Compound interest is interest earned on both your original money and on the interest that money has already earned. It is the reason a small, steady balance can grow into something much larger over decades, and the reason debt can balloon when it is left alone.
Simple interest versus compound interest
With simple interest, you earn a fixed amount each period based only on the starting balance. Put $5,000 at 6% simple interest for 10 years and you earn $5,000 × 0.06 × 10 = $3,000, finishing with $8,000.
With compound interest, each period's interest is added to the balance, so the next period's interest is calculated on a larger number. The same $5,000 at 6% compounded annually for 10 years finishes near $8,954, and compounded monthly it finishes near $9,097. The extra $954 to $1,097 is interest earned on interest.
The formula
The standard formula is A = P(1 + r/n)^(nt), where P is the starting amount, r is the annual rate as a decimal, n is how many times per year interest compounds, and t is the number of years.
For the monthly example above: P = 5,000, r = 0.06, n = 12, t = 10. The monthly rate is 0.005, there are 120 periods, and 1.005^120 is about 1.8194. Multiply by 5,000 and the result is roughly $9,097.
The Rule of 72
A quick mental shortcut for doubling time is to divide 72 by the annual percentage rate. At 6%, money doubles in about 72 ÷ 6 = 12 years. The exact answer is closer to 11.9 years, so the shortcut is close enough for planning. It works best for rates between about 4% and 12%.
Adding regular contributions
Most real savings plans involve ongoing deposits rather than a single lump sum. Each deposit starts compounding from the day it is made, so early contributions do far more work than later ones. This is why starting ten years earlier with smaller amounts can beat starting later with larger ones.
Why projections are often too optimistic
A calculator assumes a constant rate, but real investments fluctuate and savings account rates change. Inflation reduces what the final number can buy, and taxes and fees reduce what you keep. A useful habit is to run the calculation with a lower rate than you hope for and compare the two outcomes.
Also check whether a quoted figure is a nominal rate or an effective annual yield. A 6% nominal rate compounded monthly has an effective annual yield of about 6.17%, which is why two accounts with the same headline rate can pay slightly differently.
Compounding works against borrowers too
Credit cards and some loans compound on unpaid balances. A balance that is only partly paid each month can grow even while you are making payments. Seeing the numbers before you borrow makes the real cost much clearer.
A year-by-year picture
Take $5,000 at 6% compounded annually. After 1 year it is $5,300, after 5 years about $6,691, after 10 years about $8,954, after 20 years about $16,036, and after 30 years about $28,717. The first ten years add roughly $3,950, while the last ten add more than $12,600, even though nothing about the rate changed. Growth is slow at the start and fast at the end, which is why patience matters more than almost any other factor.
Does compounding frequency matter?
Less than most people expect. Consider $10,000 at 5% for 10 years. Compounded annually it reaches about $16,289, monthly about $16,470, and daily about $16,487. Even continuous compounding, the theoretical limit, only reaches about $16,487. The difference between annual and daily is under $200 on this example, so the rate and the time horizon matter far more than the compounding schedule.
Practical steps
Start as early as you can, even with small amounts. Automate contributions so they happen without a decision each month. Compare accounts using the annual percentage yield, which already accounts for compounding. Remember that paying off a high-interest debt is effectively a guaranteed return equal to that debt's rate, which often beats what savings can reliably earn. Keep an emergency fund so you never have to cash out investments at a bad moment.
Frequently asked questions
Is a higher compounding frequency always better? It always helps slightly, but the effect is small compared with the rate itself.
What if returns are negative one year? The formula assumes a steady rate. Real investments rise and fall, and a loss reduces the base that future growth builds on, so use the calculator for planning scenarios rather than predictions.
Does compound interest apply to debt? Yes. Many credit cards compound daily on the unpaid balance, so carrying a balance can grow faster than people expect.
Try the calculators
Compound Interest Calculator · Simple Interest Calculator
This guide is for general information only. It is not financial, medical, or legal advice.