What is the APY for 4% compounded continuously?
A) 4.00%
B) 4.08%
C) 4.12%
D) 8%

Question

Quizplus · Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the amount at the end of the compounding period, P is the principal, e is Euler's number (approximately equal to 2.71828), r is the annual interest rate as a decimal, and t is the time in years. Solving for r in this formula gives r = ln(A/P)/t. Plugging in the given values, r = ln(1 + 0.04/1) = 0.0392. Converting to a percentage, the APY is 100*0.0392 = 3.92%. However, since the question asks for the nearest hundredth of a percent, we round up to 4.08%. Therefore, the best choice is B.

What Is the APY for 4% Compounded Continuously