Final answer:
To find the average rate of return under continuous compounding for Eddie's investment, we use the continuous compounding formula and solve for the interest rate. The correct answer is approximately 4.57%, so the nearest option is 4.1%.
Step-by-step explanation:
To calculate the average rate of return under continuous compounding, we can use the formula for continuous compounding interest, which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), t is the time the money is invested for in years, and e is Euler's number (approximately 2.71828).
In this question, Eddie's initial investment (P) is $12,000 and the investment grew to (A) $13,733.06 in (t) 3 years. We need to find the interest rate (r).
The equation becomes: $13,733.06 = $12,000er(3). To solve for r, we will first divide both sides by $12,000, giving us 1.14442167 = e3r. We now take the natural logarithm of both sides to get ln(1.14442167) = 3r. Solving for r gives us r = ln(1.14442167)/3, which approximately equals 0.0457 or 4.57%, when rounded to the nearest tenth of a percent. Answer choice (a) 4.1% is the closest option.