Compound Interest Explained With Real Examples

Compound interest is interest earned on your original money and on the interest that has already been added. Each period, the balance grows, and the next period's interest is calculated on that larger amount. In the first year the effect looks small. Over many years it can become the main reason savings grow.

Simple interest works differently. It pays only on the original amount, so the same sum is added each period. Compound interest pays on the original amount plus everything earned so far. The gap between the two starts out tiny and widens steadily.

This article explains the formula in plain text, works through examples with round numbers, and introduces the rule of 72, a quick way to estimate doubling time. The rates used here are illustrations, not forecasts. Real investment returns vary and are not guaranteed.

The formula in plain text

Written in plain text, the formula is A = P(1 + r/n)^(nt). The caret symbol (^) means "to the power of," so the exponent is n times t.

Each letter stands for one part of the calculation:

• A is the amount you end up with, including the interest.
• P is the principal, the amount you start with.
• r is the annual interest rate written as a decimal. So 8% becomes 0.08.
• n is the number of times interest is added each year. Yearly is 1, quarterly is 4 and monthly is 12.
• t is the number of years.

To solve it, work in this order: divide r by n, add 1, raise the result to the power of n times t, then multiply by P.

Worked example one: yearly compounding

Say you invest $1,000 at 8% a year, compounded yearly, for 10 years. The 8% is an example rate only.

Step 1: Identify the values. P = 1,000, r = 0.08, n = 1 and t = 10.

Step 2: Divide r by n. 0.08 ÷ 1 = 0.08.

Step 3: Add 1. 1 + 0.08 = 1.08.

Step 4: Raise to the power of n times t, which is 1 × 10 = 10. 1.08 to the power of 10 is about 2.15892.

Step 5: Multiply by P. $1,000 × 2.15892 = $2,158.92.

After 10 years you have $2,158.92. You earned $1,158.92 in interest on a $1,000 start. The balance at the end of each year shows how the growth builds.

Notice that the balance does not simply double every decade. Each year's interest is calculated on a larger balance than the year before. Interest earned in year one is $80. Interest earned in year 10 is $159.92, nearly double, even though the rate never changed.

Worked example two: monthly compounding

Now take the same $1,000, the same 8% rate and the same 10 years, but add interest monthly.

Step 1: Identify the values. P = 1,000, r = 0.08, n = 12 and t = 10.

Step 2: Divide r by n. 0.08 ÷ 12 = 0.00667, which is the monthly rate.

Step 3: Add 1. 1 + 0.00667 = 1.00667.

Step 4: Raise to the power of n times t, which is 12 × 10 = 120. 1.00667 to the power of 120 is about 2.21964.

Step 5: Multiply by P. $1,000 × 2.21964 = $2,219.64.

Monthly compounding gives $2,219.64, compared with $2,158.92 for yearly compounding. That is $60.72 more. More frequent compounding helps, but the difference is modest next to the effects of the rate and the number of years. Many savings and investment products describe their compounding frequency in their terms, so check the details before you compare offers.

Why time matters as much as the rate

Time is often the most powerful part of the equation. Using the same $1,000 at 8%, the balance is $2,158.92 after 10 years, $4,660.96 after 20 years and $10,062.66 after 30 years. Doubling the time from 10 years to 20 years more than doubles the result, because the extra decade compounds on top of a larger balance.

The practical lesson is not to chase a higher rate at any cost. It is to start while there are years left for growth, and to avoid interrupting that growth unnecessarily.

The rule of 72

Sometimes you only need a quick answer. The rule of 72 estimates how many years it takes money to double. Divide 72 by the annual rate, written as a percentage.

• At 6%, 72 ÷ 6 = 12 years. The exact figure is about 11.9 years.
• At 8%, 72 ÷ 8 = 9 years. The exact figure is about 9.0 years.
• At 10%, 72 ÷ 10 = 7.2 years. The exact figure is about 7.3 years.

The rule is most accurate for moderate rates and becomes rougher at very high or very low ones. You can also run it in reverse. If you want money to double in 10 years, you would need a rate of about 7.2% (72 ÷ 10). You can also use it to plan a goal. If you want $20,000 to grow to $40,000 and expect about 6% a year, the rule suggests roughly 12 years, since 72 ÷ 6 = 12.

Compounding works against you too

Compounding does not only help savers. A fee that comes out of your balance each year reduces the amount that can compound. Suppose a fee cuts your effective growth from 8% to 7%. Then $1,000 grows to about $1,967.15 over 10 years, rather than $2,158.92. A one-point difference is not dramatic in one year, but it is large over a decade.

Debt works the same way. Unpaid interest is added to the balance, and the next period's interest is charged on the bigger figure. That is why paying off high-rate debt can feel like such a strong move.

This article covers a single lump sum. If you add money regularly, each new contribution starts compounding from the day it goes in, so steady saving builds on itself. Calculations with regular contributions are more involved, so a calculator is the practical route for those.

Steps to use compound interest in your planning

1. Decide your starting amount and the time frame you are planning for.
2. Find the rate, and check whether it is quoted before or after fees and tax.
3. Note how often interest is compounded, whether yearly, quarterly or monthly.
4. Run the formula by hand, or use a compound interest calculator.
5. Test two or three rates to see how sensitive your result is to a change in return.
6. Subtract any ongoing fees before judging the outcome.
7. Keep your plan realistic. Do not treat any example rate as a guaranteed return.

If you are deciding between holding cash and putting money into investments, saving vs investing sets out the trade-offs. Before any long-term plan, it also helps to have a cash reserve in place, as explained in how to build an emergency fund. For personalised advice, speak with a qualified financial adviser.

Frequently asked questions

What is the difference between simple and compound interest?

Simple interest is calculated only on the original amount. Compound interest is calculated on the original amount plus the interest already added, so growth speeds up over time.

Does compounding more often make a big difference?

Usually not by a large margin. In the example above, moving from yearly to monthly compounding added $60.72 over 10 years. The rate and the time period usually matter far more.

Is the rule of 72 exact?

No. It is a shortcut that gives a close estimate for moderate rates. For precise figures, use the full formula or a calculator, and remember that real returns are never guaranteed.

Does compound interest work on debt as well?

Yes. When unpaid interest is added to a balance, the debt grows in the same way savings do. That is one reason high-rate debt can become expensive quickly.