You are planning to retire 40 years from now. If your retirement account pays an annual rate of 6% compounded monthly and you start making a monthly contribution of $400 a month today, how much will you have when you retire in 40 years

  $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.

a

explanation:

reducti0n

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