Question

Find the effective rate corresponding to the given nominal rate. (Use a 365 -day year. Round your answer to two decimal places.) ( 4 % / ) year compounded quarterly ( % / y e a r )

Answer 1

The effective annual rate (EAR) corresponding to a 4% nominal rate compounded quarterly is approximately 4.06% per year.

Step-by-step explanation:

The question pertains to finding the effective annual rate (EAR) when given a nominal annual interest rate that is compounded quarterly. To compute the EAR from a nominal rate that is compounded quarterly, we use the formula:

EAR = (1 + (nominal rate / number of compounding periods))number of compounding periods - 1

In this case, the nominal rate is 4% (or 0.04 as a decimal) and the number of compounding periods is 4 (since it's compounded quarterly). Plugging the values into the formula, we get:

EAR = (1 + (0.04 / 4))4 - 1

EAR = (1 + 0.01)4 - 1

EAR = 1.014 - 1

EAR = 1.04060401 - 1

EAR = 0.04060401, or 4.06% when rounded to two decimal places.

Therefore, the effective annual rate corresponding to 4% nominal rate compounded quarterly is approximately 4.06% per year.