over 12 months, if you earn 0.5 percent a month in your bank account, this would be the same as earning a 6 percent annual interest rate with annual compounding

no, it is not the same

Explanation:

We can use an example to show the difference between monthly compounding interest and yearly compounding. Both accounts will generate interest during 2 years:

the future value with monthly compounding is:

FV = principal x (1 + interest rate) ⁿ

principal = $1,000 interest rate = 0.5% n = 24

future value = $1,000 x (1 + 0.5%) ²⁴ = $1,127.16

the future value with yearly compounding is:

FV = principal x (1 + interest rate) ⁿ

principal = $1,000 interest rate = 6% n = 2

future value = $1,000 x (1 + 6%) ² = $1,123.60

With monthly compounding interest you can earn $3.56 more in 2 years, which actually represents $3.56 / 123.60 = 2.88% more in interests. It may not seem like much, but after a while it can represent a significant amount.