Final answer:
The average rate of return under continuous compounding can be determined using the formula A = Pe^(rt). In this case, the rate is approximately 5.8%.
Step-by-step explanation:
The average rate of return under continuous compounding can be determined using the formula A = Pe^(rt), where A represents the final amount, P represents the principal amount, e is Euler's number (approximately 2.71828), r is the annual interest rate, and t is the time in years. In this case, P = $25,000, A = $182,790.53, and t = 15 years. By rearranging the formula, we can solve for r:
$182,790.53 = $25,000 * e^(15r)
Dividing both sides by $25,000 gives us:
e^(15r) = 7.31162
Taking the natural logarithm of both sides gives us:
15r = ln(7.31162)
Dividing both sides by 15 gives us the value of r:
r = ln(7.31162)/15 ≈ 0.0577
Converting the decimal to a percentage, the average rate of return under continuous compounding is approximately 5.8%.