Question

Suppose that $25,000 from a retirement account is invested in a large cap stock fund. After 15 yr, the value is $182,790.53. Part: 0/2 Part 1 of 2 (a) Use the model A=Pe ^rt to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps. The average rate is approximately %.

Answer 1

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%.