Can someone confrim my Futurama compoud interest?

[Themohawkninja]

So, I've been watching Futurama lately, and I am aware that the creators are quite fond of mathematics, so I have been probing almost every number that I hear in the show.

In one of the episodes, Fry finds out that he is extremely rich, as his bank account has been accruing interest for the last millenia. According to the bank teller, Fry's original balance was $0.93, compounded at 2.5% for an undefined period for 1000 years, which gives him a current balance of $4.3 billion.

Just for fun, I decided to see if the creators actually bothered to make the numbers "realistic" in the sense that the number of times compounded per year is a normal amount of money.

I did the math, but want somebody to check it.

MATH: (by the way, 'tth root of (A)' is the same as 'A^(1/t)' in case the two t's in a row were confusing)

Solving: A=p(1+r)^nt for n

-tth root of (A)=p(1+r)^n

-tth root of (A)/p=(1+r)^n

-(log base 1+r of (tth root of (A)))/p = n

When I plug it all in to Wolfram Alpha as "(log base (1+0.025) of the one thousanth root of (4.3*10^9))/0.93", out pops 0.9659... which is probably close enough to 1 to count as it being yearly compounded if you ask me.

[Tiberion]

Savings account compound on different terms, sometimes daily, sometimes yearly.

$0.93 with an APY of 2.5% for 1000 years:

Compounded daily: 66 billion

Compounded yearly: 49 billion

Interestingly, things don't really start to snowball until more than halfway through the period. Yearly compounding breaks the 10,000/year interest mark around 520 years, but by the end you're making over a billion per year in interest. Must be nice.

Honestly the suspension of belief portion of this particular cartoon comes in the fact that a bank would leave an account open for 1000 years with no activity. At some point he'd be declared dead and the assets given to a family member or the government. But you know, its Futurama, so its cool.

Link

[Themohawkninja]

Savings account compound on different terms, sometimes daily, sometimes yearly.

Right, that's what I was solving for.

[Will Fawkes]

Given Nibbler arranged for Fry to be frozen in the first place it wouldn't be hard to follow his people would make provisions to make the bank just leave that account alone.

What scratches my head is that most banks, at least the ones I've dealt with, have a minimum balance along with fees which should have nuked Fry's savings fairly quickly. However if the above is true then exceptions might have been made or... something along the lines of 'wait until account has x funds then start drawing from it) So you get 4.3 billion instead of 46/600ish billion.