Final answer:
Investing $2,000 a year for 20 years at an 11 percent annual interest rate would result in approximately $92,828.57 after 20 years, using the future value annuity formula.
Step-by-step explanation:
To calculate the future value of an annuity where $2,000 is invested each year for 20 years at an annual interest rate of 11%, we use the future value of an annuity formula:
FV = P * [((1 + r)^n - 1) / r]
Where:
FV = Future Value of the annuity
P = Payment amount per period ($2,000)
r = Periodic interest rate (11% or 0.11)
n = Total number of payments (20)
Plugging in the numbers, we get:
FV = 2000 * [((1 + 0.11)^20 - 1) / 0.11]
FV = 2000 * [(1.11^20 - 1) / 0.11]
FV = 2000 * [(6.105571 - 1) / 0.11]
FV ≈ 2000 * [46.41428364...]
FV ≈ $92,828.57
Therefore, after 20 years, you would have approximately $92,828.57 in your annuity account.