You save for retirement over 30 years by investing $850/month in a stock account that yields 10%. you invest $350/month in a bond account that yields 6%. at retirement you combine both accounts into a new account that yields 5%. how much can you withdraw each month assuming a 25 year withdrawal period?

  $13,287.70

Step-by-step explanation:

The future value of the stock account is computed as the sum of a geometric series. This computation assumes that the annual yield is compounded monthly.

  FV = p((1+r/12)^(12n) -1)/(r/12)

For the stock account, p=850, r=0.10, n=30, so the future values is ...

  FV = 850((1+.10/12)^360-1)/(.10/12)) = 1,921,414.74

For the bond account, p=350, r=.06, n=30, so the future value is ...

  FV = 350((1+.06/12)^360 -1)/(.06/12) = 351,580.26

The combined account value at the end of 30 years is ...

  $1,921,414.74 + 351,580.26 = $2,272,995.00

The monthly payment that can be made over a 25 year period is given by the amortization formula.

  A = P(r/12)/(1 -(1 +r/12)^(-12n))

  = $2,272,995.00(.05/12)/(1 -(1+.05/12)^-300) = $13,287.70

You can withdraw $13,287.70 each month assuming a 25-year withdrawal period.

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.