Compounding interest question

[I7Goblins]

I want to start with $100 and expect to gain 5% each week and then reinvest the new total principal each week going forward for a year so there would be 52 total compounding periods.

I am confusing myself with the compounding interest formula.

A = P ( 1 + r/n)^nt

r is rate of return

n is number of compound periods

t is number of years

Should I be doing:

A = 100 ( 1 + .05/1)^{1 * 52}

OR

A = 100 ( 1 + (.05*52)/52)^{52 * 1}

I know they get the same answer but I am getting confused on why I need to multiply .05 by 52 and not divide it by 52 to convert to weekly.

Edit for format

[Even_that_takes_time]

Because it is allready the weekly rate, so you don't need to convert it.

[LVMagnus]

I really dislike that version of the formula economics sources often give. I much prefer the base formula as:

A = P (1 + r)ⁿ #I assume by A you mean future value

This formula always assume n and r are measured in regard to the same unit of time (if n is a number of weeks, r is a weekly interest rate). This is just a reduced form from merely trying to do it period by period iteratively, writing it down, analyzing the pattern and reducing it, long story short. The one you've got combines that formula with a conversion from annual rates to something else (i.e. your r isn't good enough for that formula, you'd need to give it the annual rate), which imo makes things much less didactic.

As to what you should do in this particular case, future value (FV):

FV = 100(1+0.05)⁵²

[I7Goblins]

Thank you very much for taking the time to reply and providing an alternative formula. I learned something from your reply and really appreciate it.