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Gavin wants to save for a car that costs 12,000. He puts1,000 into a bank account earning 3

User Ayaz Aslam
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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%.

User Webthusiast
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