Final answer:
The effective annual yield for an investment compounded continuously at a rate of 7.6% per year is approximately 7.47%.
Step-by-step explanation:
To calculate the effective annual yield for an investment compounded continuously at a rate of 7.6% per year, we can use the formula A = P * e^(rt), where A is the future value of the investment, P is the principal amount, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years. Since we want to find the effective annual yield, we need to solve for r.
Given that the interest rate is 7.6%, we can plug in the values and solve for r:
A = P * e^(rt)
A/P = e^(rt)
e^(rt) = A/P
rt = ln(A/P)
r = ln(A/P)/t
Substituting the values, we get:
r = ln(A/P)/t = ln(1 + 0.076)/1 = 0.0747
Therefore, the effective annual yield is approximately 7.47%.