Final answer:
To calculate the effective annual interest rate, use the formula EAR = (1 + r/n)^n - 1, where r is the interest rate per compounding period and n is the number of compounding periods per year. For a 1-year continuously compounded interest rate of 12%, the effective annual interest rate can be calculated using the formula EAR = e^0.12 - 1.
Step-by-step explanation:
The effective annual interest rate can be calculated using the formula:
EAR = (1 + r/n)n - 1
Where:
EAR is the effective annual interest rate
r is the interest rate per compounding period, in decimal form
n is the number of compounding periods per year
In this case, the interest rate is 12% and it is compounded continuously, which means that the number of compounding periods per year is infinite. Therefore, the formula can be rewritten as:
EAR = e0.12 - 1
Using a calculator or a mathematical software, we can calculate the value of e0.12 to get the effective annual interest rate.
To find the effective annual interest rate for a continuously compounded interest rate of 12%, the formula EAR = er - 1 is used, resulting in an EAR of approximately 12.75%.
The question relates to the conversion of a continuously compounded interest rate to an effective annual interest rate (EAR). When we have a continuously compounded interest rate of 12%, we can use the formula EAR = er - 1, where e is the base of natural logarithms (approximately 2.71828), and r is the annual interest rate as a decimal.
Plugging in 12% (or 0.12 as a decimal) into the formula gives EAR = e0.12 - 1. Calculating this, we get EAR = 2.718280.12 - 1, which is approximately 0.1275 or 12.75%. This means the effective annual interest rate when compounded continuously at 12% is roughly 12.75%.