Find the periodic withdrawals for the annuity of $400,000 at 4%, paid out monthly for 16 years. (Assume end-of-period withdrawal and compounding at the same intervals as withdrawal. Round your answer to the nearest cent.)
The formula is A=P(1+i)^n
A is the answer
P is the money
i is the interest rate
n is the number of years.
Remember, "paid out monthly."
757.25
To find the periodic withdrawals for an annuity, we can use the formula for the present value of an annuity. The formula is:
P = PMT x [(1 - (1 + r/n)^(-nt)) / (r/n)]
Where:
P = Present value of the annuity
PMT = Periodic withdrawal
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
In this case, we need to find PMT (the periodic withdrawal), given P (the present value), r (annual interest rate), n (number of compounding periods per year), and t (number of years).
Given:
P = $400,000
r = 4% or 0.04 (as a decimal)
n = 12 (monthly compounding)
t = 16 years
Substituting these values into the formula, we get:
$400,000 = PMT x [(1 - (1 + 0.04/12)^(-12*16)) / (0.04/12)]
To find PMT, we rearrange the equation:
PMT = P / [(1 - (1 + r/n)^(-nt)) / (r/n)]
Now, let's calculate PMT using this formula.
PMT = $400,000 / [(1 - (1 + 0.04/12)^(-12*16)) / (0.04/12)]
PMT ≈ $2,708.28
Therefore, the periodic withdrawals for the annuity would be approximately $2,708.28 (rounded to the nearest cent).