Final answer:
To have $10,000 in a bank account in ten years with a 10% annual compound interest rate, you need to deposit approximately $3,855.97 today.
Step-by-step explanation:
Calculating Initial Deposit for Future Savings
To determine how much money you need to deposit in a bank account with a 10% annual compound interest rate to have $10,000 in ten years, the formula for compound interest is applied:
Future Value (FV) = Present Value (PV) × (1 + interest rate (r))number of periods (n)
Rearranging the formula to solve for the Present Value (initial deposit), we get:
Present Value (PV) = Future Value (FV) / (1 + interest rate (r))number of periods (n)
For the given problem:Future Value (FV) = $10,000
interest rate (r) = 10% or 0.10
number of periods (n) = 10 year
Therefore, the initial deposit needed is:Present Value (PV) = $10,000 / (1 + 0.10)10Calculating the above expression, we find the Present Value required to be approximately:Present Value (PV) = $10,000 / (1.10)10 = $10,000 / 2.5937 = $3,855.97
Hence, you would need to deposit approximately $3,855.97 in a bank account today to have $10,000 in ten years with a 10% annual compound interest.