Find the value of the annuity? a^1=2,000,I=0.06, n=5

What is the future value of the annuity?

To find the future value of an annuity, we can use the formula:

Future Value = Annuity Payment × (1 + Interest Rate)^(Number of Periods) - 1) / Interest Rate

Given that a^1 (annuity payment at period 1) is 2,000, I (interest rate) is 0.06, and n (number of periods) is 5, we can substitute these values into the formula and calculate the future value:

Future Value = 2000 × (1 + 0.06)^5 - 1) / 0.06

Let's solve this equation step by step:

Step 1: Calculate (1 + 0.06)^5
Using a calculator, raise 1.06 to the power of 5:
(1.06)^5 = 1.338225

Step 2: Substitute the calculated value back into the formula:
Future Value = 2000 × (1.338225 - 1) / 0.06

Step 3: Simplify the equation:
Future Value = 2000 × (0.338225) / 0.06

Step 4: Calculate the final result:
Future Value = 2000 × 5.6370833333333333333333333333333
Future Value = 11,274.17

Therefore, the future value of the annuity is $11,274.17.