Final answer:
To find the APR of a stock investment, calculate the percentage increase in stock value and adjust for a one-year period. Since the investment period was six months, double the six-month return to annualize it. The EAR is the same as the APR in this context as there's no compounding effect to consider.
Step-by-step explanation:
You bought a stock six months ago for $78.82 per share and the current share price is $83.59. To calculate the annual percentage rate (APR) and effective annual rate (EAR) of your investment, you need to look at the increase in stock value over the holding period. Since the stock paid no dividends, the return on investment is entirely through capital gains.
The calculation for the APR is straightforward; it's the percentage increase in stock value over one year. Since you've held the stock for half a year, you would double the six-month return to annualize it. The increase in value is $83.59 - $78.82 = $4.77 per share. The six-month return is therefore ($4.77 / $78.82) × 100%, which annualizes to (($4.77 / $78.82) × 100%) × 2 for the APR.
The EAR takes into account the effect of compounding, which isn't directly applicable here since there were no dividends or additional investments during the period. However, for a six-month period, EAR would mathematically be the same as APR. Therefore, EAR would typically be used if there were more frequent compounding periods (e.g., quarterly dividends) over the investment period.