Paula invests $\$10,\!000$ at the start of a 5 year period at an interest rate of $10\%$. At the end of those 5 years, how much is her investment worth if the interest is compounded quarterly?  Express your answer rounded to the nearest cent.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Paula invests $\$10,\!000$ at the start of a 5 year period at an interest rate of $10\%$. At the end of those 5 years, how much is her investment worth if the interest is compounded quarterly?  Express your answer rounded to the nearest cent.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\$16,\!386.16
Paula invests $\$10,\!000$ at the start of a 5 year period at an interest rate of $10\%$. At the end of those 5 years, how much is her investment worth if the interest is compounded quarterly?  Express your answer rounded to the nearest cent.
train