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An amount is invested at 7.6% per year compounded continuously. What is the effective annual yield?

A) 7.9%
B) 7.47%
C) 7.33%
D) 7.81%

User Ayub Malik
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1 Answer

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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%.

User Vytsalo
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