Final answer:
To have $10,000 in ten years in a bank account with a 10% annual interest rate compounded annually, you need to deposit approximately $4,046.90.
Step-by-step explanation:
To find out how much money you need to deposit into a bank account to have $10,000 in ten years with an annual interest rate of 10% compounded annually, you can use the formula for compound interest. The formula is A = P(1 + r/n)^(nt), where A is the future amount, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times that interest is compounded per year, and t is the number of years. Plugging in the values, we have 10000 = P(1 + 0.1/1)^(1*10).
Solving for P, we divide both sides of the equation by (1 + 0.1/1)^(1*10), which simplifies to 10000/(1.1^10). Using a calculator, we find that the approximate value of P is $4,046.90. Therefore, you need to deposit about $4,046.90 into the bank account to have $10,000 in ten years.