Taking monthly rate and extrapolating to annual, given monthly compounding

[johnjohn]

Online question, mb there is some error in how it is phrased.

Assume that all 12 months have the same return as the simple monthly return between the end of December 2004 and the end of January 2005 (which is -13.41%). What would be the annual return with monthly compounding in that case?

So, monthly rate = -13.41%
Compounded monthly, 12 months, 1 year

= -82.22%??

How do I set this formula up?

Edit: Is it just (1-.1341)^12-1....sure enough...I would love a conceptual of WHY that works, if that makes any sense.

I have tried permutations of compound interest, I thought I understood this, apparently not.

Thank you so much for any assistance.

 

[Ishuda]

...
Edit: Is it just (1-.1341)^12-1....sure enough...I would love a conceptual of WHY that works, if that makes any sense.
...

To walk though the general solution: Suppose the interest rate, expressed as a decimal, for the period (in this case for a month) is i and suppose we started with an initial principle P. At the end of the first period we would have
P₁ = P (1+i)
At the end of the second period we would have
P₂ = P₁ (1+i) = P (1+i)²
Continuing in this manner we have
P_n = P_n-1 (1+i) = P (1+i)ⁿ
So at the end of n periods the effective interest rate would be
i_e = 100 * (P_n - P) / P = 100 ( (1+i)ⁿ - 1 )

where i_e is the effective interest rate expressed as a percent.

That is equivalent to what you have if n=12 (except I get -82.23%)