Final answer:
To have $10,000 in ten years with a 10% interest rate compounded annually, you would need to deposit approximately $3,854.56 into the bank account.
Step-by-step explanation:
To determine how much money you need to put into a bank account that pays 10% interest compounded annually to have $10,000 in ten years, we can use the compound interest formula: A = P(1 + r/n)^(nt). In this formula, A represents the future amount, P represents the principal amount (the initial deposit), r represents the yearly interest rate (expressed as a decimal), n represents the number of times the interest is compounded per year, and t represents the number of years.
So, in this case: A = $10,000, r = 0.10 (10% expressed as a decimal), n = 1 (compounded yearly), and t = 10. Plugging these values into the formula, we get: $10,000 = P(1 + 0.10/1)^(1*10).
To solve for P, we need to isolate it on one side of the equation. By dividing both sides of the equation by (1 + 0.10/1)^(1*10), we can find the value of P. The final equation will be: P = $10,000 / (1 + 0.10/1)^(1*10). Evaluating this equation will give us the value of P, which is approximately $3,854.56.