Question

# 2. You are planning to save for retirement over the next 35 years. To do this,...

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?

Given that,

\$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.