Quickly, let's look at the difference between these.
(Interest is only calculated on the money you have invested):If you invest $10,000 (your principal) at 5% interest for 20 years:
Add this interest earned to your original $10,000
$10,000 x 5% x 20 years = $10,000 (interest earned)
$10,000 + $10,000 = $20,000
(Interest is calculated on your invested money PLUS your previously earned interest):If you invest $10,000 (your principal) at 5% interest for 20 years with compound interest you'll end up with $26,532.98 .
The formula is a bit complex and hard for me to type out, but you can look it up here if you just really need to see it for yourself.
In addition:The more often your compound is calculated (daily, monthly, yearly) the more interest you will earn. Daily Interest = $27,180.96
Monthly Interest = $27,126.40
Yearly Interest = $26,532.98
The longer your money is invested the more interest you'll earn. Your same $10,000 at 5% for 30 years turns into $43,219.42 Same money, same interest for 40 years is $70,399.89
The higher your interest rate, the more interest you'll earn. Your same $10,000 at 10% for 20 years will become $67,275.00
Combine longer time and higher interest and it starts to get really fun:
$10,000 at 10% for 30 years = $174,494.02
$10,000 at 10% for 40 years = $452,592.56
$10,000 at 12% for 20 years = $96,462.93
$10,000 at 12% for 30 years = $299,599.22
$10,000 at 12% for 40 years = $930,509.70 (yep, nearly a million $)
Imagine if you could scrape together only $10,000 by age 20 and find a good mutual fund that paid 12% interest (not that difficult really) and just LEFT YOUR MONEY THERE until you were 65 years old, you would have $1,639,876.04 That's without you ever adding one more cent of principal to this investment. The sooner you can get investing in something earning a decent interest rate, the better off you will be at retirement.
That is magic. If you want to work some magic yourself, here is a compound interest calculator. I'll warn you -- it's addictive!
P.S. Your mortgage (or car payment, student loan, credit card bill. . .) works on a compound interest formula in your lender's favor. That is why you often end up paying 3 times the cost of your house by the time your loan is completed.