IN JUPYTER NOTE

Step $4$: Reference $1$ in the Wheat and Chessboard Wikipedia page lists an article entitled "A Penny Doubled Every Day for $30$ Days $=$ $$10\mathrm{.}7$M$".$ It turns out that $$10\mathrm{.}7$M is an approximate total. Using your compound$\_$by$\_$period function, compute exactly how much money you would have if you started with a penny $($$$0\mathrm{.}01)$ and doubled it every day for $30$ days. Assign this total after $30$ days to a variable named total$\_$after$\_30.$

Note: this is a little bit different than the wheat and chessboard problem, because there the amount of wheat being placed on a square was doubled every day, but the total amount of wheat on the board is the cumulative sum over all squares up to the current one. The penny$-$doubled$-$every$-$day problem is just a more conventional problem in compound interest, where the balance gets rolled over from day$-$to$-$day.

And here is my code

def compound$\_$by$\_$period$($balance$,$ rate, num$\_$periods$)$:

balances $=[$balance$]$

for n in range$(1,$num$\_$periods$+1)$:

balance $=$ round$($balance $*(1+$rate$),2)$

balances.append$($balance$)$

return balances

balances $=$compound$\_$by$\_$period$(0\mathrm{.}01,1,30)$

total$\_$after$\_30=$sum$($balances$)$