Effects of compound interest

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.

You can find “compound interest calculators” online; here’s one 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.

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!

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.

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.

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.

Where in the US can you get a 4% interest rate on savings these days?

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.

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.

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?

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.

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.