Dr. Zaius invests $\$10,000$ in a CD with an annual interest rate of $4\%$ that compounds semi-annually (twice a year).  After six months, he rolls over the CD into another CD with an annual interest rate of $5\%$ that also compounds semi-annually.  After six months in the second CD, how much does Dr. Zaius have, in dollars?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Dr. Zaius invests $\$10,000$ in a CD with an annual interest rate of $4\%$ that compounds semi-annually (twice a year).  After six months, he rolls over the CD into another CD with an annual interest rate of $5\%$ that also compounds semi-annually.  After six months in the second CD, how much does Dr. Zaius have, in dollars?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
10455
Dr. Zaius invests $\$10,000$ in a CD with an annual interest rate of $4\%$ that compounds semi-annually (twice a year).  After six months, he rolls over the CD into another CD with an annual interest rate of $5\%$ that also compounds semi-annually.  After six months in the second CD, how much does Dr. Zaius have, in dollars?
train