } & \text { Feb. 10 } & \text { Mar. 10 } & \text { Apr. 10 } & \text { May 10 } & \text { June 10 } \\\hline 211.98 & 195.46 & 218.95 & 235.97 & 235.86 & 255.96 \\\hline \text { July 10 } & \text { Aug. 10 } & \text { Sep. 10 } & \text { Oct. 10 } & \text { Nov. 10 } & \text { Dec. 10 } \\\hline 246.94 & 260.09 & 258.77 & 294.07 & 317.13 & 317.44 \\\hline\end{array}$$ Calculate to the nearest $0.01 \%$ your annual percentage return (assuming annual compounding) if you had bought Apple stock in February and sold in June.

Finite Mathematics and Applied Calculus

Chapter 2

The Mathematics of Finance

Section 2

Compound Interest

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Here we have a table of apple stock in 2010. What we're gonna do is we're going to find out what the annual industry would be if we bought stock in february and sold it in june. So the first thing we're gonna do is we're gonna take our equation and we're going to actually solve for the rate. Now remember this is a yearly rate and then our time is in years. So we would first divide both sides by the present value. Then to get rid of that power of tea we would take both sides to one over T. And the last thing we would have to do is subtract one from both sides. So in this case we can consider that february is our present value and june is our future value. So we'll have the june price divided by the february price and there were raised to one over t now time is four out of 12 months. So when you divide by 4:12 it's like multiplying by three. So it ends up we get 1.2456. Now that's really a uh an increase of 124.56%

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Stefan Waner, Steven R. Costenoble

Finite Mathematics and Applied Calculus

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Finite Mathematics and Applied Calculus

Stefan Waner, Steven R. CostenobleFinite Mathematics and Applied Calculus

Stefan Waner, Steven R. Costenoble

Finite Mathematics and Applied Calculus