 # Guide to Compound Interest: The Miracle of Compound Returns

If you’ve heard of savings and investing, you’ve heard of “the power of compound interest! But how does compound interest work and how can you make it work for you?

Here’s what you need to know.

## What is compound interest?

Compound interest generates interest on your savings and on the interest you previously earned. People who already have money find it easier to get more simply by letting their savings grow. This is the power of compound interest.

## How does compound interest work?

When you save or invest money, you earn interest on your principal. In the second year, you earn interest on both your initial principal and the first year’s interest. The third year you earn interest on your capital and the first two years.

You get the picture. The concept of earning interest on your interest is the compounding miracle.

It’s a bit like a snowball effect. As your capital goes down the hill, it gets bigger and bigger. Even if you start with a small snowball, given enough time, you can end up with a gigantic one.

## Simple Interest vs Compound Interest

Simple interest and compound interest are similar but have slight differences.

If you lend someone £100 at 10% interest, they’ll pay you back £110 – that’s the original £100, which we call principal, plus £10 interest. You could continue to lend them the same £100 and earn £10 each time. After 10 loans you would have the original £100 plus £100 interest. This is how simple interest works.

Compound interest is more powerful. If, instead of lending someone just £100 in year two, you lend the whole £110 at the same interest rate, they’ll pay you back £121 – that’s the principal of £110, plus £11 d ‘interest. The following year you will receive £133.10. If you keep reinvesting the principal and interest, your money will grow exponentially.

Let’s take a look at the numbers.

After re-lending 10 times, you will have earned nearly 160% on top of your principal. After 25 times, you will have won almost 900%! That’s the power of compound interest – the more you reinvest your interest, the faster your investment grows.

## How to Calculate Compound Interest

An online compound interest calculator can calculate your interest for you (try the Motley Fool Savings Calculator!). But calculating compound interest yourself is also quite easy. Better, it will help you understand how the compound interest formula works.

### The compound interest formula

Above, each time we lent money, we calculated the interest and then added it to the principal. We can do this all at once by multiplying the principal by (1 + interest rate). Let’s call the principal ‘P’ and the interest rate ‘r’. If we reinvest twice, we end up with:

P x (1 + r) x (1 + r)

We can write this more clearly as P(1 + r)2

To generalize this formula:

• P is the principal amount
• r is the interest rate
• n is the number of times we compound the interest in each time period
• t is the number of time periods.

This gives us the compound interest formula:

P(1+r/n)next

Let’s look at our original loan, where you lent £100 at an annual interest rate of 10%. With annual compounding, if you loaned it out for 10 years, you would end up with:

100x(1+0.1/1)(1×10) = 100 x 1.1ten = £259.73

What if they paid the same interest rate, but it got worse every month instead of every year? If you loaned it out for the same 10 years, you would end up with:

100x(1+0.1/12)(12×10) = 100 x (1 + 0.1/12)120 = £270.70

Understanding the formula for compound interest helps you understand why you should check how often interest is compounded rather than just the interest rate. By compounding monthly rather than annually, you’ve earned an extra £11.

### The Rule of 72

There is a handy shortcut known as the rule of 72 that you can use to estimate rates of return. It says you can find out how many years it will take for your investment to double by dividing 72 by the percentage growth rate.

Thus, it will take nine years for your investments to double if they grow by 8% per year (72/8=9). But it will only take six years if your investments increase by 12% and so on. The rule of 72 only provides an approximate answer. But as shortcuts go, it is accurate enough for many calculations.

## The interest of compound interest

Compound interest grows your money in a savings account, term deposits and bonds. However, the same principles – and the same compound interest formula – apply to any investment if you reinvest your profits. This is the key to building wealth over time.

## What is the downside of compound interest?

There’s always a downside, and compound interest is no different. It’s great if you’re the person earning interest, but not if you’re the one paying it. A credit card or loan can easily spiral out of control if you don’t keep up with repayments.

To avoid this, look for a 0% credit card to dodge the negative effects of compound interest.

## The 5 Stupid Laws of Composition

At The Fool, we love the concept of compound interest so much that we came up with the Five Insane Laws of Compounding.

### 1. Start early!

The earlier you start investing, the more time you have for the miracle of compound interest to work. Someone who invests £100 a month aged 20-29 and then lets their investments grow is likely to have more money at 60 than someone who invests £100 a month aged 30-59.

### 2. Small differences in the return matter. A lot!

Over long periods, the difference between investing at, say, 7% and 8% is huge. If you don’t believe us, try experimenting with the financial calculators above.

### 3. Find a good balance between your life and your money.

Investing is not everything. Like most things in life, it’s best to find a balance. With investing, it’s the balance between having fun now and planning for your future.

### 4. Over time, saving small amounts on a regular basis can add up to an amazing amount of money.

If you save £100 a month for 40 years and your investments accumulate at 12% a year, how much will you have? The answer is an astonishing £980,000!

### 5. Time and patience are the friends of capitalization and therefore of investing.

Saving for 40 years is obviously something you can’t do overnight. You need to be patient if you want to feel the full benefits of compounding.

## Carry

The compound interest formula can help you understand what is happening to your money and why. If you keep reinvesting in a low-interest, high-interest account that accumulates frequently, your wealth will grow. This is the power of compound interest. 