To calculate the required deposit amount, we can use the formula for the future value of an annuity:
FV = PMT * [(1 + r/n)^(n*t) - 1]/(r/n)
where FV is the future value of the annuity, PMT is the payment amount, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years.
In this case, we have:
PMT = $1000 per month
r = 0.08 (8% annual interest rate)
n = 12 (compounded monthly)
t = 12 years
We need to solve for the future value, which represents the total amount of money that needs to be deposited to generate the $1000 monthly payment for 12 years. Plugging in the numbers, we get:
FV = $1000 * [(1 + 0.08/12)^(12*12) - 1]/(0.08/12) ≈ $149,139.77
Therefore, the retired officer would need to deposit approximately $149,139.77 in an account earning 8 percent compound monthly to pay a $1000 monthly payment for 12 years.