How compound interest works
With compound interest you earn interest not only on the money you put in but also on the interest already earned. The effect is small at first and large after many years, which is why starting early matters more than the exact rate.
10,000 at 5% a year, compounded yearly
- 1
Year 1
5% of 10,000 is 500, so you have 10,500.
- 2
Year 2
5% of 10,500 is 525, so you have 11,025. The interest on interest is 25.
- 3
Year 10
About 16,289: 6,289 of interest, against 5,000 with simple interest.
- 4
Year 30
About 43,219: more than four times the starting amount.
The formula
Balance = amount x (1 + rate)^years for yearly compounding. With monthly compounding use the rate divided by 12 and the number of months. Regular deposits add to the balance at each period and also earn interest from then on.
What matters most
Time matters most, then the amount you add regularly, then the rate, then how often it compounds. Fees work the same way in reverse: a yearly fee of 1% takes a growing share of a growing balance.
It works against you on debt
The same mechanism makes credit card and other loans with unpaid interest grow quickly. Paying a high-interest debt off is a guaranteed return equal to its interest rate.
Try the numbers
Questions
What is the rule of 72?
Divide 72 by the yearly rate to estimate the years to double: at 6% about 12 years. It is an approximation that works well between 4% and 12%.
Does compounding more often matter?
A little. Monthly instead of yearly at 5% gives 5.12% instead of 5%. Time matters far more.
Is the return guaranteed?
Only for fixed-rate products. Investments such as funds rise and fall, so use a range of rates.
How do inflation and tax change it?
They reduce the real result. Compare the rate with inflation to see what your money can buy.