Final answer:
The periodic deposit needed to achieve a financial goal of $10,000 in ten years with a 10% annual compound interest is $627.41. None of the provided options correctly matches this calculation.
Step-by-step explanation:
To determine the periodic deposit required to achieve a financial goal of having $10,000 in ten years with an interest rate of 10% compounded annually, we need to use the formula for the future value of an annuity:
FV = P × {[(1 + r)^n - 1] / r}
Where FV is the future value, P is the periodic deposit, r is the interest rate per period, and n is the number of periods.
For a future value (FV) of $10,000, an interest rate (r) of 10% or 0.10, and a ten-year period (n) of 10, we can solve for P (the periodic deposit).
Let's plug the given values into the formula:
$10,000 = P × {[(1 + 0.10)^10 - 1] / 0.10}
Solving for P gives us:
P = $10,000 / {[(1 + 0.10)^10 - 1] / 0.10} = $10,000 / 15.937 = $627.41
Therefore, the periodic deposit needed is $627.41. Since the options provided don't match this result, it seems there might be a typo or mistake in the question or provided options.