Question

Suppose that $12,000 is invested in a bond fund, and the account grows to $13,832.03 in 5 yr. Part 1 of 2(a) Use the model A=Pe to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. The average rate of return under continuous compounding is approximately%

a) 4.0%
b) 5.5%
c) 8.7%
d) 10.3%

Answer 1

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.