Math help please compound interest

So i'm doing a question on compound interest, and i'm so confused, just wondering if you guys can help me out, the question is short, just explaining my work/attempt makes it look long:

if an investment of $400 is getting interest at 5%, compounded quarterly, that is, every 3 months, what is the equation for this function? A(t) is the final amount and t is time in years
this is my attempt:
A(t) = 400 x (1 +0.05) ^ 4t
A(t) = 400 x 1.05^4t

how i interpreted it was that he's getting 5% every 3 months, so yearly, he would be getting 4t. if i put in a number for t, it also works out:
400 x 1.05 ^ 4(0.25) <-----1 compound period, 3 months
= 420

and then to check
400 x 0.05 = 20 <--- 5% of 400
400 + 20 = 420

they're the same, right?
but when i look on a math help website, it says that i should be dividing the interest rate by 4?! like this:

A(t) = 400 x (1 + 0.05/4) ^ 4(0.25)

i'm very confused, please help :S

A(t) = 400(1+ (0.05)/4 ) ^(4t) is correct.

The rate needs to match the compounding period.

Whenever you are given an interest rate you assume it is yearly , unless told otherwise.

So you need to get a quarterly interest rate from 5% per annum. So you divide by 4.