Comparing Future Value. Calculate the future value of a retirement account on which you deposit $2000.00 a year for 30 years with an annual interest rate of 7%.

To calculate the future value of a retirement account with annual deposits and an annual interest rate, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:
FV = Future Value
P = Annual deposit
r = Annual interest rate (as a decimal)
n = Number of years

In this case:
P = $2000.00
r = 0.07 (7% expressed as a decimal)
n = 30

Using the formula, plug in these values to calculate the future value:

FV = 2000 * [(1 + 0.07)^30 - 1] / 0.07

Now, let's calculate it step by step:

Step 1: Calculate (1 + r)^n:
(1 + 0.07)^30 = 3.386002

Step 2: Subtract 1 from the result of Step 1:
3.386002 - 1 = 2.386002

Step 3: Multiply the result of Step 2 by the annual deposit:
2.386002 * 2000 = 4772.004

Step 4: Divide Step 3 by the interest rate (r):
4772.004 / 0.07 = 68171.4857

Therefore, the future value of the retirement account after 30 years, with annual deposits of $2000.00 and an annual interest rate of 7%, would be approximately $68,171.49.