Question

A bank pays 8 percent nominal on an investment. If compounding is 6 times per year, find the effective annual rate written as a percentage, to two decimal points of accuracy. (DO NOT include the % sign. For example, if your calculated answer is 99.99%, enter 99.99 .)

Answer 1

The effective annual rate (EAR) with 8% nominal interest and compounding 6 times per year is calculated using the EAR formula (1 + r/n)ⁿ - 1, resulting in an EAR of 8.31.

Step-by-step explanation:

To find the effective annual rate (EAR) when a bank pays a nominal interest rate of 8 percent with compounding occurring 6 times per year, we use the formula for EAR which is: EAR = (1 + r/n)ⁿ - 1, where 'r' represents the nominal interest rate as a decimal and 'n' represents the number of compounding periods per year.In this case, r = 0.08 (8 percent written as a decimal) and n = 6.Plugging the values into the formula gives us: EAR = (1 + 0.08/6)⁶ - 1EAR = (1 + 0.013333...)⁶ - 1EAR = 1.013333...⁶ - EAR = 1.083141... - 1EAR = 0.083141... or 8.31%So, the effective annual rate when compounding 6 times per year is 8.31 (to two decimal points).