If the new currencies of one day are not changed with the new currencies of the following days, then you need to solve . The solution is
A country has 5 billion in paper currency. Each day, 30 million is deposited into banks and the same amount loaned out. There is a regime change and each day the 30 million is replaced by a new currency when loaned out. How long will it take for 90% of the currency to be new?
I know the answer, but I'm having trouble arriving at it.