# Calculating the yearly interest?

i am doing a task where i met the following problem:

How can I calculate the yearly interest, with at least three decimals, when the monthly interest is 3.4%?

For me it seems hard to figure out a way to return three decimals in this case. Sorry for may asking stupid.

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For one month you have $y_{n+1}=(1+r)y_n$, where $r=3.4\,\%=0.034$. Therefore $$y_{n+12}=(1+r)^{12}y_n=1.493641\ldots y_n=(1+0.493641)y_n,$$ therefore the yearly interest is $49.364\,\%$.