Final answer:
The student asked about the future value of an annuity with yearly deposits of $2,000 at an interest rate of 5.5%, compounded annually after 10 years. To solve, we use the future value of an annuity formula with the provided values to calculate the total amount available for withdrawal after the 10th deposit, assuming annual compounding.
Step-by-step explanation:
The subject of this question is mathematics, specifically dealing with concepts of finance and the future value of annuities. The question pertains to the grade range suitable for college level, as it involves the application of financial formulas and understanding of concepts such as compound interest and annuities. To solve the problem, we will use the future value of an annuity formula:
FV = P × { [(1 + r)^n - 1] / r }
Where:
- FV is the future value of the annuity.
- P is the periodic payment amount.
- r is the interest rate per period.
- n is the number of periods.
In this scenario, the periodic payment P is $2000, the interest rate r per year is 5.5% or 0.055, and the number of years n is 10. Plugging these values into the formula:
FV = 2000 × { [(1 + 0.055)^10 - 1] / 0.055 }
Thus, calculating the above expression will give us the total amount that can be withdrawn immediately after the 10th deposit. It's important to note that this scenario assumes the interest is compounded annually. Then, the compounded interest is added annually to the principal sum of each deposit. As the deposits are made at the end of each period (yearly), this is an example of an ordinary annuity.
Please remember, the actual amount will depend on how the bank compounds the interest. If it's not annually, the formula and the final amount might differ.