Final answer:
The average rate of return under continuous compounding can be found using the formula A=Pert. For an account that grows from $12,000 to $13,832.03 in 5 years, the average rate of return is approximately 2.9%, which is not listed among the provided choices.
Step-by-step explanation:
To calculate the average rate of return under continuous compounding, we use the formula 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 (as a decimal).
- t is the time in years.
- e is the base of the natural logarithm (approximately equal to 2.71828).
Given that A = $13,832.03, P = $12,000, and t = 5 years, we need to solve for r.
The equation to solve is:
13,832.03 = 12,000e5r
Dividing both sides by 12,000 gives:
1.152669 = e5r
Taking the natural logarithm of both sides gives:
ln(1.152669) = 5r
r = ln(1.152669) / 5
r ≈ 0.02852 or 2.852%
Thus, the average rate of return under continuous compounding is approximately 2.9%, which is not one of the answer choices provided. It seems there might have been a mistake since the correct answer is not listed.