# Calculating compound interest

**URL:** <https://boards.straightdope.com/t/calculating-compound-interest/233219>\
**Category:** Factual Questions\
**Created:** [March 9, 2004, 2:06am UTC](https://boards.straightdope.com/t/calculating-compound-interest/233219 "2004-03-09T02:06:26Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![emekthian](https://avatars.discourse-cdn.com/v4/letter/e/ecae2f/32.png) [@emekthian](https://boards.straightdope.com/u/emekthian)\
**Post date:** [March 9, 2004, 2:06am UTC](https://boards.straightdope.com/t/calculating-compound-interest/233219/1 "2004-03-09T02:06:26Z")

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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.

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**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\
**Post date:** [March 9, 2004, 2:13am UTC](https://boards.straightdope.com/t/calculating-compound-interest/233219/2 "2004-03-09T02:13:54Z")

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(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.

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**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\
**Post date:** [March 9, 2004, 3:18am UTC](https://boards.straightdope.com/t/calculating-compound-interest/233219/3 "2004-03-09T03:18:36Z")

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> [@emekthian](#):
>
> 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.

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.

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**Author:** ![emekthian](https://avatars.discourse-cdn.com/v4/letter/e/ecae2f/32.png) [@emekthian](https://boards.straightdope.com/u/emekthian)\
**Post date:** [March 15, 2004, 11:02pm UTC](https://boards.straightdope.com/t/calculating-compound-interest/233219/4 "2004-03-15T23:02:24Z")

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Thanks for the replies.

> [@](#):
>
> Futurama had a bunch of science and math Ph.Ds on the writing staff, so they generally get those kinds of details correct.

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

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**Author:** ![RealityChuck](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/realitychuck/32/195_2.png) [@RealityChuck](https://boards.straightdope.com/u/RealityChuck)\
**Post date:** [March 16, 2004, 1:41am UTC](https://boards.straightdope.com/t/calculating-compound-interest/233219/5 "2004-03-16T01:41:24Z")

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> [@don't ask](#):
>
> (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.

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”

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**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\
**Post date:** [March 16, 2004, 1:45am UTC](https://boards.straightdope.com/t/calculating-compound-interest/233219/6 "2004-03-16T01:45:48Z")

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Here’s a good calculator for compund interest:  
[www.1728.com/compint.htm](http://www.1728.com/compint.htm)

It has the formula too.  
(and it’s my site)  
😃