🚀 go-pugleaf

I'm coding a financial software product and am stumped in finding a
particular formula.

I am trying to solve for the present value of a series of withdrawals from
an interest earning account.  I can't seem to find a formula that does
this and accounts for inflation.

If I have an invested amount of money earning interest at 8% annually and
want to withdraw $1000 per month from that account for 10 years, or 120
months, I know that I will withdraw a total of $120,000 over the full 120
months.  The first problem is to determine the present value of the
required $120,000 in consideration of its continuing to earn interest on
the balance after each monthly withdrawal.

The second problem arises when I have to account for inflation on the
monthly withdrawal amount.  If inflation is 4% and I want my $1000 per
month to grow with inflation, the amount of the withdrawal becomes
dynamic.  The formula which I am aware of to determine the present value
of the series of withdrawals assumes that each withdrawal is the same
amount, so it can not be used if the withdrawals are changing, even if
they are changing at a fixed annual rate.

Is anyone aware of a formula to solve for this problem?  Any help would be
very greatly appreciated.

Thank you.

Dan Amberman
dan@aait.com