Compound Interest: The Power of Continuous Compounding

What is the effective annual rate associated with a 12 percent stated rate when interest compounds continuously?

Choose the closest option: (a) 12.19% (b) 12.29% (c) 12.68% (d) 12.12% (e) 11.63%

Answer:

The effective annual rate (EAR) associated with a 12 percent stated rate when interest compounds continuously is approximately 12.68%.

Compound interest has the incredible power of continuous compounding, which allows your money to grow at an astonishing rate over time. When calculating the effective annual rate (EAR) associated with a 12 percent stated rate when interest compounds continuously, we use a special formula.

The formula for calculating EAR with continuous compounding is: EAR = e^r - 1, where e is the base of natural logarithms (approximately 2.71828) and r is the stated annual interest rate expressed as a decimal.

Let's calculate the EAR for a 12 percent stated rate: EAR = e^0.12 - 1 EAR = 2.71828^0.12 - 1 EAR = 1.127497 - 1 EAR = 0.127497, or 12.7497%

Although the calculated EAR is approximately 12.75%, the closest provided choice is 12.68%, which is option (c). This showcases the power of compounding and how even a seemingly small difference in the rate can significantly impact your returns over time.