Final answer:
The question is about calculating the future value of an investment with compound interest. Using the compound interest formula, you can find out how much money will be in the account after a given number of years. For a goal of $10,000 in ten years at 10% interest compounded annually, the initial deposit required can be calculated using the formula rearranged to solve for the principal.
Step-by-step explanation:
The student's question pertains to compounded interest, which is a key concept in Mathematics dealing with how investments grow over time. To calculate the future value of an account with compound interest, we use the formula: Future Value = Principal × (1 + (Interest Rate / Number of Compounding Periods per Year))^(Number of Compounding Periods per Year × Number of Years).
For example, if Charlie has an account with a principal amount and wants to know the amount after a certain number of years with an annual interest rate compounded monthly, he would plug in the appropriate numbers into the formula mentioned above.
To address question 39 directly, where the goal is to have $10,000 in ten years with an annual compounded interest rate of 10%, you would need to rearrange the formula to solve for the principal: Principal = $10,000 / (1 + 0.10)^10.