Given the interest rate, the starting ammount, and the time period, and assuming that the interest rate remains the same, is it possible to calculate the ammount of money you will have at the end of that time period using simple algebra? If so, what’s the formula?
This isn’t homework, honest! I want to find out if the ammount of money Fry makes from his $.93 in the Futurama episode A Fishfull of Dollars is accurate.
(1+r)[sup]n[/sup] where r is the rate of interest and n isthe number of times it is compounded. Then muliply by 93 cents. So 5% compounded yearly for 10 years is 1.05)[sup]10[/sup] or 1.629 times your initial capital.
It was accurate (last time it aired, I scribbled out the numbers and checked.) Note that the Futurama universe doesn’t account for 1000 years of inflation. 
Futurama had a bunch of science and math Ph.Ds on the writing staff, so they generally get those kinds of details correct.
Thanks for the replies.
That may be, but what kind of fan would I be if I didn’t nitpick over small details like this?
Oh, for the record, the exact ammount is: $4,283,508,449.71
The formula is actually more complicated than that, since you haven’t included compounding periods.
Officially, it’s this:
F = P{(1 + r/n))sup[/sup]}
F = Value
P = principal
r = yearly interest rate (as a decimal)
n = number of times compounded per year
t = time
What’s very interesting is that if you use continuous compounding (i.e., an infinite number of compounding periods per year), the formula becomes:
F = Pe[sup]rt[/sup]
e = the mathematical constant “e”
Here’s a good calculator for compund interest:
www.1728.com/compint.htm
It has the formula too.
(and it’s my site)
