How Interest Works: Simple, Compound & the Time Value of Money

Savings accounts, credit cards, car loans, mortgages, retirement funds — they all run on one idea: interest, the price of money over time. Understand interest and the rest of personal finance stops being a wall of jargon and becomes a few simple mechanics. This guide explains the core idea and links to deeper articles on each piece.

ℹ️These articles are educational — they explain the maths so you can use the calculators with understanding. They are not financial advice.

You can put every formula here into practice with the Compound Interest Calculator and the other finance tools, all running privately in your browser.

What interest is

Interest is what money costs to borrow, or what it earns when lent out. If a bank pays you 4% on savings, it is renting your money and paying you 4% a year for the privilege. If a card charges 22%, you are renting the bank’s money and paying 22% a year. The percentage is the rate; the original sum is the principal. Everything else is detail on top of those two.

Simple interest: a straight line

Simple interest is charged only on the original principal, never on the interest already earned. The formula is short:

Put $1,000 at 5% simple interest and you earn a flat $50 every year — $50 in year one, $50 in year ten. After 10 years you have $1,500. The balance grows in a perfectly straight line because the interest never itself earns interest. Simple interest shows up in some bonds, short-term loans and car financing.

Compound interest: a curve

Compound interest changes one thing: each period’s interest is added to the balance, and the next period’s interest is calculated on that larger total. You earn interest on your interest.

At 40 years the compound balance is more than double the simple one — from the same rate and principal. The gap widens with time because the curve is exponential, not linear. This is the engine behind long-term investing, and the reason credit-card debt can spiral. The full formula and the famous “Rule of 72” are in Compound Interest Explained.

How often it compounds matters

Compound interest can be applied yearly, monthly, daily — and the more often it compounds, the more you earn (or owe). That is why two accounts advertising the “same” rate can pay different amounts, and why finance has two different percentages — APR and APY — to describe a rate before and after compounding. Confusing them is one of the most common money mistakes; the difference is untangled in APR vs APY.

Interest in reverse: loans

A loan is compounding pointed the other way — you hold the principal and pay interest on the shrinking balance over time. Each monthly payment covers that period’s interest first, and whatever is left chips away at the principal. Early on, most of your payment is interest; later, most is principal. That split, and the schedule that maps it out, is the subject of Loan Amortization, and its biggest real-world application — buying a home — is covered in How Mortgages Work.

The time value of money

One principle ties it all together: a dollar today is worth more than a dollar next year, because today’s dollar can be invested to earn interest in the meantime. This is the time value of money, and it is why lenders charge interest, why $1,000 saved at 25 dwarfs $1,000 saved at 55, and why every finance calculation ultimately reduces to moving money across time at some rate. Master that idea and the calculators stop being black boxes.

In practice

Whether you are growing savings, comparing loans, or sizing a mortgage payment, the underlying mechanic is the same — principal, a rate, and time, with compounding deciding how fast the balance bends. Explore each piece in the linked articles, and run the numbers for your own situation with the Compound Interest and Savings calculators.