Answer:
$800,579.28
Explanation:
The sum of the monthly payments can be found by the "annuity due" formula:
A = P(1 +n/r)((1 +r/n)^(nt)-1)
where P is the monthly deposit, r is the annual interest rate, n is the number of times per year it is compounded, and t is the number of years.
For this problem, we have ...
A = $400(1 +12/.06)(1(1 +.06/12)^(12·40)-1) = $400(201)(1 -1.005^480 -1)
A = $800,579.28
The account balance after 40 years will be $800,579.28.
