# Effects of compound interest **URL:** \ **Category:** Factual Questions\ **Created:** [January 28, 2014, 4:25pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956 "2014-01-28T16:25:57Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![Danger\_Man](https://avatars.discourse-cdn.com/v4/letter/d/6de8d8/32.png) [@Danger\_Man](https://boards.straightdope.com/u/Danger_Man)\ **Post date:** [January 28, 2014, 4:25pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/1 "2014-01-28T16:25:57Z")
Let’s say I put away $100 a month the next 20 years at a 4% interest rate. How much would I have both when you account for compund interest and not accounting for it. That is, if you only get interest on the money you originally put in. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 28, 2014, 5:02pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/2 "2014-01-28T17:02:09Z")
You can find “compound interest calculators” online; [here’s one](http://www.calculator.net/interest-calculator.html?cstartingprinciple=0&cannualaddition=0&cmonthlyaddition=100&cadditionat1=beginning&cinterestrate=4&ccompound=annually&cyears=20&ctaxtrate=0&cinflationrate=0&x=68&y=11) I found that provides a lot of information. The exact amount of compounded interest you’d earn would depend on how frequently it was compounded (annually? monthly? continuously?) but would in any event be over $12,500 for the interest alone (so over $36,500 for the total amount at the end of 20 years), assuming I’m doing it right. For simple interest, I think it works to just compute the simple interest on the average balance of $12,000, since the amount you’ve deposited grows linearly from $0 to $24,000 over the course of the 20 years (but correct me if I’m wrong). This would make the simple interest come out to 4% \* $12,000 \* 20 years = $9,600; and the total ending balance would be $33,600. ---
**Author:** ![Fir\_na\_tine](https://avatars.discourse-cdn.com/v4/letter/f/a587f6/32.png) [@Fir\_na\_tine](https://boards.straightdope.com/u/Fir_na_tine)\ **Post date:** [January 28, 2014, 8:06pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/3 "2014-01-28T20:06:40Z")
A number of years ago when I worked in banking, we published some “future value tables” for IRA investments. The basic comparision was a series of annual deposits from age 20 to age 30 vs. a series of deposits for the same amount from age 30 to age 65. For any interest rate the individual who set aside his money at the earlier age had a bigger nest egg at age 65! Miracle of compound interest! ---
**Author:** ![Doctor\_Jackson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/doctor_jackson/32/32_2.png) [@Doctor\_Jackson](https://boards.straightdope.com/u/Doctor_Jackson)\ **Post date:** [January 29, 2014, 10:25pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/4 "2014-01-29T22:25:10Z")
Simple interest at 4%, paid only on the amount you deposited and paid at the end of 20 year term, would yield $24,504 (100 per month \* 12 months = 1200 per year \* 20 years = 24,000 \* .04). That is, by definition, a total return of 4% **Thudlow** your calculation based on the average balance over 20 years more closely aproximates annual compounding. Monthly compounding (crediting interest earned at the end of each month making it a part of the principle) yields $36,677 according to my quick and dirty calculations. Compounding the interest results in a difference of over $11,000 - a total return of 65% and quite a substantial difference. ---
**Author:** ![muldoonthief](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/muldoonthief/32/3188_2.png) [@muldoonthief](https://boards.straightdope.com/u/muldoonthief)\ **Post date:** [January 30, 2014, 1:47pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/5 "2014-01-30T13:47:13Z")
I think the **OP** was asking if instead of depositing the interest back into the account each month, you took it in cash and put it in a shoebox, how much would be in the shoebox after 20 years, in which case **Thudlow Boink** ’s answer was correct. There’s a bit at the beginning of _Huckleberry Finn_ where Judge Thatcher tells Huck that more interest has come in on the money he & Tom found, but recommends that Huck have him just reinvest it with the original money. So once upon a time at least, you had to specifically reinvest the interest to get compounding. ---
**Author:** ![Doctor\_Jackson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/doctor_jackson/32/32_2.png) [@Doctor\_Jackson](https://boards.straightdope.com/u/Doctor_Jackson)\ **Post date:** [January 30, 2014, 3:03pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/6 "2014-01-30T15:03:13Z")
Well, sure, if you read it THAT way! Breaking it down to annual percentage yield (APY), the "take the interest and run"scenario results in a 4.0% APY. The interest reinvestment option returns 5.4% APY. ---
**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:** [January 30, 2014, 3:12pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/7 "2014-01-30T15:12:13Z")
Where in the US can you get a 4% interest rate on savings these days? ---
**Author:** ![Danger\_Man](https://avatars.discourse-cdn.com/v4/letter/d/6de8d8/32.png) [@Danger\_Man](https://boards.straightdope.com/u/Danger_Man)\ **Post date:** [January 30, 2014, 3:49pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/8 "2014-01-30T15:49:25Z")
> [@muldoonthief](#): > > I think the **OP** was asking if instead of depositing the interest back into the account each month, you took it in cash and put it in a shoebox, how much would be in the shoebox after 20 years, in which case **Thudlow Boink** ’s answer was correct. > > There’s a bit at the beginning of _Huckleberry Finn_ where Judge Thatcher tells Huck that more interest has come in on the money he & Tom found, but recommends that Huck have him just reinvest it with the original money. So once upon a time at least, you had to specifically reinvest the interest to get compounding. Yes, that is what I meant. Total amount saved: 24k Total with interest: 33.6k Total with compounding interest: 36.5k The compunding part doesn’t really add so much, does it? And the numbers would be worse if you subtract inflation. ---
**Author:** ![muldoonthief](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/muldoonthief/32/3188_2.png) [@muldoonthief](https://boards.straightdope.com/u/muldoonthief)\ **Post date:** [January 30, 2014, 4:38pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/9 "2014-01-30T16:38:44Z")
Well, it looks like it didn’t add much because it was sort of swamped by the fact you were making continuous deposits. Taking a much simpler case: Deposit $1000 at 4%. Reinvest interest. After 20 years, you have $2222, or $1222 interest. Deposit $1000 at 4%. Put interest in a box. After 20 years, you have $800 interest, less than 2/3 what you’d have had if you reinvested the interest. ---
**Author:** ![Doctor\_Jackson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/doctor_jackson/32/32_2.png) [@Doctor\_Jackson](https://boards.straightdope.com/u/Doctor_Jackson)\ **Post date:** [January 30, 2014, 10:31pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/10 "2014-01-30T22:31:17Z")
> [@Danger\_Man](#): > > Yes, that is what I meant. > > Total amount saved: 24k > Total with interest: 33.6k > Total with compounding interest: 36.5k > > The compunding part doesn’t really add so much, does it? And the numbers would be worse if you subtract inflation. Without compounding you earn $9,600, with compounding $12,500 - Compounding nets about 32% more money. To me, that’s significant. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [January 30, 2014, 10:42pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/11 "2014-01-30T22:42:50Z")
> [@Doctor\_Jackson](#): > > Without compounding you earn $9,600, with compounding $12,500 - Compounding nets about 32% more money. To me, that’s significant. Yeah, I was going to say. How is that _not_ significantly better? ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [January 31, 2014, 6:55am UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/12 "2014-01-31T06:55:02Z")
Compounding interest is good. The Canarsie Indians sold Manhattan 388 years ago for $24. Had they invested the $24 at 6% _compound_ interest, they might be able to buy the Island back today! [Our leader touches on this in one of his old columns.](http://www.straightdope.com/columns/read/715/how-much-would-the-24-paid-for-manhattan-be-worth-in-todays-money) ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [January 31, 2014, 5:44pm UTC](https://boards.straightdope.com/t/effects-of-compound-interest/679956/13 "2014-01-31T17:44:53Z")
> [@septimus](#): > > Compounding interest is good. The Canarsie Indians sold Manhattan 388 years ago for $24. Had they invested the $24 at 6% _compound_ interest, they might be able to buy the Island back today! > > [Our leader touches on this in one of his old columns.](http://www.straightdope.com/columns/read/715/how-much-would-the-24-paid-for-manhattan-be-worth-in-todays-money) Heh. $160 trillion. The trick is to find something that pays 6% after costs for four centuries… and to not be in a hurry to cash in.