I am working on retirement planning and having a problem working out an equation. I have a good model with all retirement funds and projections including deferred growth annuity equations. I am trying to figure out the correct growth factor to include for the annuity when there are other income streams involved.
Usually, retirement income comes from at least 3 sources (i) a Retirement Account distribution (401k,bonds,etc) treated as an annuity, and Other Income not in the annuity including (ii) a Pension that might have a fixed payment and (iii) Social Security that gets an annual COL increase.
Examples:
A \$6,000 required total first month's income needs to grow at 4% inflation.
Case 1 -trivial
A single source of income means the withdrawal needs to grow at 4%.
Case 2 -simple
Two sources of income at \$3,000 each. One fixed growing at 0%.
This means the withdrawal from the other needs to grow at 8%.
Case 3 -difficult
Two sources of income. One of \$4,000 growing at 2%. What is the growth required of the other \$2,000 income stream to give the overall total of 4%?
Case X, -I'm really stuck
Three sources of income. A fixed pension of \$1,200 grows at 0%. A SS payment of \$2,200 grows at 3%. What is the growth required of the other \$2,600 income stream from the annuity to give the overall total 4%?
That unknown growth rate is what I need to calculate to put into the annuity equation.
I know this is a weighted percentages problem.
I know that simple arithmetic does not work with percentages.
I can figure it out for individual cases.
But I am looking for an equation I can put in a spreadsheet to run different scenarios.
Is there a simple equation?
I have not been able to come up with one.