2. You are planning to save for retirement over the next 35 years. To do this, you will invest $400 per month in a retirement account. The rate of return for the retirement account is expected to be 6 percent per year. After you retire, you expect that the account will have an annual return of 3 percent. How much can you withdraw each month from your account assuming a 25-year withdrawal period during retirement?
$400 per month will be saved for next 35 years for retirement.
interest rate = 6% compounded monthly
So, Value of account after 35 years can be calculated using FV formula of an annuity,
FV = PMT*((1+r/n)^(n*t) - 1)/(r/n) = 400*((1 + 0.06/12)^(12*35) - 1)/(0.06/12) = $569884.12
So, amount in retirement account after 35 years = $569884.12
thereafter interest rate is 3%
An constant monthly withdrawal is made for next 25 years.
So, this monthly payment can be calculated using PV formula of annuity,
PMT = PV*(r/n)/(1 - (1+r/n)^(-n*t)) = 569884.12*(0.03/12)/(1 - (1+0.03/12)^(-12*25)) = $2702.45
So, Monthly withdrawal of $2702.45 can be made.
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