Alan saved 500 dollars in a bank account that compounds 3 percent annually.  Assuming there are no other transactions, after 10 years, how much is in Alan's bank account?  (Give your answer to the nearest dollar.)
I know that compound interest means that each year, the interest is calculated based on the current balance, not the initial deposit. So, to find the balance after 10 years, I need to apply the interest rate 10 times, each time adding it to the previous balance. This sounds like a job for exponentiation, since it involves repeated multiplication. The formula for compound interest is A = P(1 + r)^t, where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), and t is the number of years. Plugging in the given values, I get A = 500(1 + 0.03)^10. To simplify this, I can use the order of operations: parentheses, exponents, multiplication and division, and addition and subtraction. Inside the parentheses, I have 1 + 0.03, which is 1.03. Then, I need to raise 1.03 to the 10th power, which I can do with a calculator. I get 1.03^10 = 1.34391638. Next, I need to multiply this by 500, which gives me 671.95819. Finally, I need to round this to the nearest dollar, which means looking at the digit after the decimal point. Since it is 9, which is 5 or more, I need to round up. Therefore, the final answer is 672 dollars. 