How Compound Interest Works, With Worked Examples
A plain-language explanation of compound interest, the effect of time and monthly deposits, and how to read a savings projection sensibly.
Interest on interest
Simple interest pays a percentage on your original deposit only. Compound interest pays a percentage on your deposit plus the interest already earned. Each period's interest is added to the balance, and the next period's interest is calculated on that bigger balance. Over short periods the difference is tiny. Over decades it is the main event.
With a 5 percent annual rate, 1,000 earns 50 in the first year either way. In year two, simple interest earns another 50, while compound interest earns 52.50, because it is calculated on 1,050. After 30 years, simple interest has grown the money to 2,500, whereas compounding yearly has grown it to about 4,322.
The formula
For a single deposit, the future value is P × (1 + r)^n, where P is the starting amount, r is the interest rate per period as a decimal and n is the number of periods. With monthly compounding, r is the annual rate divided by 12 and n is the number of months. With regular deposits added each month, the total is the sum of the grown starting balance and the grown stream of deposits. The Savings Calculator applies exactly this model, assuming deposits at the end of each month.
Why time beats everything else
Because growth builds on growth, the later years of a long saving period add far more than the early ones. Consider saving 100 a month at 5 percent a year. After 10 years you have roughly 15,500, of which 12,000 is your own money. After 20 years it is about 41,100 (24,000 yours), and after 30 years about 83,200 (36,000 yours). The third decade added more than the first two combined.
This is why starting early, even with small amounts, usually beats starting late with larger ones. Someone who saves 100 a month for 20 years and then simply leaves it for ten more years ends with about 67,700, whereas someone who starts at year ten and saves a much larger 200 a month for ten years reaches only about 31,000. The early saver wins even though they stopped contributing.
What the projection does not know
A calculator needs a single constant rate, but real returns change. Savings accounts reset their rates, investments rise and fall, and a good average over 30 years can hide a terrible single year. Inflation reduces what money buys, so 83,200 in thirty years will not buy what 83,200 buys today. Fees also compound, in the wrong direction: a 1 percent annual fee on an investment fund can take a surprisingly large share of the final amount over decades.
Taxes depend on your country and account type. None of these are in a simple calculator, so treat the result as an illustration of how the mechanics work, not a forecast, and not financial advice.
Using the calculator well
Run it several times. Try a cautious rate and an optimistic rate to see a range. Compare saving a little more per month against waiting a year. Set the rate to zero to see how much of your final balance is simply your own deposits, then add interest back to see what compounding contributes. If you are comparing offers, make sure they quote the same rate type, because an annual percentage yield already includes the effect of compounding, while a nominal rate does not.
If you want to measure how a balance changed, the Percentage Calculator gives percentage growth between a starting and an ending value.
Inflation and the rule of 72
Inflation lowers what money buys. If prices rise 3 percent a year and your savings earn 3 percent, you are only keeping pace. The 'real' return is roughly the interest rate minus inflation. A quick way to feel growth is the rule of 72: divide 72 by the annual rate to estimate the years needed to double. At 6 percent it is about 12 years; at 3 percent it is about 24.
The same rule explains why debt can be so costly. A balance at 24 percent interest doubles in about three years if nothing is paid. Compounding works for savers and against borrowers.
Fees, taxes and where the rate comes from
A savings account quotes a rate set by the bank and can change. An investment fund has no promised rate, only past performance, which does not guarantee the future. Fees reduce growth every year: a 1.5 percent annual fee on a fund returning 6 percent leaves 4.5 percent, which over 30 years can cost a large share of your final balance.
Tax rules differ by country and account type; some accounts shelter growth from tax, and some do not. When you try the Savings Calculator, use a rate after fees as a more honest estimate, and try a lower rate as a test of how sensitive your plan is.
Turning the idea into a plan
Pick a monthly amount you can keep up even in a tight month. Automate it right after payday so the decision is made once. Review once a year, and increase the amount when your income rises. Keep a small emergency fund in an easy-access account before investing for the long term, so you are not forced to sell at a bad time. Remember that this page and calculator are general education, not financial advice; for personal decisions, consider a qualified adviser.