Final answer:
To have $10,000 in ten years with 10% interest compounded annually, you need to put approximately $3,174.13 into the bank account.
Step-by-step explanation:
To determine how much money you need to put into a bank account with 10% interest compounded annually to have $10,000 in ten years, you can use the formula for the future value of an annuity:
Future Value = P * (1 + r)^n
Where P is the initial deposit, r is the interest rate, and n is the number of years. In this case, the future value is $10,000, and the interest rate is 10%. Plugging these values into the formula, we get:
$10,000 = P * (1 + 0.10)^10
To solve for P, we can divide both sides of the equation by (1 + 0.10)^10:
P = $10,000 / (1 + 0.10)^10
Using a calculator, we can calculate that P is approximately $3,174.13.