There are 10 billion dollars circulating around. 50 Million (0.5% of total amount) is taken in everyday and replaced by new money. When the money is taken in everyday the 50 million is unbiased as to whether it is newly released or old money and is replaced regardless.
My understanding is you need to know the partial sum of the previous term (n-1) in order to determine n.
Total amount on Day 1: 50 million added
Day 2: 99.5% of day 1's "new money" retained, 50 million added
Day 3: 99.5% of day 2's "new money" retained, 50 million added etc. etc.
This seems like it works out to
(SIGMA) 50 000 000 + Sn-1
n = 1
where Sn-1 is the partial sum of the nth-1 term.
Is there no way to turn this into a function, for example if i wanted to know how much new money was in circulation on the nth day and did not know the n-1 day's total "new" money.
P.S. I was able to determine a function in Excel, for example C1's cell would read: =0.995*B2+50000000, is the computer able to determine/display the nth amount?