Compound vs Simple Interest: The Difference, With Examples

Interest comes in two flavours. Simple interest is paid only on the money you originally put in. Compound interest is paid on the original money and on all the interest it has already earned. The difference looks trivial in year one and becomes enormous over decades.

Simple interest

Interest = P × r × t

Deposit $10,000 at 5% simple interest, and you earn exactly $500 every year, forever. After 10 years you have $15,000; after 30 years, $25,000. Growth is a straight line.

Simple interest is used for some car loans, short-term personal loans, certain bonds and many informal loans between people.

Compound interest

A = P × (1 + r/n)^(n × t)

The same $10,000 at 5%, compounded annually, earns $500 in year one, then $525 in year two (5% of $10,500), then $551.25, and so on. Each year’s interest is a little larger than the last.

After 30 years, compounding has produced 73% more money than simple interest from the identical deposit and rate.

Why compounding accelerates

Think of it as a snowball. In the early years the snowball is small and picks up little snow. Later it’s large, and every roll adds a lot. Mathematically, compound growth is exponential: the balance multiplies by the same factor each period, so the dollar gains get bigger every year.

That’s why the time-based rules of thumb work so well. The Rule of 72 tells you roughly how long money takes to double; see The Rule of 72: How Long Does It Take to Double Your Money?.

The cost of waiting

Here’s the most important consequence. Imagine two savers who each invest $200 a month at 7%, compounded monthly, until age 65:

• Aisha starts at 25, invests for 10 years, then stops contributing completely.
• Ben starts at 35 and invests every month for 30 years.

Aisha contributes a third as much and still ends up ahead, purely because her money compounds for ten extra years. You can reproduce the numbers with the compound interest calculator.

Compounding works against you too

Debt compounds in exactly the same way. Credit cards typically compound daily or monthly, so an unpaid balance at 24% APR grows faster than the headline rate suggests. That’s why high-interest debt is usually the first thing to clear before investing. The loan calculator shows how much interest an amortizing loan really costs, and How to Pay Off a Loan Faster: 7 Strategies That Save Interest covers how to cut it.

How often interest compounds

The compounding frequency, whether annual, monthly or daily, changes the result slightly at the same nominal rate. More frequent compounding means interest starts earning interest sooner. The effect is real but smaller than most people expect. Compounding Frequency Explained: Daily vs Monthly vs Annual (APR vs APY) runs the numbers.

Summary

Use the calculator below to compare your own numbers. Try setting the monthly contribution to zero, then extend the period from 10 to 30 years and watch the interest line overtake your deposits.