Final answer:
To have $10,000 in ten years with an annual compound interest rate of 10%, an initial deposit of approximately $3,855.43 is needed.
Step-by-step explanation:
The student is asking about the amount of money that needs to be initially deposited in a bank account with compound interest to reach a certain future value, in this case, $10,000, in a specific time frame of ten years with an interest rate of 10% compounded annually.
To find out the initial deposit, or present value, we can use the compound interest formula, which is:
Future Value = Present Value x (1 + rate)^n
In this scenario, the future value (FV) is $10,000, the annual interest rate (r) is 10% or 0.10, and the number of years (n) is 10. We need to solve for the present value (PV). Rearranging the formula, we get:
Present Value = Future Value / (1 + rate)^n
Substituting the given values:
Present Value = $10,000 / (1 + 0.10)^10
Using a calculator:
Present Value = $10,000 / (1.10)^10 = $10,000 / 2.59374 ≈ $3,855.43
Therefore, an initial deposit of approximately $3,855.43 is required to have $10,000 in ten years with an annual compound interest rate of 10%.