Final answer:
The effective annual rate (EAR) associated with a 12 percent stated rate when interest compounds continuously is calculated using the formula EAR = e^r - 1. The calculated EAR is approximately 12.75%, but the closest provided choice is (c) 12.68%.
Step-by-step explanation:
To calculate the effective annual rate (EAR) associated with a 12 percent stated rate when interest compounds continuously, we can use the formula for continuous compounding, which is EAR = er - 1, where e is the base of natural logarithms (approximately 2.71828), and r is the stated annual interest rate expressed as a decimal. In this case, with a 12 percent stated rate, or 0.12, the calculation is:
EAR = e0.12 - 1
EAR = 2.718280.12 - 1
EAR = 1.127497 - 1
EAR = 0.127497, or 12.7497%
Therefore, the closest answer among the choices is (b) 12.75%, which is not listed. However, based on the provided choices, the closest value is (c) 12.68%.