I invest 150$ in a bank that pays me 5% per year. How much do I have after 11 years?

Step 1 ：The problem is asking for the total amount of money after 11 years of investment with an annual interest rate of 5%. This is a compound interest problem, where the interest is added to the initial amount each year, and the next year's interest is calculated based on the new total.

Step 2 ：The formula for compound interest is: \(A = P(1 + \frac{r}{n})^{nt}\) where: \(A\) is the amount of money accumulated after \(n\) years, including interest. \(P\) is the principal amount (the initial amount of money). \(r\) is the annual interest rate (in decimal). \(n\) is the number of times that interest is compounded per year. \(t\) is the time the money is invested for in years.

Step 3 ：In this case, \(P = 150\), \(r = 5% = 0.05\) (in decimal), \(n = 1\) (since interest is compounded annually), and \(t = 11\) years. We can substitute these values into the formula to find the total amount after 11 years.

Step 4 ：Substituting the values into the formula, we get \(A = 150(1 + \frac{0.05}{1})^{1*11}\)

Step 5 ：Solving the equation, we get \(A = 256.5509037174471\)

Step 6 ：Final Answer: The total amount after 11 years is approximately \(\boxed{256.55}\)