# Computing initial required cash for retirement

I am trying to create a simple retirement calculator. My inputs are:

• annual income required during retirement (before inflation)
• inflation rate
• number of years of retirement
• yield on investment

I want to calculate the amount I need initially (retirement starting cash).

The total income required over the number of years is

(UPDATE)

``````total required cash =
annual income required *
(1 + inflation rate ^ number of years) / (-inflation rate)
``````

(thanks @JB King)

Then, I believe this is essentially an annuity payment calculation, except that the payment amount increases with inflation each year.

Is this correct?

How can I calculate the initial amount required?

• The Total Required Cash could be simplified into a Geometric series, en.wikipedia.org/wiki/Geometric_series , where a total isn't that hard to compute though this does have more than a few assumptions on it. Jan 19, 2017 at 20:32
• See past answers. One rule-of-thumb approach is to take the average return percentage you expect per year, subtract the inflation percentage you expect per year (assuming it's smaller), and divide your expected cost of living (including ever-increasing medical costs) by that number (getting a much bigger number, of course). Make conservative estimates of all of these, and you'll get an amount that should outlive you. Rule of all-thumbs version, assuming market rate of return stays around 8% and inflation returns to 3%, divide expected yearly cost of living by 0.04. Jan 20, 2017 at 2:27
• 4% has historically been the safe withdrawal rate. If you wanted to be more conservative use 3.5%. Jun 1, 2020 at 11:21

How can I calculate the initial amount required?

If you are looking at easy simple way of doing, you can use a spreadsheet.

Have the below columns:

Opening Balance: [For First year this is Retirement Amount, start with some random number]. For next year/Excel Row, it is previous close Balance.
Yearly Expense: This is your expense, every year to increase this by Inflation %
Interest of Corpus: Is the Yield on Opening Balance.
Closing Balance: Is Opening - Yearly Expense + Interest

Run this for the numbers of rows as per your expectation of life post retirement.

Use Excel Goal-Seek Function to Make the Last row of Closing Balance as Zero by changing the value in First row of Opening Balance.

The value you now have in Opening Balance First Row is the initial retirement amount / corpus you need to save before retirement.

Assume you need \$1 at the beginning of every year adjusted for inflation for k years, and that r is the real rate of interest, i the inflation rate, and n the nominal rate of interest. `(1+r)(1+i)=1+n`.

So you need at the beginning of the first year to sustain you for the next k years `1+(1+i)/(1+n)+..+(1+i)^k/(1+n)^k = 1+1/(1+r)+..+1/(1+r)^(k-1) = [1-1/(1+r)^(k-1)]/[1-1/(1+r)]`

because at the beginning of the second year you will need 1(1+i) which when discounted to the beginning of the first year will yield (1+i)/(1+n), and so on for the subsequent years.

Just multiply the final expression above by your actual annual expense at the beginning of the first year to get the total required corpus of money.