Final answer:
The future value of Nina's deposits after four years at a 5% annual interest rate can be calculated using a simplified annuity formula, which yields $8620.25 when correctly calculated. However, this answer does not match the provided options, indicating there may be a mistake in the provided data or options.
Step-by-step explanation:
To determine the future value of Nina's deposits with compound interest, we can use the formula for the future value of a series of equal payments (annuity) given with an interest rate compounded annually. The formula can be represented as FV = P * [(1 + r)^nt - 1]/r, where P is the individual payment amount, r is the annual interest rate, t is the time in years, and n is the number of payments per year.
In Nina's case, she makes an annual deposit, so n = 1. Therefore, we can simplify the formula to calculate the future value of her investments after four years with an interest rate of 5% using the following steps:
- Identify the variables: P = $2000, r = 0.05 (5%), n = 1, t = 4.
- Plug the values into the annuity formula.
- Calculate the future value.
By computing FV = $2000 * [(1 + 0.05)^4 - 1]/0.05, we get $2000 * [(1.21550625 - 1) / 0.05], which equals $2000 * [0.21550625 / 0.05], and further simplifying we get $2000 * 4.310125, which equals $8620.25. However, this result is not given in the options, suggesting a calculation discrepancy or that the provided options might be incorrect. In practice, it would be ideal to recheck the question and the options provided.