A deposit of $10,000 is placed in a savings account for 4 years. The interest for the account is compounded continuously. At the end of 4 years, the balance in the account is $12,068.34. What is the annual interest rate for this account. Round your answer to one decimal places.

A) 75.2%
B) 2.0%
C) 5.2%
D) 4.7%
E) none of these

Question

Faith Moulic · Accepted Answer

Final Answer : D, Explanation :  The formula for continuously compounded interest is A = Pe^(rt), where A is the final amount, P is the principal (initial amount), e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.In this case, A = $12,068.34, P = $10,000, and t = 4 years. So, we can solve for r:12,068.34 = 10,000 * e^(4r)1.206834 = e^(4r)ln(1.206834) = 4rr = ln(1.206834) / 4r ≈ 0.047Therefore, the annual interest rate for this account is approximately 4.7%.

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